Capacitated Location-Allocation Problem in a Competitive Environment
|
|
- Derrick Lane
- 5 years ago
- Views:
Transcription
1 Capactated Locaton-Allocaton Problem n a Compettve Envronment At Bassou Azz, 2 Blal Mohamed, 3 Solh Azz, 4 El Alam Jamla,2 Unversty Mohammed V-Agdal, Laboratory of Systems Analyss, Informaton Processng and Industral Management (LASTIMI), Mohammada School of Engneers, Rabat, Morocco. 3 Prof., Natonal Hgh School of Mnes, Rabat, Morocco. 4 Prof., Unversty Mohammed V-Agdal, LASTIMI, Superor School of Technology Sale, Sale, Morocco. ORCID : , 2 ORCID: Abstract In ths paper, we propose a game theoretc model to solve the Capactated locaton-allocaton problem n a compettve envronment for a two level dstrbuton Network. The problem s a varant of the TLCLAP problem. We study the locaton allocaton decsons for two frms that wsh to extend ther dstrbuton networks. Through the ntegraton of several economc parameters, we propose an algorthm for fndng Nash equlbrum n two-player games from the proposed mathematcal model. Thus, we assumed the case of mxed strateges to establsh the frms' best response functons. An optmzaton approach s proposed to fnd equlbrum under capacty constrant. To provde a better analyss of the problem, fve scenaros were gven. Computatonal results show the effectveness of the proposed approach. Keywords: Locaton allocaton problem, Nash equlbrum, Game locaton, Dstrbuton Network INTRODUCTION Large-scale dstrbuton s experencng a boomng n recent years despte a slower growth n economes, saturaton of markets, a contnues costs rsng, fragmented markets and an ncreasng compettve envronment [].In ths context, the openng of one or more stores s one of the key decsons that must be taken to deal wth ths stuaton. In addton, the market study for the mplantaton, the number of stores to be opened and the fnancal capacty of a dstrbuton busness must take nto account the projected market share, whch s mpacted by the competton factor. Thus, the present paper ams to solve the problem of locaton-allocaton n a compettve envronment. LITERATURE REVIEW The problems of faclty locaton have been studed thoroughly durng the last decades, due to the large varety of applcatons based on ths knd of problems. The problem of locaton and allocaton was ntroduced by Alfred Weber who focused n ndustral factory ste mplantaton. Later, the noton of spatal competton n a stuaton of duopoly was ntroduced by []. In hs book, he has hghlghted the compettve nteractons between two stores n a dstrbuton network, based on the prncple of homogeneous dstrbuton of clents to determne the optmal locaton of two stores wth smlar characterstcs. In the same research focus, [2] ntroduced the competton wth mult-stores n the orgnal model [] and shows that there s no equlbrum to a pure strategy. The study of the problem of mult-store locaton on a dscrete space was the subject of the work of [3] that have generated a great nterest among researchers and a large-scale dstrbuton companes. Moreover, the assumpton that transport costs are quadratc n dstance, [4] show that companes tend to open one store. of [5] who frst ntroduce the basc elements of locaton models n a compettve envronment followed by the basc model ntroduced by []. Lately, the noton of competton n the problems of locaton/allocaton has become ncreasngly studed. For the locaton of facltes n a logstcs network, the approach adopted s to make a modelng n the form of a game whose soluton s gven by a Nash equlbrum [6]. In addton, t s mportant n any decson of locaton that the compettors revew ther strateges to constantly nnovate n order to dfferentate from the others players (compettors) [7]. The proxmty of the clent, the nteractons wth the market of the large dstrbuton referrng especally to the strategy of localzaton, and response to changes n demand offers an advantage for the company n the decson of localzaton [8]. Game theory and competton In general, the models of competton n economcs are based on the applcaton of the game theory. The objectve s to study the nteractons of the behavors of several ndvduals, FRIEDRICH, Theory of the Locaton of Industres, Unversty of Chcago Press,
2 called players, who are aware of these nteractons. The Nash equlbrum", s a fundamental noton n ths theory. In a game theory, a strategy can be reduced to an elementary decson, but can also be a complex acton plan. The notons of Nash equlbrum and the best response functon are fundamental. Indeed, they represent the solutons to the problems studed n game theory. Duopoly and olgopoly In the context of compettve strateges, frms make decsons n response to compettors. Ths reacton creates a stuaton of strategc nteractons that s accentuated by an atomstc demand n the market. In the case of two frms that compete wth one another, we speak of a duopoly. we try to llustrate the nterest of ths theory n these compettve stuatons. In the case of Bertrand's duopoly, frms compete by prces. We denote by p and p 2, the prces that the frms F and F2 must apply. These prces defne the requests addressed to F and F2. We denote by D (p, p 2 ) the demand addressed to frm, =,2, D the aggregate demand on the market and C, C 2 are respectvely the constant unt costs for frms F and F2. Each frm seeks to maxmze ts proft n the market. Therefore, the problem of the frm s formulated as follows: max π (p C )D (p, p 2 ), =,2 We assume that the frms are symmetrc n costs, C = C 2 = C and each frm serves the entre demand addressed to t. In attemptng to analyze how prce polcy can affect the compettve stuaton, we can notce that: - If p > p 2, customers wll turn to F2, whch offers low prces for the same products offered by F. Then the total demand wll be satsfed by F2. We thus have: D (p, p 2 ) = 0 and D 2 (p, p 2 ) = D; - If p < p 2, customers wll go to the frm F whch offers low prces for the same products offered by F2. Then the total demand wll be satsfed by F. We thus have: D (p, p 2 ) = D and D 2 (p, p 2 ) = 0; - If p = p 2, the demand wll be shared equally between F and F2, so we have : D (p, p 2 ) = D 2 (p, p 2 ) = D 2. Thus, the unque equlbrum of Bertrand's duopoly wth symmetrc costs s characterzed by: p = p 2 = C, whch gves: π = (p C)D (p, p 2 ) = 0. Locaton models n a compettve envronment In the models of duopoly presented by Cournot, Bertrand, the decsons of the two competng companes are taken smultaneously. The optmal solutons for these concurrent decsons are called "Nash equlbrum" or sometmes called Cournot-Nash equlbrum.the prelmnary work of locatng facltes smultaneously has been proposed n [9]. Thus, snce sequental decson-makng leads to an asymmetry between decson-makers, we must dfferentate the dentty of decson-makers. In the case of a duopoly, the company that starts wth makng the locaton decson s called the leader and the other s called the follower. The Stackelberg model s based on three major assumptons: Decsons are made once and for all, Decsons are made sequentally, The leader and the follower have a complete knowledge of the localzaton game. An extenson of the aforementoned model s gven by the sequental localzaton model proposed by [0]. It deals wth the case where a frm locates n nstallatons, but the compettor frm locates only one nstallaton. Recently, a cooperatve competton n faclty locaton problems n whch potental nvestors are n competton over acqurng sutable stes and clents s studed n []. An acceptance threshold constrant s appled to faclty allocaton that s based on a combnaton of dstance between a faclty and clents, and nvestors product prces. PROBLEM DESCRIPTION The problem consdered n the paper s a two level supply chan network nvolvng multple demand ponts and two frms that have ther own warehouses. Each frm tres to expand ts dstrbuton network by openng new stores. The objectve for both frms s to have addtonal market shares. Each frm n our paper faces demand from customers. In our problem, t s assumed that one of the two frms already has stores that are open to the market. The problem for every frm s to determne the exact locaton of the stores that wll open. Then, these stores wll have to supply a set of demand ponts. Smlarly, we wll have to determne for each store ts warehouse that wll supply t. Thus, the objectve s to determne a dstrbuton network that wll provde maxmum proft on the market. Modelng problem In ths secton, we wll formulate the Capactated locatonallocaton problem n a compettve envronment for a two level dstrbuton Network. Indeed, t s a more realstc model than the model TLCLAP [2]. The problem s consdered as localzaton game that s played between two players (frms) who want to locate stores among a predefned set of potental stes so as to satsfy demand ponts and maxmze proft. Formulaton Now we defne the notaton used n: Number of potental stes 335
