A GENERALISED PRICE-SCORING MODEL FOR TENDER EVALUATION
|
|
- Junior Nelson
- 6 years ago
- Views:
Transcription
1 rice scoring 9/20/05 12:12 PM Page 19 A GENERALISED PRICE-SCORING MODEL FOR TENDER EVALUATION Thum Peng Chew BE (Hons), M Eng Sc, FIEM, P. Eng, MIEEE ABSTRACT This aer rooses a generalised rice-scoring model derived from behavioural features of rosect theory for use in a tender evaluation rogram. It has the otential to overcome the limitations of existing rice models by allowing the withinrice attribute score variations to be adjusted by a reference factor. It imroves selectivity and incororates a reference function that emhasises the evaluator and decision maker s reference in the lowest rice by allowing a rice-scoring curve to be derived from the skewness of the distribution of tender rices and the tender articiation rate. It identifies rices that exceed the roject budget and enalises them. Statistical data from a survey of tender rices was used to secify the model for ractical use. Comarison between generic classes of models using rice difference and rice ratio functions as rice gain measures is made to illustrate the model s general alicability. With the choices made available in this generalised ricescoring model, it is ossible to comare the various methods of tender evaluation by comuter simulation. Keywords : Tender Prices, Price Comarison, Price Scoring Model, Tender Price Evaluation, Judgment, Decision Making INTRODUCTION The objective of tender rice scoring is to assign the right values to tender rices within a roject budget and to score them so that a fair evaluation that reflects the judgment and reference of the evaluator and decision maker, can be made. The rule of tender evaluation is to award a higher score to a lower rice tender because a lower rice has a higher value to the evaluator and decision maker. In manual evaluation methods, the rice values are assigned by human judgment on an ordinal scale which imlies a qualitative rice-value relationshi. If software decision-suort tools are used in integrated tender evaluation of rice and non-rice attributes, rice must be evaluated by a quantitative value function that converts rice in monetary unit to a score on an objective numerical scale. How rices are evaluated affects the final tender ranking. A survey of literature indicated that research on rice-value relationshi for the urose of tender evaluation is scarce. One simle quantitative value function that has been used by Karsak [1] for the evaluation of flexible manufacturing systems is a rice inverse model for scoring a cost-related attribute. The score synonymous with value, is derived from -1 the rice inverse, χ i = x i where x i is the rice of the i th tender. The model s weakness is its tendency towards indifference and not having the means to assign a degree of reference for low rices. Thus, there is no flexibility for it to fully exress the judgment of the evaluator and decision maker through a reference function. A wider search in the subject of judgment and decision making [7,8,9,10] revealed the existence of value functions in rosect theory roosed by Tversky and Kahneman [2,3] since The theory relaces the notion of utility with value which is defined in terms of gains and losses from a reference oint. They suggested that the value function defined over monetary gains is χ i = x i for x i above a reference rice(0) and over losses is λ( x i ) for x i below the reference rice. Determined from exerimental data, is 0.88 and λ is 2.25, indicating diminishing marginal value and asymmetry between gains and losses. The alication of the roosed value function has received attention recently [4,7,8,9] in a number of situations in which the norms and characteristics of decision makers are modelled. Variations in a tender s overall value are contributed by the within-attribute variations and the between-attribute variations. A value function deals only with the within-rice attribute variations while the weighting functions of the tender evaluation rocedures in [5,6] rovide the between-attribute variations. This aer resents a generalised rice-scoring model that determines the within-rice attribute variations from the rices of cometing tenders. Because all judgments and decisions are context-deendent [8], the credibility of a generalised rice-scoring model rests on its ability to cature an evaluator or decision maker s tendency for dominance or non-dominance and on its ability to exress mathematically the decision maker s judgment that is translated into a continuous continuum of strong to weak emhasis of tender rice. In a realistic model, the behavioural features in rosect theory have to combine with the cost objective to achieve a wide scoe of alication for situations in which the decision maker s behaviour varies. Prosect theory is helful u to this oint after which the reference factor is deendent on behaviour that has to be aroximated by information in a tender. To achieve this objective, it borrows from rosect theory some behavioural features that are not found in multi-attribute utility theory and alies it to tender rice judgment: Evaluators and decision makers are more sensitive to cost overrun than cost saving in the sense that they will reject tenders that have rices exceeding the roject budget. If there are sufficient tender roosals to select from without cost overrun, they will view the tender s lowest rice as indicative of the fair market value and the average rice lus margin as the budget s uer bound. Journal - The Institution of Engineers, Malaysia (Vol. 66, No. 1, March 2005) 19
2 rice scoring 9/20/05 12:12 PM Page 20 THUM PENG CHEW If the tender rices are significantly less than the roject budget, they become strongly gain-seeking so as to accrue larger cost savings and to comensate for the original overestimate. If the tender rices are close to but below the roject budget, their gain-seeking tendency is weaker because with lesser cost saving, attention is shifted to the non-rice attributes of the tender to accrue higher non-rice gains. This aer is organised as follows. First, a generalised rice-scoring function of a similar form as the value function of rosect theory is roosed. Next, the roject budget acting as the reference rice is defined and its imlications discussed. A reference function is develoed for strong to weak gainseeking, the strength of which is determined by the tender rice coefficient of skewness and tender articiation rate. A survey of tender rices elicits the two statistics which together with the evaluator s reference limits, are used to determine the constants of two generic classes of models. Within each generic class, comarison between rice difference and rice ratio functions as gain measures is made to illustrate the model s general alicability. Finally, aroriate alications of the two generic classes are suggested. PRICE VALUE FUNCTIONS In general, the mathematical function of a rice-scoring model that catures the essence of how a score, A relates to a rice gain variable, X must have the following roerties. (i) A monotonically increases with X (ii) 0 A 1 for 0 X 1 (iii) da 0 for 0 X 1 dx From rosect theory [2,3], the value/score, A i derived from the rice gain X i, of the i th tender rice out of m tender rices is suggested below for two generic classes of models. Un-normalised class: A i = X i Normalised class: A i = X i m X i i=1 (1a) (1b) where generally - < <. Equation 1b also ensures that m = 1 as a result of normalisation. When is negative, a Ai i=1 rice closer to the maximum rice will result in a higher score because the negative root of a small rice gain roduces a score close to unity. Because this is contrary to the tender evaluation rule of low rice-high score, the rice-scoring model must not consider values of that are negative. With this exclusion, the receding roerties are still satisfied but additional roerties are required to define the variable, for various behavioural states as follows. (i) A(X) is constant for = 0 (ii) A(X) is roortional to X for = 1 (iii) A(X 1) = 0 for = (iv) For Equation 1a, 0 1 The evaluator or decision maker s behaviour can be aroximated by the reference factor, which defines the gain-seeking tendency in the shae of the rice-scoring curve. With Equations 1a and 1b, there is no effect caused by rice gain on the scores when = 0 i.e. they all have the same unity score for the un-normalised class and 1 m for the normalised class. When increases from 0, the model starts to exhibit a lower rice-higher score characteristic, initially still having the tendency to be rice indifferent. When = 1, it scores linearly with rice gain and is not adjusted by reference (judgment). With Equation 1b, when =, the lowest rice attains the maximum score of 1 unit while the rest of the rices are scored zero irresective of their gain value. Thus, as moves from 0 to, the rice-scoring characteristic moves from one that is insensitive to rice gain, hence eliminating rice cometition, to one that exhibits the strongest reference for the lowest rice, hence creating the stiffest cometition that results in only one ossible contender. In other words, the rice-scoring model inherently allows for a range of effects to be accommodated, namely indifference, linear and non-linear deendence on rice gain through the secification of. THE PROJECT