Supply chain disruption assessment based on the newsvendor model

Transcription

1 Journal of Industrial Engineering and Management JIEM, (1): Online ISSN: Print ISSN: htt://dx.doi.org/ /jiem.613 Suly chain disrution assessment based on the newsvendor model Yisong Li 1, Xiaofei Chen 2, Lu Jia 3 1,3 School of Economics and Management, Beijing Jiaotong University (China) 2 Deartment of Mechanical and Industrial Engineering, University of Toronto (Canada) ysli@bjtu.edu.cn, xiaofei.chen@utoronto.ca, @bjtu.edu.cn Received July 2012 Acceted December 2012 Abstract: Purose: This aer focuses on suly chain disrution assessment. Design/methodology/aroach: Newsvendor Model. Findings: As both cost and income rincile will be taken into account in suly chain disrution assessment, we roosed in this aer: (1) the roblem of suly chain disrution assessment is the trade-off roblem. (2) the generic single eriod - newsvendor model can be used for caturing the critical oint, which in tradition model stands for the demarcation oint of rofit but in this aer is the least costs considering disrution costs and exected revenues. Research limitations/imlications: single eriod - newsvendor model. Practical imlications: we give an examle for test the effectiveness of this method. Originality/value: to research suly chain risk in a new aroach, that is: suly chain risk has both cost and rofit. So we can assess it with trade-off method. Keywords: suly chain disrution, risk assessment, newsvendor model

2 1. Introduction Nowadays, facing the comlicated and variable commercial environment as well as have been doing efforts in lean management for quicker resonse and lower cost, suly chain are tend to vulnerable and liable to affected by various risks. In order to managing the suly chain risk, the twin areas of risk identification and risk assessment are laying the basic and the most imortant art of the theoretical foundation and ractical value field. Wakolbinger and Cruz (2009) summarized that the risks suly chain faced can be classified into two tyes: suly-demand coordination risks and disrution risks. Moreover, the disrution risks are the most vital and most notably tye because the fact that disrution can bring about huge losses and revention cost. Zhang (2011) emhasized disrutions and figured out that cost-income rincile must be followed when build the fortification models, that is to say, the model concerned not only the cost of disrution, but also the exected cost of lost revenues. This aer aims at suly chain disrution assessment, analyzing two tyes of costs, which can be related to disrution risks. The two costs resectively stand for two kinds of attitudes towards risks- risk averse and risk aetite. Based on newsvendor model and its trade-off idea, the aer establishes one model can weigh the two costs, namely the two risk attitudes, and therefore get the otimal assessment solution. In the end, by means of the examle, we can see that, it is useful to ranking risks concerning. 2. Literature Review As it is the foundation on assessment, a lot of literatures have focused on identifying the risks of suly chain, Manuj and Mentzer (2008) categorized the risk in suly chain by means of conducting an extensive literature review. They resent a generic framework for the risk in global suly chains into the following broad classes: suly risks, oerational risks, demand risks, security risks, macro risks, olicy risks, cometitive risks, and resource risks. This categorization highlights the generic business asects of risk, and was widely acceted in the research of suly chain risk management (SCRM). The general aroach of suly chain risk management (SCRM) starts with the identification of business objectives, and then links the erformance goals with the risks. Ritchie and Brindley (2004) gives an examle to shows that the identifying risk can lead to increasing its visibility in the erformance evaluation rocess, and this can leads to risk minimization strategies that can contribute to erformance gains. The identification of suly chain risk gives us a clue of assessment of the risk in a suly chain

3 In the assessment of the risk in a suly chain, Harland, Brenchley and Walker (2003). rovided a standard formula for the quantitative definition of suly chain risk. That is: Risk = P x L (1) Where Risk is the assessment result; P means the robability or ossibility; L means the loss of consequences. Now, most of the researches take two tyes variables (P and L) into consideration. The literature on assessment of the suly chain risk usually defines risk in urely negative terms, and leading to undesired results or consequences. Some model of SCRM are based on this asect. Ding (2004) rovided a fuzzy factor technique to evaluate risks; Ericsson develoed a series of tools named ERMET (Ericsson Risk Management Evaluation); Meng (2009) built an evaluation model based on grey relational analysis combining the fuzzy assessment. But, SCRM not only takes negative but also takes ositive to the suly chain. Christoher (2006) gave an integrated definitions develoed by others that the management of suly chain risks through coordination or collaboration among the suly chain artners so to ensure rofitability and continuity. We can infer from the descrition that the objectives of suly chain risk management (SCRM) fall into two asects: the one is to enhance rofit, the other is to lower the disrutions existing suly chain. Moreover, to reduce the disrutions means must to ay more costs for recautions and controls in a suly chain, but at the same time, it also means that rotect rofit will ask costcontrol. The ersective of this view can be resulted in the tradeoff roblem. And it leads to the new direction of taking the newsvendor model into account. Traditionally, newsvendor models is manly refer to the vendor of the suly chain, and mostly assumed to be risk-neutral and insensitive to rofit variations with the objective of exected rofit maximization or exected cost minimization. Recently, the vulnerability and risks in the suly chains remind the managers of the tradeoff exected rofit for downside rotection against ossible losses (Xu & Li, 2010). In this resect, Werner & Peter (2007, 2008, 2011) secially romoted this issues. They formulated the newsvendor model of the same kind that tradeoff between service level (target value) and resulting losses by the target. Qin, Wang, Vakharia, Chen and Seref (2011) enriched the theory by considering the attitude of decisionmaker towards the risks, devoted to the analysis newsvendor model with various risk