3 m: Number of frm pre-exstng opened stores N: Number of demand ponts : Index of potental stes : {,2,.., n} j: Index of demand ponts j = {,2,.., N} f: Index of frms f = {,2} w j : Demand quantty expected by ste from demand pont j C f : Transportaton cost pad by frm f to supply stores from warehouses Pr f : The prce fxed by the frm f F f : Fxed cost assocated wth frm f for openng a store at ste Γ f : Capacty avalable of store, estmated by a frm f. A j : Attractveness of demand pont j wth respect to store Decson varables: f X j : Bnary varable ndcatng whether demand pont j s assgned to store of frm f Z f : Bnary varable ndcatng whether store s opened by frm f Prce polcy s not defned by frms. We may consder that we are dealng wth a factory prce polcy [3]snce the prce n each locaton s fxed and the customers nsure ther own transport. The prce s ndependent of the chosen stes and s set by each frm. The fact that customers provde ther own transport justfes the fact that demand wll not ncrease wth dstance, and customers of a demand pont wll tend to frequent the store wth greater attractveness. Smlarly, t s assumed that both frms have the same Transportaton costng product from warehouses to ther stores. For smplcty, ths cost s assumed to be fxed. As a game, we consder certan rules of the game. These rules are defned as follows: - The pre-establshed stores of frm reman open; - Whenever the two frms decde to locate a servce on a gven ste, only frm s able to do so. Thus, co-locaton s forbdden. Ths can be wrtten as follows: Z =(-Z 2 ); - A customer belongng to a demand pont j wll be served by a store wth more attractveness. Ths can be wrtten as follows: f X j = { Z f f A j A kj 0 otherwse Frm decdes to open exactly p stores, ths s expressed by the equaton: n Z = p It can also be seen that the total cost of openng stores can be wrtten as follows: φ(z, Z 2 n ) = F Z To explan the problem, we defne the proft equatons for each frm. Ths proft corresponds to the dfference between the revenues and operatng cost of each frm. Takng the case of frm, we have ts charge whch corresponds to the Transportaton costng the total quantty of products between an open node j and warehouse and the cost of openng node j. Moreover, the frm's total revenue corresponds to the product of the quanttes and prces appled by the frm. The proft formula s gven as follow: π (σ, σ 2 ) = (Pr C ) N j n+m w j X j n F Z Wth σ and σ 2 are the locaton and allocaton strateges respectvely for frm and frm 2. Thus, σ can be expressed as a par (X j, Z ) and σ 2 can be expressed as a par (X 2 j, Z 2 ). For frm 2, ts proft equaton s as follows: π 2 (σ, σ 2 ) = (Pr 2 C 2 ) w j N j n 2 X j n 2 F 2 Z In the context of a game of Nash, σ, σ 2 are actons for frm and frm 2, respectvely, whch we wll call player and player 2. These actons concern store locatons and ther assgnments to a set of demand ponts. We want to make predctons about the outcome of the game. In some cases we wll be able to fnd an acton for each player so that each player's acton s the best response to the other's acton. Ths means that even f one player can guess the other's acton, he wll not be able to change hs chosen acton, and ths s vald for both players. Calculatng Nash Equlbrum Nash's theorem guarantees the exstence of a Nash equlbrum, possbly nvolvng mxed strateges for one or both actors, n each non-cooperatve fnte set such as the one consdered n ths paper. Moreover, t s mportant to note that, gven the strateges, we do not assume that frms choose a random acton, but only that the acton of each frm can be seen as random by the other frm [4]. Based on the approach adopted by [5], a Nash equlbrum s calculated for the game. Thus, an algorthm based on the best 336
4 responses of each player to the strategy of the other. Let σ t and σ 2 t be the vectors of strategy such that σ t s strategy t taken by the frm and σ 2 t by the frm 2. To smplfy the mplementaton of the algorthm, we assume that we wll start wth the localzaton. Snce we consder that the game s played smultaneously we suppose that the Player always has the prvlege of startng the game. Ths player starts by choosng, randomly, a locaton strategy σ. Then, t wll have to buld ts dstrbuton network by: - Assgn to each open ste a set of demand ponts so as to respect the capacty constrant; - Assgn to each open ste ts supply warehouse The second player looks for the best response for the strategyσ. We note ths strategy σ 2. Player 2 have also to buld hs network dstrbuton wth the same procedure adopted by player. Faced wth ths strategy, player must fnd the best response that wll be noted by σ 2. The game contnues, untl we fnd the Nash equlbrum. To better understand how ths game wll enable us to seek the resoluton of the problem, we present the matrx payoff as follows: Frm Frm2 σ σ 2 σ s sequence where all the demand ponts are satsfed (assgned to a frm). Algorthm : Locaton allocaton game progress Whle (t<s) t=, Strategy ( σ f t ) Best response to Strategy ( σ f t ) t=t+ End whle The strategy of a player conssts, frstly, to locate the stes and then to allocate them to the demand ponts and the warehouses. Suppose t s frm that wll start the game, then t wll choose p canddate stes to open. Ths choce s made randomly. Then, the frm wll try to allocate each selected ste. The algorthm s based on the method of fndng the demand ponts havng a good attractveness wth respect to the chosen ste. In addton, ths allocaton must take nto account the capacty parameter of the nstallaton. However, t can be noted that n the algorthm the assgnment of the stes to the warehouses was omtted. Ths s due to the fact that the transport cost s fxed for each frm whch wll change nothng n the calculaton of the proft. Algorthm 2 gves how a frm's strategy s constructed. Note that we have marked a frm by f, to say that t s possble to start the game ether by frm or frm 2. σ 2 π, π 2 π 2, π 2 π s, π 2 Algorthm 2: Gettng a strategy locaton allocaton.. σ 2 s π s, π 2 s Fgure : Matrx of game payoffs Where, π s = π ( σ s, σ 2 s ) and π 2 s = π 2 ( σ s, σ 2 s ) Moreover, by referrng to the work of (Godnho and Das 200), when one begns wth an acton n whch a gven player does not open any store, he tends to lead the algorthm to reach a balance whch slghtly benefts the other player. In order to avod ths bas, n computatonal experments we wll always apply the algorthm twce: The frst conssts n startng wth a zero acton for frm (e the acton n whch the frm does not open a store) and the second conssts of a null acton for frm 2. As we can see n algorthm, a sequence of actons s played. A player chooses hs strategy then the other player seeks the best response to ths strategy. The game contnues untl reachng the maxmum value S, whch corresponds to the Strategy ( σ f t ) Begn End Let E p be a set of p potental stes, E p {,2,.., n}; Frm f: Choose randomly E p For each k n E p do N Whle (Γ kf j= w kj X kj ) Begn for j= to N do If A kj s maxmal then f X kj = End End whle Return σ f t 337