BUDGET AS A REFERENCE PRICE Before tenders are called, a value of the roject cost xˆ is estimated. Based on this value, a roject budget is given taking into account an assigned contingency cost which is rovided to mitigate situations of cost overrun caused by residual roject risk. If the contingency cost allocated is c, the roject budget, x B is xˆ + c. When tender submissions are received, their rices are comared with either the roject cost estimate or the budget allocation. Evaluators refer not to risk cost overrun and will be reluctant to recommend award of a contract whose rice exceeds the roject cost estimate or the budget. As a means of control, a rice-scoring model must assign the lowest rice score, usually zero, to rices exceeding the budget i.e. the value function for losses is set to zero for exclusion urose and is restricted to coding of rice gains. The budget is a reference rice on an objective scale and has the same meaning as that of rosect theory discussed in [2,3,4,7]. If cost overrun is limited by x B, then the rice gain has a range x B - x min. If the tender rices are ordered in ascending value in the sequence, x (1), x (2),.., x (j),.., x (m-1), x (m), then x min = x (1). Any rice, x (q) that exceeds x B should either be assigned an evaluation-adjusted value equal to x B or should be automatically excluded from the evaluation. If x (1) exceeds x B, it will be the only rice allowed to articiate in the evaluation with gain equal to zero. This requirement ensures that in the event that all tender rices exceed the budget value, the lowest rice tender will be the only alternative worthy of any consideration as far as tender rice evaluation is concerned. By accurate estimation, an under-budget situation can be avoided most of the time. PRICE-SCORING CURVES The exonent, in Equations 1a and 1b determines the shae of the rice-scoring curve. Strong gain-seeking means a 20 Journal - The Institution of Engineers, Malaysia (Vol. 66, No. 1, March 2005)
3 rice scoring 9/20/05 12:12 PM Page 21 A GENERALISED PRICE-SCORING MODEL FOR TENDER EVALUATION high reference ( > 1) for low rice. In zero (neutral) reference cases ( = 1), it would exhibit a straight line obtained by joining the lowest rice score with the score at x B over the rice difference range, x B - x min. Weak gain-seeking means a tendency to de-emhasise rice reference (0 < < 1). At the limit when = 0, all rices are treated equally and the scores are imartial to rice difference. To illustrate the rice-scoring curve, the highest score, Amax from Equation 1b is given by X A max = A (1) = (1) (1- P m = (1) ) (2) m X i (1- P i ) i=1 i=1 where the normalised rice is for simlicity, exressed as P i = 1- X i. If the highest score A (1), is set to unity, A (1) is exressed as follows: A (i) A max A (i) = = 1- P (i) 1- P (1) A continuous lot of A (i) against P i is shown in Figure 1 for various value of > 0 to illustrate the shae of the rice-scoring curves. Using the curves, the evaluator and decision maker can selected the degree of reference to match their judgment. (3) The coefficient of skewness, υ is roosed as a measure of the degree of gain-seeking. It qualifies by having the following roerties. (i) (ii) Its magnitude monotonically increases with skew For a ositive (right) asymmetry, it is ositive and it must reresent a strong gain-seeking characteristic that favours the lowest rice from the bunch of rices by making the scores reduce very quickly to zero for excetional rices that are located much higher than the lowest rice. (iii) For symmetry of rices, it is zero and it must not contribute to any reference by being neutral. (iv) For a negative (left) asymmetry, it is negative and it must reresent a weak gain-seeking characteristic that still favours the lowest rice but the scores of the bunch of rices are not reduced too quickly. The lowest rice is distant from the central bunch of rices because the ricing of the lowest tender is either made under a different condition or with a different strategy from those of the central bunch. The lowest tenderer may have a legitimate advantage over the rest because of technology, available caacity, resources and location which can be evaluated outside the rice domain as in [4,5]. Or in an attemt to win the contract, the lowest rice tenderer may resort to higher risk- Figure 1: Normalised score against normalised relative rice DISTRIBUTION OF PRICES Information about the tender can be extracted from the rice distribution statistics. In an ideally cometitive environment, the coefficient of variation and the variance are indicative of the degree of dissimilarity of the ricing characteristics of the tenderers. Price skew is an asymmetry arising out of either legitimate reasons or collusion [11,12]. It is not the urose here to determine its cause but to use it to determine reference. The existence of a low rice located to a distant left of a central bunch of rices (Figure 2a) gives rise to left asymmetry and a negative coefficient of skewness. If the rices are ideally symmetrical about their mean (Figure 2b), then the coefficient of skewness is zero. The existence of a high rice located to the distant right of a central bunch of rices (Figure 2c) gives rise to a right asymmetry and a ositive coefficient of skewness. Figure 2: Illustration of skewness in frequency distribution Journal - The Institution of Engineers, Malaysia (Vol. 66, No. 1, March 2005) 21
4 rice scoring 9/20/05 12:12 PM Page 22 THUM PENG CHEW taking and cutting rofit margin, a strategy that the others may not be willing to adot. If the determination of the roject budget is accurately done, such extreme rice deviation from the cost estimate must signal the need for extra caution during the evaluation and to uncover the hidden roject risks. While giving the highest score, the evaluator is risk-averse and must rudently limit the emhasis of the lowest rice. A similar effect may also be created from strategies that defeat fair cometition by many forms of cartel collusion. Non-cometing cartel rices are increased and the cartel-romoted tenderer s rice is raised to just below the next-lowest rice [12,13] as illustrated in the comarison between Figures 2a and 2b. If such strategies are revealed in the skew, they are enalised through exclusion by the budget limit as well as by rice deemhasis. When automatic action could not be taken effectively by the software rogram, re-assignment of (<1) is the way to counter this roblem. If behaviour is exressed in the reference factor, the distribution s coefficient of skewness υ, is a behaviour variable that induces a reference such that the relation between and υ meets the following: (i) > 0 for - < υ < (ii) = if υ (iii) = 1 if υ 0 (iv) = 0 if υ - A ossible general olynomial exression that satisfies these roerties is the skewness factor, k 1 given as follows: L1 k 1 = α2i-1υ2i-1 i =1 where α 2i-1 s are ositive constants to be determined for L 1 terms. υ is zero if the number of tenders evaluated is less than 3. TENDER PARTICIPATION RATE If there are sufficient tender roosals to select from without incurring cost overrun, the rice-scoring model should allow for increase in its rice selectivity under a situation of high tender articiation rate. When υ is very negative, is near zero. The scores tend to equalise and lose their discriminative ability. In Equation 1b, high tender articiation rate decreases the absolute scores by the effect of a larger denominator. The consequence is that when the rice scores are brought into the aggregation rocess with other non-rice factors, they become less contributory from their low score values and the lack of discrimination. This effect is counteracted by increasing the value of with tender articiation rate. One way is to include in, a searate tender articiation factor, k 2 which is a function of the number of tenderers, m being evaluated. It should have increasing monotonically with m i.e. d > 0 for m > 0. dm It is suggested that k 2 adots a general ositive olynomial function of m in the form L2 k 2 = β 0 + βjmj where β 0 is a constant and β j s are ositive constants to be j =1 (4) (5) determined for L 2 terms. When m = 1, there is no cometition and k 2 can be set to zero thus, β 0 = - βj. GENERAL PREFERENCE FUNCTION How k 1 and k 2 should be combined to obtain does not have a unique aroach. It must be alication deendent and satisfy ractical and intuitive requirements. One aroach is to add the effects of distribution skew, k 1 and the effects of tender articiation rate, k 2 i.e. k 1 + k 2. An additive effect has advantage over the multilicative one ( k 1 k 2 ) because it would not nullify the effect of tender articiation rate if the skewness were zero. However, addition alone cannot satisfy all the roerties of. A non-nullifying and roerty-comlying exression for as a function of k 1 and k 2 is suggested as follows: = ex(k 1 + k 2) (6) This exression restricts the value of to > 0 and thus, satisfies the required roerties of. k 1 contributes to by ensuring the ossibility of secifying a strong reference for low rice with ositive skew or a de-emhasis of reference for low rice with negative skew. It ensures that when υ = 0, zero (neutral) reference results from it. The tender articiation rate, m contributes ositively to through k 2. Exonentiation ensures a ositive all the time and it