4 references, including, but not limited to, risk-averse and risk-seeking references. Besides, they also reviewed and directed the future research in newsvendor roblem, modeled how the buyer s risk rofile moderates the newsvendor order quantity decision. Anastasios, Dimitrios and Eleftherios (2011) develo a newsvendor model for both risk neutral and risk-averse decision-makers and can be alicable for different tyes of disrutions related among others to the suly of raw materials, the roduction rocess, and the distribution system, as well as security breaches and natural disaster. To sum u, the new direction of SCRM and newsvendor roblem will be of tradeoff value target and losses may resulting in. Risk attitude of decision-maker is also a crucial oint to be regarded. 3. Newsvendor model for suly chain disrution assessment The idea of traditional newsvendor model is that: when the demand is Stochastic, the managers exect to achieve rofit maximization or loss minimization by otimum order quantity. In fact, the order quantity is a ratio based on a critical oint, which makes the otimal robability of target function. In addition, traditional newsvendor managers bear the risk neutral attitude towards the risks. There is the robabilities assessment in the evaluation of suly chain risks. No matter by means of qualitative exert evaluation method or quantitative methods emerging continuously in the academic circles, it is exected to make a best assessment of suly chain risks. By virtue of thought of newsvendor model, it is a feasible aroach to get the risks assessment on the foundation of an otimal critical oint ratio weighing against costs, and the target function is to make the risks revention cost and risks resonse cost minimum. Besides, the weight of two costs, at the same time, is also the weight of two attitudes-risk averse and risk aetite Model foundation This model considers risks robability as a continuous variable. To assess the robability of a risk occurring, it introduces two tyes of costs to weigh against. That is called oortunity cost and disrution cost in this model. The former is the cost sends on reventing risks from haening, and the latter is the loss to resonse the consequences after risks occur. Assume a certain risk s robability is stochastic and obeys a known distribution. Evaluate an occurrence robability of the risk is P

5 If P is higher than the actual robability. That is to say, risk averse decision overestimates the risk giving rise to an overdone revention and emergence action, which generates oortunity cost. If P is lower than the actual robability. That is to say, risk aetite decision underestimates the risk binging about a otential disrution oint in suly chains, which a liable to generate disrution cost. Assume a certain risk is named N i. Its actual occurrence robability is r, obeying a distribution with density function ф(r), namely r ( r) dr 1 0 (2) In one risk assessment rocess, its calculating robability is. In order to get the otimal solution *, define the two concerned cost in the first lace. Oortunity Cost L When risks are overestimated ( r), oortunity cost haens and the loss is: ( - r) L, so its exectation value is: L r r dr ( ) ( ) 0 (3) Disrution Cost C 1 When risks are underestimated (<r), disrution cost haens and its loss is: (r - ) C 1, so its exectation value is: C 1( r ) ( r ) dr (4) 3.2. The otimal decision When a risk N i and its calculated robability is, combining the mentioned above(1) and(2), the total exectation losses are: [ ( )] ( ) ( ) 1 ( ) ( ) 0 (5) E C L r r dr C r r dr Target function is min E[C(P)]. Here follows the differentiation method inference rocess of newsvendor model:

6 When is continuous variable, E[C(P)] is continuous function about. de[ C( )] d L r r dr C r r dr d d So, [ ( ) ( ) 1 ( ) ( ) ] 0 = ( ) 1 ( ) 0 (6) L r dr C r dr Let de[ C( )] =0 d (7) If r dr 0 (8) ( r) ( ) Then L C ( ) 1 [1 ( )] 0 (9) and C 1 ( ) L C1 (10) Therefore, is solved from the arithmetic exression above, and be denoted as P*, then P* is the stationary oint of E[C(P)]. And because 2 d E C P [ ( )] L C 2 d ( ) 1( ) 0 (11) It is clear that * is the limited minimum oint of E[C(P)], minimum oint of the model Model analysis It can be inferred from the otimal decision: C * 1 ( ) L C1 (12)