5 Aganst the strategy of frm, frm 2 must also take ts strategy whch wll present the correct answer to that taken by frm. Indeed, the dea descrbed n ths paper conssts n maxmzng the proft of frm 2 by choosng stes wth a low ste establshment cost. Ths choce wll concern a set of canddates' stes whose cardnalty s r. Ths set corresponds to the stes to be opened by frm 2. Algorthm to get a best response to a strategy σ f t Algorthm : Best response to Strategy σ f t Begn Choose the potental stes for whch capacty s mnmal F f s mnmal Let E r be a set of r potental stes, E r {{,2,.., n} E p }; For each k n E r do Whle (Γ kf j= w kj X kj ) Begn N For each j n Not Selected demand pont {,.,N} f X kj = If A kj s maxmal then End End whle Return Br(σ f t ) End As ths game s n a strategc form, the payoff matrx, establshed by the strateges gven by the algorthms, provdes all necessary nformaton for fndng the Nash equlbrum. Algorthm : Nash equlbrum procedure Begn For t= to S For t2= to S If ( Br(σ t )= σ 2 t2 ) and ( Br(σ 2 t2 )= σ t ) End Then ( σ t, σ 2 t2 ) s a Nash equlbrum σ t, σ 2 t2 are the solutons for the problem PROBLEM RESOLUTION To allow the model to be used as a tool of analyss, we developed an algorthm whch solves several scenaros. It was then mplemented n a computer va a programmng language. Experments Desgn In order to provde better solutons for a good analyss, an Object-Orented Programmng approach was chosen. Indeed, we have defned several classes of objects that represent all the elements of the game. Whch are as follows : The Node class: It s used to manage node objects. It has all the propertes for a node: node type (stores, warehouse or request pont), node ndex, node setup cost f t s to be opened as a store, and fnally the capacty. In addton to the propertes, ths class also ncludes the method of retrevng the ndex from the node, snce the matrces related to the dstrbuton network requre t. The Network class: It s used to manage the dstrbuton network. It contans all the propertes relatng to a network: the lst of objects of the node class, the number of nodes of the network, the matrx of requests for each node wth respect to another, the attractveness matrx for each node wth respect to another. In addton, two methods are mplemented: the method that allows to know the state of a node durng the course of a game, and the method of ntalzaton of the network. The latter conssts n creatng the network accordng to the number of fxed nodes, categorzng the nodes by type and nsertng logstc data of each node and defnng the nodes already opened by a gven frm. The Frms class: It allows to manage the frms that performs the allocaton locaton set. It ncludes all the propertes relatve to a player: The player's ndex, the prce he apples to the stores, the Transportaton costng the merchandse the network object representng the dstrbuton network of each frm, the lst of the stes to be opened and the assgnment matrx of each node. As for the methods, ths class ncludes two essental functons that are to locate and allocate. The Games class: Ths object class s used to manage the game. Ths class s responsble for generatng the game nstances related to stores to be opened by a frm, the number of nodes, logstcs cost lmts to allow generaton of random values. Consequently, t mplements the algorthm, and makes t possble to recover the results of each game. Smlarly, ths class allows you to calculate the profts for each player n a gven experment of the game. Instantaton of the problem The procedure for generatng each problem nstance runs as follows: A gven number of canddate stes are chooses among the nodes of the network. Ths choce s made accordng to the 338
6 capacty of each ste. Thus, only those nodes wth a large capacty are retaned. Ths crteron allows to satsfy as much as possble the capacty constrant. A frm defnes the number of stes to open. Through a random functon, we choose arbtrarly, among the canddate stes, those to be opened for each frm. For allocaton, a ste s assgned to a node wth the greatest attractveness. Ths operaton s repeated untl the maxmum of the network s covered. Program sequence The program was mplemented wth "C #" language, on a 2.53 Intel 5 machne wth 4 GB of RAM. A random functon was used to generate the problem nstances. Durng the ntalzaton phase,we defne the global logstc network wth the nodes and the dfferent logstc parameters, we create the players through ther parameters, and then the game starts wth an arbtrary chosen player. He performs two operatons: selectng stes to open and allocatng each ste to demand ponts. The other player performs the same approach untl fndng the best response to the choces made by the frst player. Numercal tests We conducted numercal tests to evaluate the relevance of the chosen approach to determne the equlbrum of the game. We start by the nstantaton of the tests objects. Indeed, a set of nstances based on a dstrbuton network has been generated n a random manner that nclude the number m and n. Those data are related to potental stes, logstcs values, warehouse locatons and demand ponts. Smlarly, an attractveness value has been assgned for each potental ste wth respect the nodes. Furthermore, n order to evaluate the varaton of the results accordng to partcular parameters of the problem, we defned 9 sets of experments. Each set ncludes nstances. On the other hand, because the objectve of the problem presented s to look for the localzaton and allocaton Table contans the results obtaned for the case of the scenaro. We note that n all the strateges consdered for frm, proft s always lower than that of frm 2. Ths s explaned by the number of open nodes. Indeed, ncreasng the number of stes to be opened for frm 2 enhance ts proft advantage over that of frm even f the preferental advantage has been granted to frm. Ths experment has been repeated several tmes and a proft rato of less than s solutons n the case of competton, we wll then consder how to look for possble Nash equlbrum. For ths purpose, we wll consder nstances of small sze so that we can use a smple algorthm wthout facng the constrant of the executon tme. Therefore, we defned a network wth 200 nodes. For each experment, we retans the proft of the frm and the proft of the frm 2 whch corresponds to the best response to the strategy of locaton and allocaton of the frm. We wll also be nterested n the relatve advantage of the Frm on frm 2, whch we measure as the rato between the two profts. To better analyze the establshed model, we have assumed 5 scenaros whch are as follows: Scenaro : Both frms opt for the same prce and the same freght cost. Frm opens p stores and frm 2 opens r stores wth p r 0,25; Scenaro 2: Both frms opt for the same prce and for the same freght cost. Frm opens p stores and frm 2 opens r stores wth 0,75 p r ; Scenaro 3: Frm 2 adopts a double prce compared to frm. Frm opens p stores and frm 2 opens r stores wth 0,75 p r ; Scenaro 4: Frm 2 whch adopted a double prce compared to frm. Frm opens p magaznes and frm 2 opens r magaznes wth 0,75 r p ; Scenaro 5: Frm 2 apples the same prce as frm. Frm opens p magaznes and frm 2 opens r magaznes wth 0,75 p wth advantage to frm 2. r Results and analyss In ths secton, we wll analyze the results obtaned through the varous pre-establshed scenaros n order to seek not only the solutons of the problem but also to examne the mpact of the mportant parameters defnng the problem. Thus, we wll study the mpact of the number of stores to be opened and the prces appled n the frms dstrbuton network. always obtaned and the average of the proft ratos always approxmates to 0.2. In Table 2, a smlar experence to that of scenaro was carred out except that ths tme we assgn 6 stes to be opened by frm and 8 stes by frm 2. It s noted that Always frm 2 has a compettve advantage snce only for strateges 4 and 8 t s surpassed by frm. In addton, there s always an average proft rato of