amlifies the combined effects, thus making the influence of stronger. Flexibility is given such that without the aid of these two factors, the evaluator and decision maker can still assign the value of indeendently. At this oint, it is seen that the rice-scoring model combines the ideas of rice gain measure, X and of the degree of reference, which is a function of the skewness of the rice distribution and the number of tenders evaluated, to calculate the rice scores, either un-normalised or normalised resectively. ANALYSIS OF TENDER PRICES If the urose of tender evaluation is to select an otimum tender, then the information that reveal rice relativities should be ut into good use for decision making. A survey was conducted to gather data on tender articiation rate and tender rices with the aim of obtaining statistics on tender articiation rate and on tender coefficients of variation and skewness. The range of values of m and υ can then be established for use in the rice-scoring model. From a total of 75 data sets from ast tender exercises, the coefficients of variation (deviation/mean) and skewness for each data set were calculated. From their distributions, the coefficients means, medians and deviations were obtained from statistical analysis and are summarised in Table 1. The coefficient of skewness is exected to vary from negative values to ositive values while the coefficient of variation is always ositive. 95% of the tenders has a articiation rate below 10 and the median is 4. The rice coefficient of variation s mean and median are close to each other at and resectively while its deviation is small at The survey data are indeed from tenderers who shared similar localised L2 j =1 22 Journal - The Institution of Engineers, Malaysia (Vol. 66, No. 1, March 2005)
5 rice scoring 9/20/05 12:12 PM Page 23 A GENERALISED PRICE-SCORING MODEL FOR TENDER EVALUATION Table 1: Analysis of tender articiation rate and tender rices Tender Price Tender Price Coefficient Price Coefficient Coefficients Particiation of Variation, of Skewness, Statistics Rate, m σ/µ υ Mean Median Deviation th Percentile α = q min υ min β = q max υ min - q min υ max υ min (m max - 1) If β = β(m max-1), (9) (10a) 95th Percentile characteristics [13] and quoted rices with small deviations from the mean rice. 95% of the coefficients of variation is below A budget u to times the roject cost estimate will cature most tender rices for evaluation. The mean of the coefficient of skewness, µ υ is and its deviation, σ υ is larger at % of its variations lies within the range of and with a median of The large σ υ is an indication of the sensitivity of skewness to extreme values and υ can be suitably emloyed to vary the reference over a wide range. SPECIFIC PREFERENCE FUNCTION A secific reference function for the rice-scoring model adots the first order functions of k 1 = αυ from Equation 4 and of k 2 = β(m-1) from Equation 5, where α and β are the ositive constants in the exression of as follows: Thus, = ex[αυ + β(m-1)] (7a) or q = ln = αυ + β(m-1) (7b) The rice-scoring model is to work within the secified limits determined by: The maximum tender articiation rate, m max and the minimum, which is 1. The uer and lower ercentiles of the coefficient of skewness (υ max and υ min) of the tender distribution. The uer and lower limits ( max and min) of the reference factor The tender articiation rate can be estimated from the number of tender documents collected and thus a maximum can be set. A minimum of 1 is set to ensure that the effect of tender articiation rate could be felt at 2 onwards according to Equation 7a. Equation 7b shows that the variation of the model constants, α and β are deendent on the logarithm of the reference limits. They are less sensitive to the variations of and can accommodate the fuzziness of subjective judgments without large changes in value. Figure 1 rovides the evaluator and decision maker a means of secifying the limits by insection. Thus, q max = ln max = αυ max + β(m max - 1) q min = ln min = αυ min Solving for α and β, (8a) (8b) then, β = (10b) To ensure that α is ositive (> 0), then v min and q min must have the same sign. For β 0, (q max υ min q min υ max)/ υ min 0 (11a) (11b) max min κ (11c) min min κ (11d) The choice of is guided by the intuitive requirement that the effect of υ should be greater than that of m. λ Thus, α > β and max < min (12) 1 where λ = = κ + υ min. For a given min, combining Equations 11c and 12 gives the range of max. κ λ min < max < min q max υ min - q min υ max υmin ln ma x υ max = κ ln min υ min 1+υ max υ min 1 (13a) Similarly given max, λ max > min > κ max (13b) From the rice survey, υˆ min, υˆ max can be obtained for secified ercentile limits of its distribution. κ can be calculated. ˆmin is secified to calculate α. max is then selected so that β and β are ket ositive. In this aer, the range of the skewness coefficient is fixed at and at to give κ equals to To cater for at least 95% of tender cases, m max is fixed at 11. The corresonding values of α and β are shown in Table 2 for each air of min and max. The effect of tender articiation can be nullified (β = 0) by either min or max determined from Equations 11c and 11d. For a given min, the evaluator and decision maker can choose the strength of tender articiation rate from the range of values of max determined from Equation 13a. Nullification will not occur if max is larger than the lower extreme value. With 3 arameters fixed, the reference function, is determined from min and max for λ = as follows. Given min = 0.2, < max < and given max = 5.0, > min > Journal - The Institution of Engineers, Malaysia (Vol. 66, No. 1, March 2005) 23
6 rice scoring 9/20/05 12:12 PM Page 24 THUM PENG CHEW PRICE GAIN FUNCTIONS Only rice gains are of interest. At this oint, the model excludes the coding of losses which is done in rosect theory. In an integrated tender evaluation rocedure, rice gain must be dimensionless. When rice is in monetary unit, it must be evaluated searately because it is not comatible with other dimensionless attributes. One roerty of a rice gain function is that for rices, x i > x j > x k, the rice gains derived from these rices must satisfy the condition X i < X j < X k. Transitivity of rice gains must be assured. The qualitative ordinal scale commonly used cannot be adoted here because it fails to reserve the numerical information of rice. Value scores must be made on quantitative scales. From exerience, both rice difference and rice ratio have been use in tender evaluation. Price difference is a comarison of rices in an interval scale whereas rice ratio reresents relative value comarison in a ratio scale. PRICE DIFFERENCE MODEL SUB-CLASS For the rice difference model, the rice gain variable is a measure of the distance of a rice from an uer rice limit and is exressed as follows. X i = x max - x i x (14) max - x min where x max is the reference rice on the interval scale and x min is the lower rice limit in the tender and x i is the tender rice of the i th tender alternative. The rice gain, 0 X i 1 is a normalised measure of rice difference. It is small if x i is close to the reference rice, x max and it is largest (unity) when x i = x min. With the roject budget x B, the rice gain in dimensionless unit is adjusted to X i = Table 2: Values of α and β for the reference function (υˆ max = and υˆ min = ) min max α x B - x (i) x B - x min such that x min = x (1) and if x min > x B, all X i s = 0. An un-normalised rice gain in monetary unit is given by X i = x B - x (i) β (m max = 11) (15a) (15b) This is a straightforward relation that equates rice score with rice difference. It is a useful measure for evaluation methods that comare marginal benefit with rice and evaluate rice searately from the other criteria. Although it does not satisfy the condition 0 X 1, it can be included in the generalised model as a secial case in which the rice gain value is equated with the rice difference. Corresondingly from Equation 15a and 15b, the ordered rice gain sequence, X (1), X (2),.., X (j),.., X (m-1), X (m) in descending rice difference, is obtained for calculating their scores, A (i). Thus, this method is a comarison based on ordered absolute values with reference to an artificial zero at x B. It also satisfies the transitivity roerty. PRICE RATIO MODEL SUB-CLASS If X is allowed to assume other non-linear functions of rice, -1 it is ossible to incororate X i = χ i = x i, Karsak s value function, into the generalised rice-scoring model. Although equals to unity, its scoring curve is strictly not linear. If x i = x min+ x i, where x i is a small ositive difference of the i th rice above the minimum rice, x min, then the value function is given by X i = 1 1 x 1- (16) min + x i x x i min x min If normalisation is done, the value function reresents a ratio as follows: X i = x min 1- x i (17) x min + x i x min Both Equations 16 and 17, when substituted into Equation 1b roduce identical effects. Both differ from the rice difference function. The generalised model accets both these two rice ratio functions but Equation 16 can only be used in the normalised class of models because on its own it is not dimensionless. Cost control is imlemented by excluding rices that exceed x B from evaluation. The largest rice does not necessarily have a low value because Equations 