7 That the otimal assessment result towards some certain risks comrehensively affected by followings: Oortunity cost L This art of cost in reality reflects that manager is risk averse attitude, which means the loss of otential rofits. Because of the averse of risk, manager takes vigorous revention and emergence measures so as to be more defensive to disrutions in suly chain. Corresondingly, the overrotection needs more cost inut, so the oortunity cost is come into being. This kind of cost is inversely roortional to the result *. The higher some certain kinds of risks oortunity cost is, the lower their otimal assessment robability is. Disrution cost C 1 When manager s reference towards risk is risk aetite, the cost inut to revent risk from occurring is much more than the risk averse manager. But in contrast, there are more risk events haen, and can bring more disrution cost. The otimal risk assessment will be a tradeoff between the two tyes of costs. Density function This is the general rule of the occurrence of risk. And generally normal distribution is the most universal used one. Its density function can be showed as following: 2 ( r ) ( r) e, 2 r, (13) Where is mean value, and is standard deviation. 4. Examle 4.1. Background and risks identification An enterrise wants to rebuild its suly chain network, in order to imrove its erformance and cometitiveness. But as its limited resources and funds, it is necessary to evaluating the costs and benefits of each risk in its suly chain, and to rebuild the suly chain network from the most imortance arts

8 Identification Details Symbol lack of caacity N 1 Suly risk technology retardation N 2 Poor credit N 3 traffic inconvenience N 4 natural disaster N 5 Demand risk customer churn N 6 lower rediction N 7 demand fluctuations N 8 manufacturing interrut N 9 Product risk roduct diversification N 10 roduct substitution N 11 stockiling N 12 Information risk system aralysis N 13 communication outage N 14 oor information N 15 Finance risk exchange fluctuations N 16 sulier bankrutcy N 17 customer bankrutcy N 18 Table 1. Suly Chain Risks Identification According to the identification of the suly chain risk, the enterrise classifies its risks into: suly risk, manufacture risk, demand risk, information risk and finance risk. Moreover, the enterrise analysis the above risks of suly chain in detail as the table 1. These are the factors of the suly chain network. The table 2 is arameters demonstration used in newsvendor model to assess suly chain disrution.identification Suly risk Demand risk Product risk Information risk Finance risk Details Number Prevent cost Cost Interrut cost Risk obedient earnings Profit Oortunity cost lack of caacity N 1 C 01 C 11 L 01 L 11 technology retardation N 2 C 02 C 12 L 02 L 12 oor credit N 3 C 03 C 13 L 03 L 13 traffic inconvenience N 4 C 04 C 14 L 04 L 14 natural disaster N 5 C 05 C 15 L 05 L 15 customer churn N 6 C 06 C 16 L 06 L 16 lower rediction N 7 C 07 C 17 L 07 L 17 demand fluctuations N 8 C 08 C 18 L 08 L 18 manufacturing interrut N 9 C 09 C 19 L 09 L 19 roduct diversification N 10 C 010 C 110 L 010 L 110 roduct substitution N 11 C 011 C 111 L 011 L 111 stockiling N 12 C 012 C 112 L 012 L 112 system aralysis N 13 C 013 C 113 L 013 L 113 communication outage N 14 C 014 C 114 L 014 L 114 oor information N 15 C 015 C 115 L 015 L 115 exchange fluctuations N 16 C 016 C 116 L 016 L 116 sulier bankrutcy N 17 C 017 C 117 L 017 L 117 customer bankrutcy N 18 C 018 C 118 L 018 L 118 Table 2. Parameters Demonstration 4.2. The trade-off of the costs and rofits We need evaluating the costs and rofits according to the factors in table 1 of the Suly Chain Risks Identification, before we made trade-off analysis of the suly chain risk when rebuild the suly chain network

9 In the front of suly chain risk, manager must assess the robability of each factors and its cost, which are revent cost and interrut cost. And if manager is obedient to the suly chain risks, he can obtain revenue from it, which are risk obedient earnings and oortunity cost. When manager is obedient to the suly chain risk, he has to take risk of interrut of suly chain Simulation Based on formula (12), we have: C1 ( ) C0 C1 2 ( L0 L1) (14) For examle of the N 10, which is a factor of the suly chain risk, its cost and rofit can be calculate from usual financial data. The revent cost of N 10 is RMB. The interrut cost of N 10 is RMB. The risk obedient earnings of N 10 is 26300RMB. The oortunity cost of N 10 is 44900RMB. That is: C 0=45.18, C 1=41.11, L 010=2.63, L 110=4.49. Cost Profit Prevent cost Interrut cost Risk obedient earnings Oortunity cost N Table 3. Parameters Demonstration of N 10 So, we can calculate: *)=0.57 If P is subject to standard normal distribution, it can be seen that P * = , this is the otimal evaluation to the risk of N 10 by trade-off its cost and rofit. Number Cost Profit Prevent cost C 0 Interrut cost C 1 Risk obedient earnings L 0 Oortunity cost L 1 Simulation results N N N N N N N N N N N N N N N N N N Table 4. Calculation-result