7 Table : Scenaro results Strateges - Number of stes to be opened: (Frm: 2, Frm2: 0) - Transportaton cost: (Frm: 200, Frm2: 200) - Appled Prce: (Frm: 42, Frm2: 42) Proft Frm Proft best response Frm 2 Proft/Proft2 220, , , , , , , , , , ,2853 0, , , , , , , , ,2702 0, , , , , , , , , , , , , , , , , , , , ,5587 0, , , , , , , , , , , ,7666 0, , ,6523 0, Strateges Table 2: Scenaro 2 results - Number of stes to be opened: (Frm: 6, Frm2: 8) - Transportaton cost: (Frm: 200, Frm2: 200) - Appled Prce: (Frm: 42, Frm2: 42) Proft Frm Proft best response Frm 2 Proft/Proft2 3037, ,734 0, , , , , ,3264 0, , ,864, , , ,
8 , ,6996 0, , , , , , , , ,8938 0, , ,9054 0, , , , , , , , ,0409 0, , , , , ,3439, , , , , ,8492 0, , ,6785 0, , ,2935 0, In Experment 3, the objectve s to see the mpact of prce on equlbrum. Values gven n Table 3 ndcate that the prce has a certan mpact on the proft of the frms. As shown n ths table, the frm 2 whch has adopted a double prce compared to frm have a hgh proft for all strateges. But lookng at the prevous experments ths polcy wll be n van n case the frm adjusts ts opened nodes number. It s nterestng to study ths case and analyze the mpact of approprate number of nodes to reach a game equlbrum aganst a hgh prcng polcy of the compettor. To confrm the remark rased n scenaro 3, we conducted an experment n whch we keep the same assumptons as the prevous scenaro, except for the number of magaznes to open ( Table 2).. Indeed, we opted for 80 stores for frm wth a low prce compared to that of frm 2. We note that n strateges 8 and 3, the gan of frm s clearly hgher than that of the frm 2. Smlarly, t has been observed that, on average, the proft rato s close to Ths means that aganst an unfavorable prce polcy, t s possble to revew the number of stores to reverse the stuaton to ts beneft and reach equlbrum of close profts. In ths way, the stes to open are qualfed as a best strategy for a frm to deal wth unfar prcng polcy of compettors. Table 3: Scenaro 3 results Strateges - Number of stes to be opened: (Frm: 80, Frm2: 40) - Transportaton cost: (Frm: 200, Frm2: 200) - Appled Prce: (Frm: 400, Frm2: 800) Proft Frm Proft best response Frm 2 Proft/Proft2 4350, ,88 0, , ,977 0, , ,237 0, , ,827 0, , ,3729 0,
9 , ,464 0, , ,5785 0, , ,6757 0, , ,462 0, , ,842 0, , , , , ,79 0, , ,28 0, , ,008 0, , ,546 0, , ,6229 0, , ,2352 0, , ,543 0, , , , In Scenaro 5, t s assumed that both frms decde to open the same number of stores, to use the same prce, and they have the same transport cost. Table 5, shows the results obtaned for ths scenaro. It can be noted that the frm always has the advantage and t has a consderable gan compared to the frm 2. Thus, the frm 2 has no nterest n keepng the same prces as those appled by the frm, or to downsze the number of opened stores compared to the compettor frm. Table 4: Scenaro 4 results Strateges - Number of stes to be opened: (Frm: 80, Frm2: 40) - Transportaton cost: (Frm :200, Frm2 :200) - Appled Prce: (Frm : 400, Frm2 : 800) Proft Frm Proft best response Frm 2 Proft/Proft , ,0470 0, , ,9657 0, , , , , , , , , , , ,687 0, , ,72382, , ,6238, , , , , , , , ,9922 0, , , , , ,67786, , ,3255 0,
10 , ,4086 0, , ,7643 0, , , , , ,9978 0, , , , Strateges Table 5: Scenaro5 results - Number of stes to be opened: (Frm: 35, Frm2: 40) - Transportaton cost: (Frme :200, Frme2 :200) - Appled Prce: (Frme : 400, Frme2 : 400) Proft Frm Proft best response Frm 2 Proft/Proft , ,50483, , ,0294, , ,2233, , ,70393, , ,6295, , ,8603, , ,62397, , ,424, , ,94388, , ,96873, , ,0049, , ,0462, , ,65835, , ,00393, , ,58845, , ,06476, , ,99899, , ,39079, , ,2559, It should be ponted out that besde the studed scenaros; we analyze through other experments the mpact of transport costs n the frst level of the dstrbuton network. It appears that ths parameter has lttle mpact on the profts of frms n relaton to the prce and the number of stes to be opened. As a matter of fact, n a problem of locaton allocaton n a compettve envronment, the prce to apply remans an mportant parameter that gves a real compettve advantage. Nevertheless, ths parameter must be studed accordng to the number of stores to be opened by the compettor. But n realty, ths number depends closely on the nvestment budget of the frm. Ths budgetary constrant lmts the leeway of frms n settng the number of stores to open. Therefore, emphass should be placed on the prcng polcy to be adopted. 343
11 CONCLUSION The model we have developed deals wth the problem of localzaton of new stores and proposes a modelng of the dstrbuton network, an enumeraton of the parameters and logstc constrants lnked to the dstrbuton actvty as well as a resoluton approach by the game theory. The purpose s to determne the optmal locaton of the extensons to operate on the dstrbuton network that leads to a mnmzaton of the overall cost. The choce of locaton n an exstng dstrbuton network obvously takes n account a customer demand and servce objectves n the relevant geographcal area and t s concerned also by nternal and external logstcs and techncal parameters related to competton. The resoluton of the model requres an analyss of the locaton and allocaton strategy. Thus, face to a strategy of a gven frm, the compettor must develop the best response that lead to the Nash equlbrum of the game. Ths model, whch can be used to search for nvestment opportuntes n optmal areas, also proposes an analyss of the commercal actvty and the detecton of geographcal locaton possbltes, based on logstc performance crtera derved from the strategy of the company and takng nto account those of the compettors. The game theory used for ths problem takes nto account nteractons wth stores through the attractveness parameter whch has an mportant role n any locaton and allocaton strategy. However, ths work can be mproved n the future by other work ncludng the selecton of other specfc parameters, testng for large problems and comparson of results wth other methods wthn the spatal approach. REFERENCES [] H. Hotellng, Stablty n competton, Econ. J., vol. 39, no. 53, pp. 4 57, 929. [2] M. B. Tetz, Locatonal strateges for compettve systems, J. Reg. Sc., vol. 8, no. 2, pp , 968. [3] D. L. Huff, Defnng and estmatng a tradng area, J. Mark., pp , 964. [4] X. Martnez-Gralt and D. J. Neven, Can prce competton domnate market segmentaton?, J. Ind. Econ., pp , 988. [5] H. A. Eselt and G. Laporte, EQUILmRIUM RESULTS IN COMPETITIVE LOCATION MODELS, 996. [6] N. Sadan, F. Chu, and H. Chen, Compettve faclty locaton and desgn wth reactons of compettors already n the market, Eur. J. Oper. Res., vol. 29, no., pp. 9 7, 202. [7] J. Vogel, Servce Management:Strategc Servce Innovaton Management n Retalng. Sprnger New York, 202, pp [8] Ó. González-Bento, P. A. Muñoz-Gallego, and P. K. Kopalle, Asymmetrc competton n retal store formats: Evaluatng nter- and ntra-format spatal effects, J. Retal., vol. 8, no., pp , [9] H. Von Stackelberg, The theory of the market economy. Oxford Unversty Press, 952. [0] M. B. Tetz and P. Bart, Heurstc methods for estmatng the generalzed vertex medan of a weghted graph, Oper. Res., vol. 6, no. 5, pp , 968. [] M. Rohannejad, H. Navd, B. V. Nour, and R. Kamranrad, A new approach to cooperatve competton n faclty locaton problems: Mathematcal formulatons and an approxmaton algorthm, Comput. Oper. Res., vol. 83, pp , 207. [2] A. AIT BASSOU, M. Hlyal, A. Soulh, and J. El Alam, New varable neghborhood search method for a two level capactated locaton allocaton problem, J. Theor. Appl. Inf. Technol., vol. 83, no. 3, p. 442, 206. [3] H. A. Eselt, Equlbra n compettve locaton models, n Foundatons of locaton analyss, Sprnger, 20, pp [4] R. Gbbons, A prmer n game theory. Harvester Wheatsheaf, 992. [5] R. Porter, E. Nudelman, and Y. Shoham, Smple search methods for fndng a Nash equlbrum, Games Econ. Behav., vol. 63, no. 2, pp ,