16 and 17 work in an ordered ratio scale with natural zero. Thus, a restriction to good discrimination is imosed. From the rice survey, the standard deviation of rice is small, making x i of Equations 16 and 17 small relative to x min. X i is thus closer to unity than to zero. These two rice gain functions satisfy the transitivity roerty but not the referencing roerty required in rosect theory. They reresent a secific sub-class that works on ratio comarison. COMPARISON BETWEEN PRICE DIFFERENCE AND PRICE RATIO MODELS Discrimination and cost control are the bases of comarison between the two model sub-classes. One set of tender rices for low-rice bunching and one set for high-rice bunching are used to illustrate the characteristics of the rice ratio and rice difference models. The two tender sets have the same minimum and maximum rices. Their statistics are tabulated in Tables 3 and 4 for both tenders. The higher rice tender naturally has the higher mean rice. When the large extreme rices are eliminated by cost control, the mean rices are reduced slightly but they remain relatively robust enough to continue to indicate the market norm. The behaviours of their standard deviations and coefficient of skewness are less redictable because they are deendent on the rice distribution after cost control action. A more reliable indication of the direction of change is seen in the reductions in the coefficients of variation after cost control. The tender with low-rice bunching has coefficient of skewness of for 8 rices and decreases to for 7 rices after cost control. The corresonding values of are and resectively. For the set with high-rice bunching the coefficient of skewness is for 8 rices and increases to for 7 rices after cost control. The skew has 24 Journal - The Institution of Engineers, Malaysia (Vol. 66, No. 1, March 2005)
7 rice scoring 9/20/05 12:12 PM Page 25 A GENERALISED PRICE-SCORING MODEL FOR TENDER EVALUATION Table 3: Statistics from low-rice bunching tender Tender Prices, Values RM Million Statistics (Cost-Controlled (Low-Price Bunching) Values in Brackets) Mean (5.952) Standard Deviation (0.2201) Coefficient of Variation (0.0370) Coefficient of Skewness (1.324) Table 4: Statistics from high-rice bunching tender Tender Prices, Values RM Million Statistics (Cost-Controlled (Low-Price Bunching) Values in Brackets) Mean (6.451) Standard Deviation (0.3846) Coefficient of Variation (0.0596) Coefficient of Skewness (-1.274) increased for high rice bunching because the extreme (lowest) rice is not eliminated by cost control in this case. The corresonding values of are and resectively. For a set of tender rices, 3 sets of normalised scores and 2 sets of un-normalised scores are calculated using a common reference function, whose coefficients α and β determined earlier were adoted. The rice scores from these 5 models are shown in Table 5 for low-rice bunching and in Table 6 for high-rice bunching. All 5 models show some degree of score bunching corresonding to rice bunching. In Karsak s model, equals to 1(α and β equal to zero) without cost control. Its scores are smaller comared with those of the rice ratio model in the next column. Tables 5 and 6 show that the rice ratio models do not convey significant score differences if the rice differences are small when comared to their absolute values. As illustrated in Table 6, they more effectively rovide information in terms of relative differences but are articularly weak in discriminating rices when there is highrice bunching. Comaratively, the rice difference models are more discriminating because they enhance the scores of the low rices and reduce the scores of the high rices. As a result, they will tend to strengthen the effect of rice when an overall tender evaluation is made together with the other non-rice attributes. By cost control, the over-riced scores of both the rice ratio and the rice difference models are set to zero, effectively eliminating over-riced tenders from consideration. To a small extent, cost control increases the normalised scores because the sum of scores is reduced by the elimination of the over-riced tender. The weakness of the rice ratio model in not being able to score the budget rice to zero is obvious here. Normalisation makes the sum of scores equals to 1 and the individual scores less than 1. An un-normalised model enhances all rice scores by making the score of the lowest rice equal to 1. The larger score magnitude in the un-normalised rice-scoring model has a greater ability to create rice dominance in the evaluation because it always starts with a score of 1 irresective of the number of tender rices. PRICE-SCORING MODELS From the generalised rice-scoring model, a number of ossible models for articular alications are derived as shown in Figure 3. The un-normalised class using the un-normalised rice-difference function with = 1 is erhas the simlest model and has attracted the widest alication, esecially in the 2-enveloe system of tender evaluation in which rice is searated from the non-rice attributes. This model suits direct rice comarison methods. Price difference in the mind of the evaluator is a straight forward and logical means of comaring rices in common monetary units. One would exect that a rocedure by rice difference is attractive because evaluators naturally judge and rank on the basis of rice difference. By assigning = 0.88, it becomes the original value function of rosect theory. Table 5: Comarison among the rice ratio models and the rice difference models in low-rice bunching case Normalised Price Scores Tender Prices, Karsak s Price Ratio Model Price Difference Model RM Million Model (xb = RM6.88million) (xb = RM6.88million) (α=0, β=0) (α=0.8904, β= ) (α=0.8904, β= ) (0.8530) (0.4063) (1.0000) (1.0000) (0.8918) (0.5378) (0.8334) (0.3473) (0.6717) (0.0464) (0.8774) (0.4867) (0.9724) (0.8689) (0.0000) (0.0000) Note: Price scores in bracketed italic are un-normalised scores using Equation 1a. Table 6: Comarison among the rice ratio models and the rice difference models in high-rice bunching case Normalised Price Scores Tender Prices, Karsak s Price Ratio Model Price Difference Model RM Million Model (xb =RM6.88million) (xb =RM6.88million) (α=0, β=0) (α=0.8904, β= ) (α=0.8904, β= ) (0.9465) (0.5423) (1.0000) (1.0000) (0.9457) (0.5271) (0.9547) (0.6648) (0.9364) (0.1050) (0.9700) (0.8147) (0.9572) (0.6936) (0.0000) (0.0000) Note: Price scores in bracketed italic are un-normalised scores using Equation 1a. Journal - The Institution of Engineers, Malaysia (Vol. 66, No. 1, March 2005) 25
8 rice scoring 9/20/05 12:12 PM Page 26 THUM PENG CHEW Figure 3: Particular rice-scoring models from the generalised model The un-normalised class using normalised rice gain functions are suitable for integrated evaluation of both rice and other nonrice attributes in a comuter rogram. Because of their larger score values comared with those of the normalised class, they have rice dominant tendencies. The rice-difference function can be adoted if dominance by a single rice is desired. On the other hand, the rice-ratio function will tend to move the scores away from singlerice dominance. When rice bunching occurs, collective dominance exists in the un-normalised function. The normalised class using normalised rice gain functions have different characteristics comared with those of the un-normalised class of models. They roduce an effect that tends not to emhasise on rice nor discriminate between rices thus, allow the other attributes to lay more influential roles in the evaluation. Their smaller scores are controlled by the number of tenders evaluated. The more tenders, the smaller the scores and the lesser the ability to dominate. The choice of any of the above models should be made by matching their characteristics with the evaluation objective. If the lowest rice is to dominate, then an un-normalised class of ricedifference scoring model is aroriate. If rice dominance is not intended, then a normalised class of rice-ratio scoring model is more effective. Both the un-normalised and normalised classes that use a dimensionless rice gain function based on either rice difference or rice ratio meets the requirement of dimensionless attribute scores in Thum s fuzzy tender evaluation model [5]. CONCLUSION A generalised rice-scoring model is develoed by incororating two rice gain functions, one based on rice difference on an interval scale and the other on rice ratio on a ratio scale. It attemts to revent cost overrun by eliminating over-riced tenders by comarison with the roject budget. The behaviour of evaluators and decision makers is modelled in the reference factor which is a function of the tender articiation rate and its rice distribution skew. In the resence of unusual influences or when fair cometition is threatened, the model will attemt to counteract the negative strategies adoted by tenderers, failing which a reassignment otion built into the rogram allows the evaluator to make judgment outside the model. The generalised rice-scoring model roduces two generic rice model classes. The un-normalised class tend to roduce rice dominant effects while the normalised class tends to allow non-rice attributes to have more influence in the overall evaluation. These two classes roduce their own rice ratio sub-class using a rice gain derived