10 We can assignment to the 18 factors in table 2, those are from N 1 to N 18, with the same methods of N 10. And Hyothesis C 0, C 1~U[0,100], L 0, L 1~U[0,10]. Using RAND function for 3 times, the simulation results are in table 4, table 5 and table 6. Number Cost Profit Prevent cost C 0 Interrut cost C 1 Risk obedient earnings L 0 Oortunity cost L 1 Simulation results N N N N N N N N N N N N N N N N N N Table 5. Calculation-result 2 Number Cost Profit Prevent cost C 0 Interrut cost C 1 Risk obedient earnings L 0 Oortunity cost L 1 Simulation results N N N N N N N N N N N N N N N N N N Table 6. Calculation-result 3 5. Conclusions This aer builds a newsvendor model for suly chain disrution assessment, which alies the tradeoff idea of newsvendor to this model. This model considers both oortunity cost and disrution cost, between which is a cost-income rincile tradeoff. When a risk s assessment is higher than otimum, disrution cost will descend whereas oortunity cost ascend ; when the risk s assessment is lower than the otimal one, disrution cost will ascend while oortunity cost descend. Among which, the otimum is the critical oint deducted by the disrution assessment in newsvendor model. The critical oint can minimize the exectation loss of

11 these both costs. At the same time, the two cost stand for two oosite attitudes and references towards risks. Oortunity cost is on behalf of risk averse; disrution cost stand for risk aetite. That can extend the traditional risk neutral newsvendor. Simultaneously, this model can be also used to rank a series of risk events N i (i = 1, 2, 3 ) may haen in every link of a suly chain according to their imortance. Pi* can reresent the robability of risk Ni, whose exectation loss is the least one. Taking another look at it, the lower Pi* is, the more likely the risk event causing cost, the more attention should be aid, the more vital the risk event. In contrast, when P i* is lower, the risk event is not that imortant than the former. References Anastasios X., Dimitrios, V., & Eleftherios, I. (2012). Otimal newsvendor olicies for dualsouring suly chains: A disrution risk management framework. Comuters & Oerational Research, 39, htt://dx.doi.org/ /j.cor Christoher S.T. (2006). Persective in suly chain risk management. International Journal of Production Economics, 103, htt://dx.doi.org/ /j.ije Ding, W., Liu K., & He, G., (2003). Study on risk of suly chain. China Safety Science Journal, 13(4), Harland, C., Brenchley, R., & Walker, H. (2003). Risk in suly networks. Journal in Purchasing and Suly Management, 9(2), htt://dx.doi.org/ /s (03) Manuj, I., & Mentzer, J. (2008). Global suly chain risk management. Journal of Business Logistics, 29(1), htt://dx.doi.org/ /j tb00072.x Meng, K. (2009). Comrehensive grey fuzzy evaluation on research on suly chain risk based on. The Friend of the Head, 58(10). Qin, Y., Wang, R., Vakharia, A.J., Chen, Y., & Seref, M.M.H. (2011). The newsvendor roblem: Review and directions for future research. Euroean Journal of Oerational Research, 213, htt://dx.doi.org/ /j.ejor Ritchie, B., & Brindley, C. (2004). Risk characteristics of the suly chain-a contingency framework. Suly Chain Risk. Wakolbinger, T. & Cruz, J.M. (2011). Suly chain disrution risk management through strategic information acquisition and sharing and risk-sharing contracts. International Journal of Production Research, 49(13), htt://dx.doi.org/ /

12 Werner, J., & Peter K. (2011). Risk references of a news vendor with service and loss constraints. International Journal of Production Economics. Werner, J., & Peter, K. (2008). A newsvendor model with service and loss constraints. Jena Research Paers in Business and Economics. Werner. J., & Peter, K. (2007). Risk-averse and risk-taking newsvendors: A conditional exected value aroach. Review of Management Science, 1(1), htt://dx.doi.org/ /s Xu, M., & Li, J. (2010). Otimal decision when balancing exected rofit and confidention value-at-risk in newsvendor model. Journal of Systems Science & Comlexity, 23, htt://dx.doi.org/ /s y Zhang, S. (2011). Fortification models hedging disrution risks based on arborescent suly chain. Oerations research and managment science, 20(1), Journal of Industrial Engineering and Management, 2013 ( El artículo está con Reconocimiento-NoComercial 3.0 de Creative Commons. Puede coiarlo, distribuirlo y comunicarlo úblicamente siemre que cite a su autor y a Intangible Caital. No lo utilice ara fines comerciales. La licencia comleta se uede consultar en htt://creativecommons.org/licenses/by-nc/3.0/es/