OPERATIONS RESEARCH. Game Theory
OPERATIONS RESEARCH Chapter 2 Game Theory Prof. Bbhas C. Gr Department of Mathematcs Jadavpur Unversty Kolkata, Inda Emal: bcgr.umath@gmal.com 1.0 Introducton Game theory was developed for decson makng
More informationA MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME
A MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME Vesna Radonć Đogatovć, Valentna Radočć Unversty of Belgrade Faculty of Transport and Traffc Engneerng Belgrade, Serba
More informationElements of Economic Analysis II Lecture VI: Industry Supply
Elements of Economc Analyss II Lecture VI: Industry Supply Ka Hao Yang 10/12/2017 In the prevous lecture, we analyzed the frm s supply decson usng a set of smple graphcal analyses. In fact, the dscusson
More informationPrice and Quantity Competition Revisited. Abstract
rce and uantty Competton Revsted X. Henry Wang Unversty of Mssour - Columba Abstract By enlargng the parameter space orgnally consdered by Sngh and Vves (984 to allow for a wder range of cost asymmetry,
More informationFlight Delays, Capacity Investment and Welfare under Air Transport Supply-demand Equilibrium
Flght Delays, Capacty Investment and Welfare under Ar Transport Supply-demand Equlbrum Bo Zou 1, Mark Hansen 2 1 Unversty of Illnos at Chcago 2 Unversty of Calforna at Berkeley 2 Total economc mpact of
More informationCyclic Scheduling in a Job shop with Multiple Assembly Firms
Proceedngs of the 0 Internatonal Conference on Industral Engneerng and Operatons Management Kuala Lumpur, Malaysa, January 4, 0 Cyclc Schedulng n a Job shop wth Multple Assembly Frms Tetsuya Kana and Koch
More information15-451/651: Design & Analysis of Algorithms January 22, 2019 Lecture #3: Amortized Analysis last changed: January 18, 2019
5-45/65: Desgn & Analyss of Algorthms January, 09 Lecture #3: Amortzed Analyss last changed: January 8, 09 Introducton In ths lecture we dscuss a useful form of analyss, called amortzed analyss, for problems
More informationIntroduction to game theory
Introducton to game theory Lectures n game theory ECON5210, Sprng 2009, Part 1 17.12.2008 G.B. Ashem, ECON5210-1 1 Overvew over lectures 1. Introducton to game theory 2. Modelng nteractve knowledge; equlbrum
More information- contrast so-called first-best outcome of Lindahl equilibrium with case of private provision through voluntary contributions of households
Prvate Provson - contrast so-called frst-best outcome of Lndahl equlbrum wth case of prvate provson through voluntary contrbutons of households - need to make an assumpton about how each household expects
More informationUNIVERSITY OF NOTTINGHAM
UNIVERSITY OF NOTTINGHAM SCHOOL OF ECONOMICS DISCUSSION PAPER 99/28 Welfare Analyss n a Cournot Game wth a Publc Good by Indraneel Dasgupta School of Economcs, Unversty of Nottngham, Nottngham NG7 2RD,
More informationLecture 7. We now use Brouwer s fixed point theorem to prove Nash s theorem.
Topcs on the Border of Economcs and Computaton December 11, 2005 Lecturer: Noam Nsan Lecture 7 Scrbe: Yoram Bachrach 1 Nash s Theorem We begn by provng Nash s Theorem about the exstance of a mxed strategy
More informationTests for Two Correlations
PASS Sample Sze Software Chapter 805 Tests for Two Correlatons Introducton The correlaton coeffcent (or correlaton), ρ, s a popular parameter for descrbng the strength of the assocaton between two varables.
More informationECE 586GT: Problem Set 2: Problems and Solutions Uniqueness of Nash equilibria, zero sum games, evolutionary dynamics
Unversty of Illnos Fall 08 ECE 586GT: Problem Set : Problems and Solutons Unqueness of Nash equlbra, zero sum games, evolutonary dynamcs Due: Tuesday, Sept. 5, at begnnng of class Readng: Course notes,
More informationCS 286r: Matching and Market Design Lecture 2 Combinatorial Markets, Walrasian Equilibrium, Tâtonnement
CS 286r: Matchng and Market Desgn Lecture 2 Combnatoral Markets, Walrasan Equlbrum, Tâtonnement Matchng and Money Recall: Last tme we descrbed the Hungaran Method for computng a maxmumweght bpartte matchng.
More informationQuiz on Deterministic part of course October 22, 2002
Engneerng ystems Analyss for Desgn Quz on Determnstc part of course October 22, 2002 Ths s a closed book exercse. You may use calculators Grade Tables There are 90 ponts possble for the regular test, or
More informationProblem Set 6 Finance 1,
Carnege Mellon Unversty Graduate School of Industral Admnstraton Chrs Telmer Wnter 2006 Problem Set 6 Fnance, 47-720. (representatve agent constructon) Consder the followng two-perod, two-agent economy.
More informationFacility Location Problem. Learning objectives. Antti Salonen Farzaneh Ahmadzadeh
Antt Salonen Farzaneh Ahmadzadeh 1 Faclty Locaton Problem The study of faclty locaton problems, also known as locaton analyss, s a branch of operatons research concerned wth the optmal placement of facltes
More informationPivot Points for CQG - Overview
Pvot Ponts for CQG - Overvew By Bran Bell Introducton Pvot ponts are a well-known technque used by floor traders to calculate ntraday support and resstance levels. Ths technque has been around for decades,
More informationInstituto de Engenharia de Sistemas e Computadores de Coimbra Institute of Systems Engineering and Computers INESC - Coimbra
Insttuto de Engenhara de Sstemas e Computadores de Combra Insttute of Systems Engneerng and Computers INESC - Combra Joana Das Can we really gnore tme n Smple Plant Locaton Problems? No. 7 2015 ISSN: 1645-2631
More informationreferences Chapters on game theory in Mas-Colell, Whinston and Green
Syllabus. Prelmnares. Role of game theory n economcs. Normal and extensve form of a game. Game-tree. Informaton partton. Perfect recall. Perfect and mperfect nformaton. Strategy.. Statc games of complete
More informationFinancial mathematics
Fnancal mathematcs Jean-Luc Bouchot jean-luc.bouchot@drexel.edu February 19, 2013 Warnng Ths s a work n progress. I can not ensure t to be mstake free at the moment. It s also lackng some nformaton. But
More informationScribe: Chris Berlind Date: Feb 1, 2010
CS/CNS/EE 253: Advanced Topcs n Machne Learnng Topc: Dealng wth Partal Feedback #2 Lecturer: Danel Golovn Scrbe: Chrs Berlnd Date: Feb 1, 2010 8.1 Revew In the prevous lecture we began lookng at algorthms
More informationLecture Note 2 Time Value of Money
Seg250 Management Prncples for Engneerng Managers Lecture ote 2 Tme Value of Money Department of Systems Engneerng and Engneerng Management The Chnese Unversty of Hong Kong Interest: The Cost of Money
More informationEvaluating Performance
5 Chapter Evaluatng Performance In Ths Chapter Dollar-Weghted Rate of Return Tme-Weghted Rate of Return Income Rate of Return Prncpal Rate of Return Daly Returns MPT Statstcs 5- Measurng Rates of Return
More informationChapter 10 Making Choices: The Method, MARR, and Multiple Attributes
Chapter 0 Makng Choces: The Method, MARR, and Multple Attrbutes INEN 303 Sergy Butenko Industral & Systems Engneerng Texas A&M Unversty Comparng Mutually Exclusve Alternatves by Dfferent Evaluaton Methods
More informationProblem Set #4 Solutions
4.0 Sprng 00 Page Problem Set #4 Solutons Problem : a) The extensve form of the game s as follows: (,) Inc. (-,-) Entrant (0,0) Inc (5,0) Usng backwards nducton, the ncumbent wll always set hgh prces,
More informationVolume 30, Issue 1. Partial privatization in price-setting mixed duopoly. Kazuhiro Ohnishi Institute for Basic Economic Science, Japan
Volume 3, Issue 1 Partal prvatzaton n prce-settng mxed duopoly Kazuhro Ohnsh Insttute for Basc Economc Scence, Japan Abstract Ths paper nvestgates a prce-settng mxed model nvolvng a prvate frm and a publc
More information/ Computational Genomics. Normalization
0-80 /02-70 Computatonal Genomcs Normalzaton Gene Expresson Analyss Model Computatonal nformaton fuson Bologcal regulatory networks Pattern Recognton Data Analyss clusterng, classfcaton normalzaton, mss.