from the ratio of the minimum tender rice to a rice, and their rice difference sub-class derived from the rice gain measure of a rice with reference to the roject budget. A survey of tender rices rovides data for estimating the tender articiation rate and the range of variations of the rice distribution s coefficient of skewness to be used in the reference function. By aroriate choice of rice gain function and of the reference function, 5 articular rice-scoring models are derived. Price difference models are found to be better at discriminating rices than rice ratio models. Price ratio models are more suitable for matching tender evaluation objectives that do not emhasise rice. The combination of the value functions and the rice gain functions with built-in cost control roduces a diverse number of models for secific alications in a tender evaluation comuter rogram. Further investigation is required to test them with the nonrice attributes in order to define their alication in a tender evaluation rocedure. The generalised rice-scoring model hence, rovides a means of studying the existing methods of tender evaluation by comuter simulation. For examle, comarisons can be made between an integrated aroach in which rice and other attributes are combined in a 1-stage evaluation rocedure, and one in which rice is evaluated after the evaluation of other non-rice attributes is comleted in a 2-stage evaluation rocedure. REFERENCES [1] E. E. Karsak, Fuzzy MCDM Procedure for Evaluating Flexible Manufacturing System Alternatives, Proceedings of the 2000 IEEE Engineering Management Society, , Albuquerque, New Mexico, USA, [2] D. Hahneman and A. Tversky, Prosect theory: An Analysis of Decision Under Risk, Econometrica Vol.74, , [3] A. Tversky and D. Hahneman, Advances in Prosect Theory: Cumulative Reresentation of Uncertainty, Journal of Risk and Uncertainty Vol. 5, , [4] W. S. Neilson and J. Stowe, A Further Examination of Cumulative Prosect Theory Parameterizations, Journal of Risk and Uncertainty Vol. 24(1), , Jan [5] P. C. Thum, A Fuzzy Multile Attribute Decision-Making Aroach to Tender Evaluation, Journal, The Institution of Engineers, Malaysia, Vol.64, No. 3,. Set [6] P. C. Thum and K. S. Rao, A Multi-level Imlementation of a Fuzzy Tender Evaluation Procedure, Journal, The Institution of Engineers, Malaysia, Vol.65, No.4,. Dec [7] R. Hastie and R. M. Dawes, Chater 13, Rational Choice in an Uncertain World: The Psychology of Judgment and Decision Making (Book), Sage Publication, [8] S. Plous, The Psychology of Judgment and Decision Making (Book), McGraw Hill, [9] T. Connolly, H. R. Arkes and K. R. Hammond, Judgment and Decision Making: An Interdiscilinary Reader (Book) 2nd Edition, Cambridge University Press, [10] C. Starmer, Develoment in Non-Exected Utility Theory: The Hunt for a Descritive Theory of Choice under Risk, Journal of Economic Literature Vol. XXXVIII, , June [11] P. Bajari and L. Ye, Cometition Versus Collusion in Procurement Auctions: Identification and Testing, Stanford University Working Paer, [12] P. Bajari and G. Summers, Detecting Collusion in Procurement Auctions, Antitrust Law Journal Vol. 70, , [13] L. M. Froeb and M. Shor, Auctions, Evidence and Antitrust in The Use of Econometrics In Antitrust, edited by John Harkrider, American Bar Association, Journal - The Institution of Engineers, Malaysia (Vol. 66, No. 1, March 2005)
Confidence Intervals for a Proportion Using Inverse Sampling when the Data is Subject to False-positive Misclassification
Journal of Data Science 13(015), 63-636 Confidence Intervals for a Proortion Using Inverse Samling when the Data is Subject to False-ositive Misclassification Kent Riggs 1 1 Deartment of Mathematics and
More informationCapital Budgeting: The Valuation of Unusual, Irregular, or Extraordinary Cash Flows
Caital Budgeting: The Valuation of Unusual, Irregular, or Extraordinary Cash Flows ichael C. Ehrhardt Philli R. Daves Finance Deartment, SC 424 University of Tennessee Knoxville, TN 37996-0540 423-974-1717
More informationSampling Procedure for Performance-Based Road Maintenance Evaluations
Samling Procedure for Performance-Based Road Maintenance Evaluations Jesus M. de la Garza, Juan C. Piñero, and Mehmet E. Ozbek Maintaining the road infrastructure at a high level of condition with generally
More informationA Comparative Study of Various Loss Functions in the Economic Tolerance Design
A Comarative Study of Various Loss Functions in the Economic Tolerance Design Jeh-Nan Pan Deartment of Statistics National Chen-Kung University, Tainan, Taiwan 700, ROC Jianbiao Pan Deartment of Industrial
More informationA Multi-Objective Approach to Portfolio Optimization
RoseHulman Undergraduate Mathematics Journal Volume 8 Issue Article 2 A MultiObjective Aroach to Portfolio Otimization Yaoyao Clare Duan Boston College, sweetclare@gmail.com Follow this and additional
More informationStatistics and Probability Letters. Variance stabilizing transformations of Poisson, binomial and negative binomial distributions
Statistics and Probability Letters 79 (9) 6 69 Contents lists available at ScienceDirect Statistics and Probability Letters journal homeage: www.elsevier.com/locate/staro Variance stabilizing transformations
More informationSINGLE SAMPLING PLAN FOR VARIABLES UNDER MEASUREMENT ERROR FOR NON-NORMAL DISTRIBUTION
ISSN -58 (Paer) ISSN 5-5 (Online) Vol., No.9, SINGLE SAMPLING PLAN FOR VARIABLES UNDER MEASUREMENT ERROR FOR NON-NORMAL DISTRIBUTION Dr. ketki kulkarni Jayee University of Engineering and Technology Guna
More informationInformation and uncertainty in a queueing system
Information and uncertainty in a queueing system Refael Hassin December 7, 7 Abstract This aer deals with the effect of information and uncertainty on rofits in an unobservable single server queueing system.
More informationSetting the regulatory WACC using Simulation and Loss Functions The case for standardising procedures
Setting the regulatory WACC using Simulation and Loss Functions The case for standardising rocedures by Ian M Dobbs Newcastle University Business School Draft: 7 Setember 2007 1 ABSTRACT The level set
More informationCausal Links between Foreign Direct Investment and Economic Growth in Egypt
J I B F Research Science Press Causal Links between Foreign Direct Investment and Economic Growth in Egyt TAREK GHALWASH* Abstract: The main objective of this aer is to study the causal relationshi between
More informationQuantitative Aggregate Effects of Asymmetric Information
Quantitative Aggregate Effects of Asymmetric Information Pablo Kurlat February 2012 In this note I roose a calibration of the model in Kurlat (forthcoming) to try to assess the otential magnitude of the
More informationSupplemental Material: Buyer-Optimal Learning and Monopoly Pricing
Sulemental Material: Buyer-Otimal Learning and Monooly Pricing Anne-Katrin Roesler and Balázs Szentes February 3, 207 The goal of this note is to characterize buyer-otimal outcomes with minimal learning
More informationForward Vertical Integration: The Fixed-Proportion Case Revisited. Abstract
Forward Vertical Integration: The Fixed-roortion Case Revisited Olivier Bonroy GAEL, INRA-ierre Mendès France University Bruno Larue CRÉA, Laval University Abstract Assuming a fixed-roortion downstream
More informationAnnex 4 - Poverty Predictors: Estimation and Algorithm for Computing Predicted Welfare Function
Annex 4 - Poverty Predictors: Estimation and Algorithm for Comuting Predicted Welfare Function The Core Welfare Indicator Questionnaire (CWIQ) is an off-the-shelf survey ackage develoed by the World Bank
More informationVolumetric Hedging in Electricity Procurement
Volumetric Hedging in Electricity Procurement Yumi Oum Deartment of Industrial Engineering and Oerations Research, University of California, Berkeley, CA, 9472-777 Email: yumioum@berkeley.edu Shmuel Oren
More informationA NOTE ON SKEW-NORMAL DISTRIBUTION APPROXIMATION TO THE NEGATIVE BINOMAL DISTRIBUTION
A NOTE ON SKEW-NORMAL DISTRIBUTION APPROXIMATION TO THE NEGATIVE BINOMAL DISTRIBUTION JYH-JIUAN LIN 1, CHING-HUI CHANG * AND ROSEMARY JOU 1 Deartment of Statistics Tamkang University 151 Ying-Chuan Road,
More informationThe Supply and Demand for Exports of Pakistan: The Polynomial Distributed Lag Model (PDL) Approach
The Pakistan Develoment Review 42 : 4 Part II (Winter 23). 96 972 The Suly and Demand for Exorts of Pakistan: The Polynomial Distributed Lag Model (PDL) Aroach ZESHAN ATIQUE and MOHSIN HASNAIN AHMAD. INTRODUCTION
More informationQuality Regulation without Regulating Quality
1 Quality Regulation without Regulating Quality Claudia Kriehn, ifo Institute for Economic Research, Germany March 2004 Abstract Against the background that a combination of rice-ca and minimum uality
More informationCS522 - Exotic and Path-Dependent Options
CS522 - Exotic and Path-Deendent Otions Tibor Jánosi May 5, 2005 0. Other Otion Tyes We have studied extensively Euroean and American uts and calls. The class of otions is much larger, however. A digital
More informationINDEX NUMBERS. Introduction
INDEX NUMBERS Introduction Index numbers are the indicators which reflect changes over a secified eriod of time in rices of different commodities industrial roduction (iii) sales (iv) imorts and exorts
More informationAre capital expenditures, R&D, advertisements and acquisitions positive NPV?