More informationGlobal Optimization in Multi-Agent Models
Global Optmzaton n Mult-Agent Models John R. Brge R.R. McCormck School of Engneerng and Appled Scence Northwestern Unversty Jont work wth Chonawee Supatgat, Enron, and Rachel Zhang, Cornell 11/19/2004
More informationUnderstanding Annuities. Some Algebraic Terminology.
Understandng Annutes Ma 162 Sprng 2010 Ma 162 Sprng 2010 March 22, 2010 Some Algebrac Termnology We recall some terms and calculatons from elementary algebra A fnte sequence of numbers s a functon of natural
More informationCh Rival Pure private goods (most retail goods) Non-Rival Impure public goods (internet service)
h 7 1 Publc Goods o Rval goods: a good s rval f ts consumpton by one person precludes ts consumpton by another o Excludable goods: a good s excludable f you can reasonably prevent a person from consumng
More informationEconomic Design of Short-Run CSP-1 Plan Under Linear Inspection Cost
Tamkang Journal of Scence and Engneerng, Vol. 9, No 1, pp. 19 23 (2006) 19 Economc Desgn of Short-Run CSP-1 Plan Under Lnear Inspecton Cost Chung-Ho Chen 1 * and Chao-Yu Chou 2 1 Department of Industral
More informationChapter 5 Student Lecture Notes 5-1
Chapter 5 Student Lecture Notes 5-1 Basc Busness Statstcs (9 th Edton) Chapter 5 Some Important Dscrete Probablty Dstrbutons 004 Prentce-Hall, Inc. Chap 5-1 Chapter Topcs The Probablty Dstrbuton of a Dscrete
More informationPrivatization and government preference in an international Cournot triopoly
Fernanda A Ferrera Flávo Ferrera Prvatzaton and government preference n an nternatonal Cournot tropoly FERNANDA A FERREIRA and FLÁVIO FERREIRA Appled Management Research Unt (UNIAG School of Hosptalty
More information4: SPOT MARKET MODELS
4: SPOT MARKET MODELS INCREASING COMPETITION IN THE BRITISH ELECTRICITY SPOT MARKET Rchard Green (1996) - Journal of Industral Economcs, Vol. XLIV, No. 2 PEKKA SULAMAA The obect of the paper Dfferent polcy
More informationLeast Cost Strategies for Complying with New NOx Emissions Limits
Least Cost Strateges for Complyng wth New NOx Emssons Lmts Internatonal Assocaton for Energy Economcs New England Chapter Presented by Assef A. Zoban Tabors Caramans & Assocates Cambrdge, MA 02138 January
More informationA New Uniform-based Resource Constrained Total Project Float Measure (U-RCTPF) Roni Levi. Research & Engineering, Haifa, Israel
Management Studes, August 2014, Vol. 2, No. 8, 533-540 do: 10.17265/2328-2185/2014.08.005 D DAVID PUBLISHING A New Unform-based Resource Constraned Total Project Float Measure (U-RCTPF) Ron Lev Research
More informationAppendix - Normally Distributed Admissible Choices are Optimal
Appendx - Normally Dstrbuted Admssble Choces are Optmal James N. Bodurtha, Jr. McDonough School of Busness Georgetown Unversty and Q Shen Stafford Partners Aprl 994 latest revson September 00 Abstract
More informationTests for Two Ordered Categorical Variables
Chapter 253 Tests for Two Ordered Categorcal Varables Introducton Ths module computes power and sample sze for tests of ordered categorcal data such as Lkert scale data. Assumng proportonal odds, such
More informationMoney, Banking, and Financial Markets (Econ 353) Midterm Examination I June 27, Name Univ. Id #
Money, Bankng, and Fnancal Markets (Econ 353) Mdterm Examnaton I June 27, 2005 Name Unv. Id # Note: Each multple-choce queston s worth 4 ponts. Problems 20, 21, and 22 carry 10, 8, and 10 ponts, respectvely.
More informationWage-rise contract and endogenous timing in international mixed duopoly
Wage-rse contract and endogenous tmng n nternatonal med duopoly Kazuhro Ohnsh Osaka Unversty, Ph. D. July 007 Abstract The study of Matsumura (003) nvestgates a med duopoly model, where a domestc publc
More informationTCOM501 Networking: Theory & Fundamentals Final Examination Professor Yannis A. Korilis April 26, 2002
TO5 Networng: Theory & undamentals nal xamnaton Professor Yanns. orls prl, Problem [ ponts]: onsder a rng networ wth nodes,,,. In ths networ, a customer that completes servce at node exts the networ wth
More informationMgtOp 215 Chapter 13 Dr. Ahn
MgtOp 5 Chapter 3 Dr Ahn Consder two random varables X and Y wth,,, In order to study the relatonshp between the two random varables, we need a numercal measure that descrbes the relatonshp The covarance
More informationGames and Decisions. Part I: Basic Theorems. Contents. 1 Introduction. Jane Yuxin Wang. 1 Introduction 1. 2 Two-player Games 2
Games and Decsons Part I: Basc Theorems Jane Yuxn Wang Contents 1 Introducton 1 2 Two-player Games 2 2.1 Zero-sum Games................................ 3 2.1.1 Pure Strateges.............................
More informationOptimising a general repair kit problem with a service constraint
Optmsng a general repar kt problem wth a servce constrant Marco Bjvank 1, Ger Koole Department of Mathematcs, VU Unversty Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands Irs F.A. Vs Department
More informationOnline Appendix for Merger Review for Markets with Buyer Power
Onlne Appendx for Merger Revew for Markets wth Buyer Power Smon Loertscher Lesle M. Marx July 23, 2018 Introducton In ths appendx we extend the framework of Loertscher and Marx (forthcomng) to allow two
More informationMultifactor Term Structure Models
1 Multfactor Term Structure Models A. Lmtatons of One-Factor Models 1. Returns on bonds of all maturtes are perfectly correlated. 2. Term structure (and prces of every other dervatves) are unquely determned
More informationUniversity of Toronto November 9, 2006 ECO 209Y MACROECONOMIC THEORY. Term Test #1 L0101 L0201 L0401 L5101 MW MW 1-2 MW 2-3 W 6-8
Department of Economcs Prof. Gustavo Indart Unversty of Toronto November 9, 2006 SOLUTION ECO 209Y MACROECONOMIC THEORY Term Test #1 A LAST NAME FIRST NAME STUDENT NUMBER Crcle your secton of the course:
More informationUniversity of Toronto November 9, 2006 ECO 209Y MACROECONOMIC THEORY. Term Test #1 L0101 L0201 L0401 L5101 MW MW 1-2 MW 2-3 W 6-8
Department of Economcs Prof. Gustavo Indart Unversty of Toronto November 9, 2006 SOLUTION ECO 209Y MACROECONOMIC THEORY Term Test #1 C LAST NAME FIRST NAME STUDENT NUMBER Crcle your secton of the course:
More informationLinear Combinations of Random Variables and Sampling (100 points)
Economcs 30330: Statstcs for Economcs Problem Set 6 Unversty of Notre Dame Instructor: Julo Garín Sprng 2012 Lnear Combnatons of Random Varables and Samplng 100 ponts 1. Four-part problem. Go get some
More information3: Central Limit Theorem, Systematic Errors
3: Central Lmt Theorem, Systematc Errors 1 Errors 1.1 Central Lmt Theorem Ths theorem s of prme mportance when measurng physcal quanttes because usually the mperfectons n the measurements are due to several
More informationClearing Notice SIX x-clear Ltd
Clearng Notce SIX x-clear Ltd 1.0 Overvew Changes to margn and default fund model arrangements SIX x-clear ( x-clear ) s closely montorng the CCP envronment n Europe as well as the needs of ts Members.
More informationEquilibrium in Prediction Markets with Buyers and Sellers
Equlbrum n Predcton Markets wth Buyers and Sellers Shpra Agrawal Nmrod Megddo Benamn Armbruster Abstract Predcton markets wth buyers and sellers of contracts on multple outcomes are shown to have unque
More informationStochastic ALM models - General Methodology
Stochastc ALM models - General Methodology Stochastc ALM models are generally mplemented wthn separate modules: A stochastc scenaros generator (ESG) A cash-flow projecton tool (or ALM projecton) For projectng
More information5. Market Structure and International Trade. Consider the role of economies of scale and market structure in generating intra-industry trade.
Rose-Hulman Insttute of Technology GL458, Internatonal Trade & Globalzaton / K. Chrst 5. Market Structure and Internatonal Trade Learnng Objectves 5. Market Structure and Internatonal Trade Consder the
More informationThe Integration of the Israel Labour Force Survey with the National Insurance File
The Integraton of the Israel Labour Force Survey wth the Natonal Insurance Fle Natale SHLOMO Central Bureau of Statstcs Kanfey Nesharm St. 66, corner of Bach Street, Jerusalem Natales@cbs.gov.l Abstact:
More informationOptimal policy for FDI incentives: An auction theory approach
European Research Studes, Volume XII, Issue (3), 009 Optmal polcy for FDI ncentves: An aucton theory approach Abstract: Israel Lusk*, Mos Rosenbom** A multnatonal corporaton s (MNC) entry nto a host country
More informationAC : THE DIAGRAMMATIC AND MATHEMATICAL APPROACH OF PROJECT TIME-COST TRADEOFFS
AC 2008-1635: THE DIAGRAMMATIC AND MATHEMATICAL APPROACH OF PROJECT TIME-COST TRADEOFFS Kun-jung Hsu, Leader Unversty Amercan Socety for Engneerng Educaton, 2008 Page 13.1217.1 Ttle of the Paper: The Dagrammatc
More informationOptimal Service-Based Procurement with Heterogeneous Suppliers
Optmal Servce-Based Procurement wth Heterogeneous Supplers Ehsan Elah 1 Saf Benjaafar 2 Karen L. Donohue 3 1 College of Management, Unversty of Massachusetts, Boston, MA 02125 2 Industral & Systems Engneerng,
More informationEDC Introduction
.0 Introducton EDC3 In the last set of notes (EDC), we saw how to use penalty factors n solvng the EDC problem wth losses. In ths set of notes, we want to address two closely related ssues. What are, exactly,
More informationSolution of periodic review inventory model with general constrains
Soluton of perodc revew nventory model wth general constrans Soluton of perodc revew nventory model wth general constrans Prof Dr J Benkő SZIU Gödöllő Summary Reasons for presence of nventory (stock of
More informationMacroeconomic Theory and Policy
ECO 209 Macroeconomc Theory and Polcy Lecture 7: The Open Economy wth Fxed Exchange Rates Gustavo Indart Slde 1 Open Economy under Fxed Exchange Rates Let s consder an open economy wth no captal moblty
More informationMacroeconomic Theory and Policy
ECO 209 Macroeconomc Theory and Polcy Lecture 7: The Open Economy wth Fxed Exchange Rates Gustavo Indart Slde 1 Open Economy under Fxed Exchange Rates Let s consder an open economy wth no captal moblty
More informationISyE 512 Chapter 9. CUSUM and EWMA Control Charts. Instructor: Prof. Kaibo Liu. Department of Industrial and Systems Engineering UW-Madison
ISyE 512 hapter 9 USUM and EWMA ontrol harts Instructor: Prof. Kabo Lu Department of Industral and Systems Engneerng UW-Madson Emal: klu8@wsc.edu Offce: Room 317 (Mechancal Engneerng Buldng) ISyE 512 Instructor:
More informationAn Application of Alternative Weighting Matrix Collapsing Approaches for Improving Sample Estimates
Secton on Survey Research Methods An Applcaton of Alternatve Weghtng Matrx Collapsng Approaches for Improvng Sample Estmates Lnda Tompkns 1, Jay J. Km 2 1 Centers for Dsease Control and Preventon, atonal
More informationRaising Food Prices and Welfare Change: A Simple Calibration. Xiaohua Yu
Rasng Food Prces and Welfare Change: A Smple Calbraton Xaohua Yu Professor of Agrcultural Economcs Courant Research Centre Poverty, Equty and Growth Unversty of Göttngen CRC-PEG, Wlhelm-weber-Str. 2 3773
More informationLOCATION TAXI RANKS IN THE URBAN AGGLOMERATION
LOCATION TAXI RANKS IN THE URBAN AGGLOMERATION ABSTRACT Lokace stanovšť taxslužby v městské aglomerac Ing. Mchal Turek, Ph.D. College of Logstcs, Department of Logstcs and Techncal Dscplnes e-mal: mchal.turek@vslg.cz
More informationECO 209Y MACROECONOMIC THEORY AND POLICY LECTURE 8: THE OPEN ECONOMY WITH FIXED EXCHANGE RATES
ECO 209 MACROECONOMIC THEOR AND POLIC LECTURE 8: THE OPEN ECONOM WITH FIXED EXCHANGE RATES Gustavo Indart Slde 1 OPEN ECONOM UNDER FIXED EXCHANGE RATES Let s consder an open economy wth no captal moblty
More informationA DUAL EXTERIOR POINT SIMPLEX TYPE ALGORITHM FOR THE MINIMUM COST NETWORK FLOW PROBLEM
Yugoslav Journal of Operatons Research Vol 19 (2009), Number 1, 157-170 DOI:10.2298/YUJOR0901157G A DUAL EXTERIOR POINT SIMPLEX TYPE ALGORITHM FOR THE MINIMUM COST NETWORK FLOW PROBLEM George GERANIS Konstantnos
More informationBid-auction framework for microsimulation of location choice with endogenous real estate prices
Bd-aucton framework for mcrosmulaton of locaton choce wth endogenous real estate prces Rcardo Hurtuba Mchel Berlare Francsco Martínez Urbancs Termas de Chllán, Chle March 28 th 2012 Outlne 1) Motvaton
More informationREFINITIV INDICES PRIVATE EQUITY BUYOUT INDEX METHODOLOGY
REFINITIV INDICES PRIVATE EQUITY BUYOUT INDEX METHODOLOGY 1 Table of Contents INTRODUCTION 3 TR Prvate Equty Buyout Index 3 INDEX COMPOSITION 3 Sector Portfolos 4 Sector Weghtng 5 Index Rebalance 5 Index
More informationHighlights of the Macroprudential Report for June 2018
Hghlghts of the Macroprudental Report for June 2018 October 2018 FINANCIAL STABILITY DEPARTMENT Preface Bank of Jamaca frequently conducts assessments of the reslence and strength of the fnancal system.
More informationLikelihood Fits. Craig Blocker Brandeis August 23, 2004
Lkelhood Fts Crag Blocker Brandes August 23, 2004 Outlne I. What s the queston? II. Lkelhood Bascs III. Mathematcal Propertes IV. Uncertantes on Parameters V. Mscellaneous VI. Goodness of Ft VII. Comparson
More informationProceedings of the 2nd International Conference On Systems Engineering and Modeling (ICSEM-13)
Proceedngs of the 2nd Internatonal Conference On Systems Engneerng and Modelng (ICSEM-13) Research on the Proft Dstrbuton of Logstcs Company Strategc Allance Based on Shapley Value Huang Youfang 1, a,
More informationMathematical Thinking Exam 1 09 October 2017
Mathematcal Thnkng Exam 1 09 October 2017 Name: Instructons: Be sure to read each problem s drectons. Wrte clearly durng the exam and fully erase or mark out anythng you do not want graded. You may use
More informationRandom Variables. b 2.