Are caital exenditures, R&D, advertisements and acquisitions ositive NPV? Peter Easton The University of Notre Dame and Peter Vassallo The University of Melbourne February, 2009 Abstract The focus of this
More informationNon-Inferiority Tests for the Ratio of Two Correlated Proportions
Chater 161 Non-Inferiority Tests for the Ratio of Two Correlated Proortions Introduction This module comutes ower and samle size for non-inferiority tests of the ratio in which two dichotomous resonses
More informationEVIDENCE OF ADVERSE SELECTION IN CROP INSURANCE MARKETS
The Journal of Risk and Insurance, 2001, Vol. 68, No. 4, 685-708 EVIDENCE OF ADVERSE SELECTION IN CROP INSURANCE MARKETS Shiva S. Makki Agai Somwaru INTRODUCTION ABSTRACT This article analyzes farmers
More informationAnalysis on Mergers and Acquisitions (M&A) Game Theory of Petroleum Group Corporation
DOI: 10.14355/ijams.2014.0301.03 Analysis on Mergers and Acquisitions (M&A) Game Theory of Petroleum Grou Cororation Minchang Xin 1, Yanbin Sun 2 1,2 Economic and Management Institute, Northeast Petroleum
More informationManagement of Pricing Policies and Financial Risk as a Key Element for Short Term Scheduling Optimization
Ind. Eng. Chem. Res. 2005, 44, 557-575 557 Management of Pricing Policies and Financial Risk as a Key Element for Short Term Scheduling Otimization Gonzalo Guillén, Miguel Bagajewicz, Sebastián Eloy Sequeira,
More informationAsymmetric Information
Asymmetric Information Econ 235, Sring 2013 1 Wilson [1980] What haens when you have adverse selection? What is an equilibrium? What are we assuming when we define equilibrium in one of the ossible ways?
More informationTESTING THE CAPITAL ASSET PRICING MODEL AFTER CURRENCY REFORM: THE CASE OF ZIMBABWE STOCK EXCHANGE
TESTING THE CAPITAL ASSET PRICING MODEL AFTER CURRENCY REFORM: THE CASE OF ZIMBABWE STOCK EXCHANGE Batsirai Winmore Mazviona 1 ABSTRACT The Caital Asset Pricing Model (CAPM) endeavors to exlain the relationshi
More informationLECTURE NOTES ON MICROECONOMICS
LECTURE NOTES ON MCROECONOMCS ANALYZNG MARKETS WTH BASC CALCULUS William M. Boal Part : Consumers and demand Chater 5: Demand Section 5.: ndividual demand functions Determinants of choice. As noted in
More informationThe Relationship Between the Adjusting Earnings Per Share and the Market Quality Indexes of the Listed Company 1
MANAGEMENT SCİENCE AND ENGİNEERİNG Vol. 4, No. 3,,.55-59 www.cscanada.org ISSN 93-34 [Print] ISSN 93-35X [Online] www.cscanada.net The Relationshi Between the Adusting Earnings Per Share and the Maret
More informationFUNDAMENTAL ECONOMICS - Economics Of Uncertainty And Information - Giacomo Bonanno ECONOMICS OF UNCERTAINTY AND INFORMATION
ECONOMICS OF UNCERTAINTY AND INFORMATION Giacomo Bonanno Deartment of Economics, University of California, Davis, CA 9566-8578, USA Keywords: adverse selection, asymmetric information, attitudes to risk,
More informationOnline Robustness Appendix to Are Household Surveys Like Tax Forms: Evidence from the Self Employed
Online Robustness Aendix to Are Household Surveys Like Tax Forms: Evidence from the Self Emloyed October 01 Erik Hurst University of Chicago Geng Li Board of Governors of the Federal Reserve System Benjamin
More informationEffects of Size and Allocation Method on Stock Portfolio Performance: A Simulation Study
2011 3rd International Conference on Information and Financial Engineering IPEDR vol.12 (2011) (2011) IACSIT Press, Singaore Effects of Size and Allocation Method on Stock Portfolio Performance: A Simulation
More informationFORECASTING EARNINGS PER SHARE FOR COMPANIES IN IT SECTOR USING MARKOV PROCESS MODEL
FORECASTING EARNINGS PER SHARE FOR COMPANIES IN IT SECTOR USING MARKOV PROCESS MODEL 1 M.P. RAJAKUMAR, 2 V. SHANTHI 1 Research Scholar, Sathyabama University, Chennai-119, Tamil Nadu, India 2 Professor,
More informationRevisiting the risk-return relation in the South African stock market
Revisiting the risk-return relation in the South African stock market Author F. Darrat, Ali, Li, Bin, Wu, Leqin Published 0 Journal Title African Journal of Business Management Coyright Statement 0 Academic
More information: now we have a family of utility functions for wealth increments z indexed by initial wealth w.
Lotteries with Money Payoffs, continued Fix u, let w denote wealth, and set u ( z) u( z w) : now we have a family of utility functions for wealth increments z indexed by initial wealth w. (a) Recall from
More informationBA 351 CORPORATE FINANCE LECTURE 7 UNCERTAINTY, THE CAPM AND CAPITAL BUDGETING. John R. Graham Adapted from S. Viswanathan
BA 351 CORPORATE FINANCE LECTURE 7 UNCERTAINTY, THE CAPM AND CAPITAL BUDGETING John R. Graham Adated from S. Viswanathan FUQUA SCHOOL OF BUSINESS DUKE UNIVERSITY 1 In this lecture, we examine roject valuation
More informationLIS Working Paper Series
LIS Working Paer Series No. 648 Relative income change and ro-oor growth Marek Kośny, and Gastón Yalonetzky Setember 2015 Luxembourg Income Study (LIS), asbl Relative income change and ro-oor growth Marek
More informationThird-Market Effects of Exchange Rates: A Study of the Renminbi
PRELIMINARY DRAFT. NOT FOR QUOTATION Third-Market Effects of Exchange Rates: A Study of the Renminbi Aaditya Mattoo (Develoment Research Grou, World Bank), Prachi Mishra (Research Deartment, International
More informationAnalytical support in the setting of EU employment rate targets for Working Paper 1/2012 João Medeiros & Paul Minty
Analytical suort in the setting of EU emloyment rate targets for 2020 Working Paer 1/2012 João Medeiros & Paul Minty DISCLAIMER Working Paers are written by the Staff of the Directorate-General for Emloyment,
More informationInventory Systems with Stochastic Demand and Supply: Properties and Approximations
Working Paer, Forthcoming in the Euroean Journal of Oerational Research Inventory Systems with Stochastic Demand and Suly: Proerties and Aroximations Amanda J. Schmitt Center for Transortation and Logistics
More informationDo Poorer Countries Have Less Capacity for Redistribution?
Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Policy Research Working Paer 5046 Do Poorer Countries Have Less Caacity for Redistribution?
More informationFeasibilitystudyofconstruction investmentprojectsassessment withregardtoriskandprobability
Feasibilitystudyofconstruction investmentrojectsassessment withregardtoriskandrobability ofnpvreaching Andrzej Minasowicz Warsaw University of Technology, Civil Engineering Faculty, Warsaw, PL a.minasowicz@il.w.edu.l
More informationWe connect the mix-flexibility and dual-sourcing literatures by studying unreliable supply chains that produce
MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol. 7, No. 1, Winter 25,. 37 57 issn 1523-4614 eissn 1526-5498 5 71 37 informs doi 1.1287/msom.14.63 25 INFORMS On the Value of Mix Flexibility and Dual Sourcing
More informationGrowth, Distribution, and Poverty in Cameroon: A Poverty Analysis Macroeconomic Simulator s Approach
Poverty and Economic Policy Research Network Research Proosal Growth, istribution, and Poverty in Cameroon: A Poverty Analysis Macroeconomic Simulator s Aroach By Arsene Honore Gideon NKAMA University
More informationAsian Economic and Financial Review A MODEL FOR ESTIMATING THE DISTRIBUTION OF FUTURE POPULATION. Ben David Nissim.