Random Varables Generally the object of an nvestgators nterest s not necessarly the acton n the sample space but rather some functon of t. Techncally a real valued functon or mappng whose doman s the sample
More informationNetworks in Finance and Marketing I
Networks n Fnance and Marketng I Prof. Dr. Danng Hu Department of Informatcs Unversty of Zurch Nov 26th, 2012 Outlne n Introducton: Networks n Fnance n Stock Correlaton Networks n Stock Ownershp Networks
More informationProblems to be discussed at the 5 th seminar Suggested solutions
ECON4260 Behavoral Economcs Problems to be dscussed at the 5 th semnar Suggested solutons Problem 1 a) Consder an ultmatum game n whch the proposer gets, ntally, 100 NOK. Assume that both the proposer
More informationAnalysis of Variance and Design of Experiments-II
Analyss of Varance and Desgn of Experments-II MODULE VI LECTURE - 4 SPLIT-PLOT AND STRIP-PLOT DESIGNS Dr. Shalabh Department of Mathematcs & Statstcs Indan Insttute of Technology Kanpur An example to motvate
More informationStatic (or Simultaneous- Move) Games of Complete Information
Statc (or Smultaneous- Move) Games of Complete Informaton Nash Equlbrum Best Response Functon F. Valognes - Game Theory - Chp 3 Outlne of Statc Games of Complete Informaton Introducton to games Normal-form
More informationA Theory of Bilateral Oligopoly with Applications to Vertical Mergers
A Theory of Blateral Olgopoly wth Applcatons to Vertcal Mergers Kenneth Hendrcks UBC and Unversty of Texas and R. Preston McAfee Unversty of Texas Exxon Mobl Merger Refnng s concentrated n CA Retal Sales
More informationMeasures of Spread IQR and Deviation. For exam X, calculate the mean, median and mode. For exam Y, calculate the mean, median and mode.
Part 4 Measures of Spread IQR and Devaton In Part we learned how the three measures of center offer dfferent ways of provdng us wth a sngle representatve value for a data set. However, consder the followng
More informationCOS 511: Theoretical Machine Learning. Lecturer: Rob Schapire Lecture #21 Scribe: Lawrence Diao April 23, 2013
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #21 Scrbe: Lawrence Dao Aprl 23, 2013 1 On-Lne Log Loss To recap the end of the last lecture, we have the followng on-lne problem wth N
More informationSingle-Item Auctions. CS 234r: Markets for Networks and Crowds Lecture 4 Auctions, Mechanisms, and Welfare Maximization
CS 234r: Markets for Networks and Crowds Lecture 4 Auctons, Mechansms, and Welfare Maxmzaton Sngle-Item Auctons Suppose we have one or more tems to sell and a pool of potental buyers. How should we decde
More informationSpatial Variations in Covariates on Marriage and Marital Fertility: Geographically Weighted Regression Analyses in Japan
Spatal Varatons n Covarates on Marrage and Martal Fertlty: Geographcally Weghted Regresson Analyses n Japan Kenj Kamata (Natonal Insttute of Populaton and Socal Securty Research) Abstract (134) To understand
More informationFinance 402: Problem Set 1 Solutions
Fnance 402: Problem Set 1 Solutons Note: Where approprate, the fnal answer for each problem s gven n bold talcs for those not nterested n the dscusson of the soluton. 1. The annual coupon rate s 6%. A
More informationStochastic optimal day-ahead bid with physical future contracts
Introducton Stochastc optmal day-ahead bd wth physcal future contracts C. Corchero, F.J. Hereda Departament d Estadístca Investgacó Operatva Unverstat Poltècnca de Catalunya Ths work was supported by the
More informationApplications of Myerson s Lemma
Applcatons of Myerson s Lemma Professor Greenwald 28-2-7 We apply Myerson s lemma to solve the sngle-good aucton, and the generalzaton n whch there are k dentcal copes of the good. Our objectve s welfare
More informationISE High Income Index Methodology
ISE Hgh Income Index Methodology Index Descrpton The ISE Hgh Income Index s desgned to track the returns and ncome of the top 30 U.S lsted Closed-End Funds. Index Calculaton The ISE Hgh Income Index s
More informationII. Random Variables. Variable Types. Variables Map Outcomes to Numbers
II. Random Varables Random varables operate n much the same way as the outcomes or events n some arbtrary sample space the dstncton s that random varables are smply outcomes that are represented numercally.
More informationMacroeconomic equilibrium in the short run: the Money market
Macroeconomc equlbrum n the short run: the Money market 2013 1. The bg pcture Overvew Prevous lecture How can we explan short run fluctuatons n GDP? Key assumpton: stcky prces Equlbrum of the goods market
More informationPetroleum replenishment and routing problem with variable demands and time windows
Petroleum replenshment and routng problem wth varable demands and tme wndows Yan Cheng Hsu Jose L. Walteros Rajan Batta Department of Industral and Systems Engneerng, Unversty at Buffalo (SUNY) 34 Bell
More informationA Network Modeling Approach for the Optimization of Internet-Based Advertising Strategies and Pricing with a Quantitative Explanation of Two Paradoxes
A Network Modelng Approach or the Optmzaton o Internet-Based Advertsng Strateges and Prcng wth a Quanttatve Explanaton o Two Paradoxes Lan Zhao Department o Mathematcs and Computer Scences SUNY/College
More informationA Single-Product Inventory Model for Multiple Demand Classes 1
A Sngle-Product Inventory Model for Multple Demand Classes Hasan Arslan, 2 Stephen C. Graves, 3 and Thomas Roemer 4 March 5, 2005 Abstract We consder a sngle-product nventory system that serves multple
More informationSC Design Facility Location Sections 4.1, 4.2 Chapter 5 and 6
SC Desgn Faclty Locaton Sectons 4., 4.2 Chapter 5 and 6 Outlne Frequency decomposton of actvtes A strategc framework for faclty locaton Mult-echelon networks Analytcal methods for locaton 2 Frequency Decomposton
More informationMultiobjective De Novo Linear Programming *
Acta Unv. Palack. Olomuc., Fac. rer. nat., Mathematca 50, 2 (2011) 29 36 Multobjectve De Novo Lnear Programmng * Petr FIALA Unversty of Economcs, W. Churchll Sq. 4, Prague 3, Czech Republc e-mal: pfala@vse.cz
More informationNetwork Analytics in Finance
Network Analytcs n Fnance Prof. Dr. Danng Hu Department of Informatcs Unversty of Zurch Nov 14th, 2014 Outlne Introducton: Network Analytcs n Fnance Stock Correlaton Networks Stock Ownershp Networks Board
More informationNew Distance Measures on Dual Hesitant Fuzzy Sets and Their Application in Pattern Recognition
Journal of Artfcal Intellgence Practce (206) : 8-3 Clausus Scentfc Press, Canada New Dstance Measures on Dual Hestant Fuzzy Sets and Ther Applcaton n Pattern Recognton L Xn a, Zhang Xaohong* b College
More informationParallel Prefix addition
Marcelo Kryger Sudent ID 015629850 Parallel Prefx addton The parallel prefx adder presented next, performs the addton of two bnary numbers n tme of complexty O(log n) and lnear cost O(n). Lets notce the
More informationLecture Note 1: Foundations 1
Economcs 703 Advanced Mcroeconomcs Prof. Peter Cramton ecture Note : Foundatons Outlne A. Introducton and Examples B. Formal Treatment. Exstence of Nash Equlbrum. Exstence wthout uas-concavty 3. Perfect
More information