Asian Economic and Financial Review journal homeage: htt://www.aessweb.com/journals/5 A MODEL FOR ESTIMATING THE DISTRIBUTION OF FUTURE POPULATION Ben David Nissim Deartment of Economics and Management,
More informationAppendix Large Homogeneous Portfolio Approximation
Aendix Large Homogeneous Portfolio Aroximation A.1 The Gaussian One-Factor Model and the LHP Aroximation In the Gaussian one-factor model, an obligor is assumed to default if the value of its creditworthiness
More informationCONSUMER GUIDE TO ARMA-Q. Big changes are coming to the way your managing agent is regulated
CONSUMER GUIDE TO ARMA-Q Big changes are coming to the way your managing agent is regulated 2 3 ARMA-Q: QUALITY STANDARDS FOR LEASEHOLD PROPERTY MANAGEMENT Who are we? ARMA is the leading trade association
More information***SECTION 7.1*** Discrete and Continuous Random Variables
***SECTION 7.*** Discrete and Continuous Random Variables Samle saces need not consist of numbers; tossing coins yields H s and T s. However, in statistics we are most often interested in numerical outcomes
More informationMatching Markets and Social Networks
Matching Markets and Social Networks Tilman Klum Emory University Mary Schroeder University of Iowa Setember 0 Abstract We consider a satial two-sided matching market with a network friction, where exchange
More informationON JARQUE-BERA TESTS FOR ASSESSING MULTIVARIATE NORMALITY
Journal of Statistics: Advances in Theory and Alications Volume, umber, 009, Pages 07-0 O JARQUE-BERA TESTS FOR ASSESSIG MULTIVARIATE ORMALITY KAZUYUKI KOIZUMI, AOYA OKAMOTO and TAKASHI SEO Deartment of
More informationModeling and Estimating a Higher Systematic Co-Moment Asset Pricing Model in the Brazilian Stock Market. Autoria: Andre Luiz Carvalhal da Silva
Modeling and Estimating a Higher Systematic Co-Moment Asset Pricing Model in the Brazilian Stock Market Autoria: Andre Luiz Carvalhal da Silva Abstract Many asset ricing models assume that only the second-order
More informationPublication Efficiency at DSI FEM CULS An Application of the Data Envelopment Analysis
Publication Efficiency at DSI FEM CULS An Alication of the Data Enveloment Analysis Martin Flégl, Helena Brožová 1 Abstract. The education and research efficiency at universities has always been very imortant
More information2/20/2013. of Manchester. The University COMP Building a yes / no classifier
COMP4 Lecture 6 Building a yes / no classifier Buildinga feature-basedclassifier Whatis a classifier? What is an information feature? Building a classifier from one feature Probability densities and the
More informationUtility and the Skewness of Return in Gambling
The Geneva Paers on Risk and Insurance Theory, 9: 145 163, 004 c 004 The Geneva Association Utility and the Skewness of Return in Gambling MICHAEL CAIN School of Business, University of Wales, Hen Goleg,
More informationRisk and Return. Calculating Return - Single period. Calculating Return - Multi periods. Uncertainty of Investment.
Chater 10, 11 Risk and Return Chater 13 Cost of Caital Konan Chan, 018 Risk and Return Return measures Exected return and risk? Portfolio risk and diversification CPM (Caital sset Pricing Model) eta Calculating
More informationCash-in-the-market pricing or cash hoarding: how banks choose liquidity
Cash-in-the-market ricing or cash hoarding: how banks choose liquidity Jung-Hyun Ahn Vincent Bignon Régis Breton Antoine Martin February 207 Abstract We develo a model in which financial intermediaries
More informationECONOMIC GROWTH CENTER
ECONOMIC GROWTH CENTER YALE UNIVERSITY P.O. Box 208269 New Haven, CT 06520-8269 htt://www.econ.yale.edu/~egcenter/ CENTER DISCUSSION PAPER NO. 844 COMPETITION IN OR FOR THE FIELD: WHICH IS BETTER? Eduardo
More information( ) ( ) β. max. subject to. ( ) β. x S
Intermediate Microeconomic Theory: ECON 5: Alication of Consumer Theory Constrained Maimization In the last set of notes, and based on our earlier discussion, we said that we can characterize individual
More informationA Graphical Depiction of Hicksian Partial-Equilibrium Welfare Analysis
A rahical eiction of Hicksian Partial-quilibrium Welfare Analysis Keir. Armstrong eartment of conomics Carleton University Ottawa, ON KS 5B6 karmstro@ccs.carleton.ca May 22, 23 Abstract An inescaable conclusion
More informationBIS Working Papers. Liquidity risk in markets with trading frictions: What can swing pricing achieve? No 663. Monetary and Economic Department
BIS Working Paers No 663 Liquidity risk in markets with trading frictions: What can swing ricing achieve? by Ulf Lewrick and Jochen Schanz Monetary and Economic Deartment October 207 JEL classification:
More informationDP2003/10. Speculative behaviour, debt default and contagion: A stylised framework of the Latin American Crisis
DP2003/10 Seculative behaviour, debt default and contagion: A stylised framework of the Latin American Crisis 2001-2002 Louise Allso December 2003 JEL classification: E44, F34, F41 Discussion Paer Series
More informationA Variance Estimator for Cohen s Kappa under a Clustered Sampling Design THESIS
A Variance Estimator for Cohen s Kaa under a Clustered Samling Design THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State
More informationCHOICE THEORY, UTILITY FUNCTIONS AND RISK AVERSION
CHOICE THEORY, UTILITY FUNCTIONS AND RISK AVERSION Szabolcs Sebestyén szabolcs.sebestyen@iscte.pt Master in Finance INVESTMENTS Sebestyén (ISCTE-IUL) Choice Theory Investments 1 / 65 Outline 1 An Introduction
More informationHow Large Are the Welfare Costs of Tax Competition?
How Large Are the Welfare Costs of Tax Cometition? June 2001 Discussion Paer 01 28 Resources for the Future 1616 P Street, NW Washington, D.C. 20036 Telehone: 202 328 5000 Fax: 202 939 3460 Internet: htt://www.rff.org
More informationInternational Journal of Education and Social Science Research
International Journal of Education and Social Science Research Vol. 1, No. 02; 2018 DOES INFLATION LEAD TO CURRENCY DEPRECIATION IN NIGERIA? AN AUTOREGRESSIVE DISTRIBUTED LAG (ARDL) BOUND TESTING Umar
More informationCONSUMER CREDIT SCHEME OF PRIVATE COMMERCIAL BANKS: CONSUMERS PREFERENCE AND FEEDBACK
htt://www.researchersworld.com/ijms/ CONSUMER CREDIT SCHEME OF PRIVATE COMMERCIAL BANKS: CONSUMERS PREFERENCE AND FEEDBACK Rania Kabir, Lecturer, Primeasia University, Bangladesh. Ummul Wara Adrita, Lecturer,
More informationThe Effect of Prior Gains and Losses on Current Risk-Taking Using Quantile Regression
The Effect of rior Gains and Losses on Current Risk-Taking Using Quantile Regression by Fabio Mattos and hili Garcia Suggested citation format: Mattos, F., and. Garcia. 2009. The Effect of rior Gains and
More informationVI Introduction to Trade under Imperfect Competition
VI Introduction to Trade under Imerfect Cometition n In the 1970 s "new trade theory" is introduced to comlement HOS and Ricardo. n Imerfect cometition models cature strategic interaction and roduct differentiation:
More informationProfessor Huihua NIE, PhD School of Economics, Renmin University of China HOLD-UP, PROPERTY RIGHTS AND REPUTATION
Professor uihua NIE, PhD School of Economics, Renmin University of China E-mail: niehuihua@gmail.com OD-UP, PROPERTY RIGTS AND REPUTATION Abstract: By introducing asymmetric information of investors abilities
More informationSharpe Ratios and Alphas in Continuous Time
JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS VOL. 39, NO. 1, MARCH 2004 COPYRIGHT 2004, SCHOOL OF BUSINESS ADMINISTRATION, UNIVERSITY OF WASHINGTON, SEATTLE, WA 98195 Share Ratios and Alhas in Continuous
More informationStochastic modelling of skewed data exhibiting long range dependence
IUGG XXIV General Assembly 27 Perugia, Italy, 2 3 July 27 International Association of Hydrological Sciences, Session HW23 Analysis of Variability in Hydrological Data Series Stochastic modelling of skewed
More informationApplication of Monte-Carlo Tree Search to Traveling-Salesman Problem
R4-14 SASIMI 2016 Proceedings Alication of Monte-Carlo Tree Search to Traveling-Salesman Problem Masato Shimomura Yasuhiro Takashima Faculty of Environmental Engineering University of Kitakyushu Kitakyushu,
More informationWorst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
Worst-case evaluation comlexity for unconstrained nonlinear otimization using high-order regularized models E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos and Ph. L. Toint 2 Aril 26 Abstract
More informationDoes Hedging Reduce the Cost of Delegation?
Does Hedging Reduce the Cost of Delegation? Sanoti K. Eswar Job Market Paer July 2014 Abstract I incororate the choice of hedging instrument into a moral hazard model to study the imact of derivatives
More informationOutline. Simple, Compound, and Reduced Lotteries Independence Axiom Expected Utility Theory Money Lotteries Risk Aversion
Uncertainty Outline Simple, Compound, and Reduced Lotteries Independence Axiom Expected Utility Theory Money Lotteries Risk Aversion 2 Simple Lotteries 3 Simple Lotteries Advanced Microeconomic Theory
More informationNon-Exclusive Competition and the Debt Structure of Small Firms
Non-Exclusive Cometition and the Debt Structure of Small Firms Aril 16, 2012 Claire Célérier 1 Abstract This aer analyzes the equilibrium debt structure of small firms when cometition between lenders is
More informationMaximize the Sharpe Ratio and Minimize a VaR 1
Maximize the Share Ratio and Minimize a VaR 1 Robert B. Durand 2 Hedieh Jafarour 3,4 Claudia Klüelberg 5 Ross Maller 6 Aril 28, 2008 Abstract In addition to its role as the otimal ex ante combination of
More informationCross-border auctions in Europe: Auction prices versus price differences
Cross-border auctions in Euroe: Auction rices versus rice differences Natalie Glück, Christian Redl, Franz Wirl Keywords Cross-border auctions, electricity market integration, electricity rice differences
More informationLemons Markets and the Transmission of Aggregate Shocks
Lemons Markets and the Transmission of Aggregate Shocks Pablo Kurlat Stanford University July 21, 2011 Abstract I study a dynamic economy featuring adverse selection in asset markets. Borrowingconstrained
More informationBuyer-Optimal Learning and Monopoly Pricing
Buyer-Otimal Learning and Monooly Pricing Anne-Katrin Roesler and Balázs Szentes January 2, 217 Abstract This aer analyzes a bilateral trade model where the buyer s valuation for the object is uncertain
More informationWe are going to delve into some economics today. Specifically we are going to talk about production and returns to scale.
Firms and Production We are going to delve into some economics today. Secifically we are going to talk aout roduction and returns to scale. firm - an organization that converts inuts such as laor, materials,
More information1 < = α σ +σ < 0. Using the parameters and h = 1/365 this is N ( ) = If we use h = 1/252, the value would be N ( ) =
Chater 6 Value at Risk Question 6.1 Since the rice of stock A in h years (S h ) is lognormal, 1 < = α σ +σ < 0 ( ) P Sh S0 P h hz σ α σ α = P Z < h = N h. σ σ (1) () Using the arameters and h = 1/365 this
More informationGottfried Haberler s Principle of Comparative Advantage
Gottfried Haberler s rincile of Comarative dvantage Murray C. Kem a* and Masayuki Okawa b a Macquarie University b Ritsumeiken University bstract Like the Torrens-Ricardo rincile of Comarative dvantage,
More informationObjectives. 3.3 Toward statistical inference
Objectives 3.3 Toward statistical inference Poulation versus samle (CIS, Chater 6) Toward statistical inference Samling variability Further reading: htt://onlinestatbook.com/2/estimation/characteristics.html
More informationSummary of the Chief Features of Alternative Asset Pricing Theories
Summary o the Chie Features o Alternative Asset Pricing Theories CAP and its extensions The undamental equation o CAP ertains to the exected rate o return time eriod into the uture o any security r r β
More informationInterest Rates in Trade Credit Markets
Interest Rates in Trade Credit Markets Klenio Barbosa Humberto Moreira Walter Novaes December, 2009 Abstract Desite strong evidence that suliers of inuts are informed lenders, the cost of trade credit
More informationPartially Ordered Preferences in Decision Trees: Computing Strategies with Imprecision in Probabilities
Partially Ordered Preferences in Decision Trees: Comuting trategies with Imrecision in Probabilities Daniel Kikuti scola Politécnica University of ão Paulo daniel.kikuti@oli.us.br Fabio G. Cozman scola
More information2002 Qantas Financial Report. The Spirit of Australia
2002 Financial Reort The Sirit of Australia Airways Limited ABN 16 009 661 901 contents age Statements of financial erformance 2 Statements of financial osition 3 Statements of cash flows 4 Notes to the
More informationEXPOSURE PROBLEM IN MULTI-UNIT AUCTIONS
EXPOSURE PROBLEM IN MULTI-UNIT AUCTIONS Hikmet Gunay and Xin Meng University of Manitoba and SWUFE-RIEM January 19, 2012 Abstract We characterize the otimal bidding strategies of local and global bidders
More informationEconomic Performance, Wealth Distribution and Credit Restrictions under variable investment: The open economy
Economic Performance, Wealth Distribution and Credit Restrictions under variable investment: The oen economy Ronald Fischer U. de Chile Diego Huerta Banco Central de Chile August 21, 2015 Abstract Potential
More informationInternational Journal of Scientific & Engineering Research, Volume 4, Issue 11, November ISSN
International Journal of Scientific & Engineering Research, Volume 4, Issue 11, November-2013 1063 The Causality Direction Between Financial Develoment and Economic Growth. Case of Albania Msc. Ergita
More informationECON 2100 Principles of Microeconomics (Fall 2018) Government Policies in Markets: Price Controls and Per Unit Taxes
ECON 21 Princiles of icroeconomics (Fall 218) Government Policies in arkets: Price Controls and Per Unit axes Relevant readings from the textbook: ankiw, Ch. 6 Suly,, and Government Policies ankiw, Ch.
More informationEquity Incentive Model of Crowdfunding in Different Types of Projects
Equity Incentive Model of in Different Tyes of Proects Lingling Huang, Li Xin School of Economics and Management, orth China University of Technology, Beiing,China Abstract As a new financing tool for
More informationSupply chain disruption assessment based on the newsvendor model
Journal of Industrial Engineering and Management JIEM, 2013 6(1):188-199 Online ISSN: 2013-0953 Print ISSN: 2013-8423 htt://dx.doi.org/10.3926/jiem.613 Suly chain disrution assessment based on the newsvendor
More informationAnalysing indicators of performance, satisfaction, or safety using empirical logit transformation
Analysing indicators of erformance, satisfaction, or safety using emirical logit transformation Sarah Stevens,, Jose M Valderas, Tim Doran, Rafael Perera,, Evangelos Kontoantelis,5 Nuffield Deartment of
More informationIndividual Comparative Advantage and Human Capital Investment under Uncertainty
Individual Comarative Advantage and Human Caital Investment under Uncertainty Toshihiro Ichida Waseda University July 3, 0 Abstract Secialization and the division of labor are the sources of high roductivity
More informationOliver Hinz. Il-Horn Hann
REEARCH ARTICLE PRICE DICRIMINATION IN E-COMMERCE? AN EXAMINATION OF DYNAMIC PRICING IN NAME-YOUR-OWN PRICE MARKET Oliver Hinz Faculty of Economics and usiness Administration, Goethe-University of Frankfurt,
More informationLiving in an irrational society: Wealth distribution with correlations between risk and expected profits
Physica A 371 (2006) 112 117 www.elsevier.com/locate/hysa Living in an irrational society: Wealth distribution with correlations between risk and exected rofits Miguel A. Fuentes a,b, M. Kuerman b, J.R.
More informationAdverse Selection in an Efficiency Wage Model with Heterogeneous Agents
Adverse Selection in an Efficiency Wage Model with Heterogeneous Agents Ricardo Azevedo Araujo Deartment of Economics, University of Brasilia (UnB), Brazil Adolfo Sachsida Brazilian Institute for Alied
More informationInformal Lending and Entrepreneurship
Informal Lending and Entrereneurshi Pinar Yildirim Geyu Yang Abstract How does the informal economy affect financial inclusion and entrereneurial activity of consumers? We investigate the imact of informal
More information