Supply 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 http://dx.doi.org/10.3926/jiem.613 - 188 - Supply chain disruption assessment based on the newsvendor model Yisong Li1, Xiaofei Chen 2, Lu Jia 3 1,3School of Economics and Management, Beijing Jiaotong University (China) 2 Department of Mechanical and Industrial Engineering, University of Toronto (Canada) [email protected], [email protected], [email protected] Received July 2012 Accepted December 2012 Abstract: Purpose: This paper focuses on supply chain disruption assessment. Design/methodology/approach: Newsvendor Model. Findings: As both cost and income principle will be taken into account in supply chain disruption assessment, we proposed in this paper: (1) the problem of supply chain disruption assessment is the trade-off problem. (2) the generic single period - newsvendor model can be used for capturing the critical point, which in tradition model stands for the demarcation point of profit but in this paper is the least costs considering disruption costs and expected revenues. Research limitations/implications: single period - newsvendor model. Practical implications: we give an example for test the effectiveness of this method. Originality/value: to research supply chain risk in a new approach, that is: supply chain risk has both cost and profit. So we can assess it with trade-off method. Keywords: supply chain disruption, risk assessment, newsvendor model. Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.613 - 189 - 1. Introduction Nowadays, facing the complicated and variable commercial environment as well as have been doing efforts in lean management for quicker response and lower cost, supply chain are tend to vulnerable and liable to affected by various risks. In order to managing the supply chain risk, the twin areas of risk identification and risk assessment are playing the basic and the most important part of the theoretical foundation and practical value field． Wakolbinger and Cruz (2009) summarized that the risks supply chain faced can be classified into two types: supply-demand coordination risks and disruption risks. Moreover, the disruption risks are the most vital and most notably type because the fact that disruption can bring about huge losses and prevention cost. Zhang (2011) emphasized disruptions and figured out that cost-income principle must be followed when build the fortification models, that is to say, the model concerned not only the cost of disruption, but also the expected cost of lost revenues. This paper aims at supply chain disruption assessment, analyzing two types of costs, which can be related to disruption risks. The two costs respectively stand for two kinds of attitudes towards risksrisk averse and risk appetite. Based on newsvendor model and its trade-off idea, the paper establishes one model can weigh the two costs, namely the two risk attitudes, and therefore get the optimal assessment solution. In the end, by means of the example, 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 supply chain, Manuj and Mentzer (2008) categorized the risk in supply chain by means of conducting an extensive literature review. They present a generic framework for the risk in global supply chains into the following broad classes: supply risks, operational risks, demand risks, security risks, macro risks, policy risks, competitive risks, and resource risks. This categorization highlights the generic business aspects of risk, and was widely accepted in the research of supply chain risk management (SCRM). The general approach of supply chain risk management (SCRM) starts with the identification of business objectives, and then links the performance goals with the risks. Ritchie and Brindley (2004) gives an example to shows that the identifying risk can lead to increasing its visibility in the performance evaluation process, and this can leads to risk minimization strategies that can contribute to performance gains. The identification of supply chain risk gives us a clue of assessment of the risk in a supply chain. Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.613 - 190 - In the assessment of the risk in a supply chain, Harland, Brenchley and Walker (2003). provided a standard formula for the quantitative definition of supply chain risk. That is: Risk = P x L (1) Where Risk is the assessment result; P means the probability or possibility; L means the loss of consequences. Now, most of the researches take two types variables (P and L) into consideration. The literature on assessment of the supply chain risk usually defines risk in purely negative terms, and leading to undesired results or consequences. Some model of SCRM are based on this aspect. Ding (2004) provided a fuzzy factor technique to evaluate risks; Ericsson developed 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 positive to the supply chain. Christopher (2006) gave an integrated definitions developed by others that “the management of supply chain risks through coordination or collaboration among the supply chain partners so to ensure profitability and continuity”. We can infer from the description that the objectives of supply chain risk management (SCRM) fall into two aspects: the one is to enhance profit, the other is to lower the disruptions existing supply chain. Moreover, to reduce the disruptions means must to pay more costs for precautions and controls in a supply chain, but at the same time, it also means that protect profit will ask costcontrol. The perspective of this view can be resulted in the tradeoff problem. 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 supply chain , and mostly assumed to be risk-neutral and insensitive to profit variations with the objective of expected profit maximization or expected cost minimization. Recently, the vulnerability and risks in the supply chains remind the managers of the tradeoff expected profit for downside protection against possible losses (Xu & Li, 2010). In this respect, Werner & Peter (2007, 2008, 2011) specially promoted 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 Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.613 - 191 - preferences, including, but not limited to, risk-averse and risk-seeking preferences. Besides, they also reviewed and directed the future research in newsvendor problem, modeled how the buyer’s risk profile moderates the newsvendor order quantity decision. Anastasios, Dimitrios and Eleftherios (2011) develop a newsvendor model for both risk neutral and risk-averse decision-makers and can be applicable for different types of disruptions related among others to the supply of raw materials, the production process, and the distribution system, as well as security breaches and natural disaster. To sum up, the new direction of SCRM and newsvendor problem will be of tradeoff value target and losses may resulting in. Risk attitude of decision-maker is also a crucial point to be regarded. 3. Newsvendor model for supply chain disruption assessment The idea of traditional newsvendor model is that: when the demand is Stochastic, the managers expect to achieve profit maximization or loss minimization by optimum order quantity. In fact, the order quantity is a ratio based on a “critical point”, which makes the optimal probability of target function. In addition, traditional newsvendor managers bear the risk neutral attitude towards the risks. There is the probabilities assessment in the evaluation of supply chain risks. No matter by means of qualitative expert evaluation method or quantitative methods emerging continuously in the academic circles, it is expected to make a best assessment of supply chain risks. By virtue of thought of newsvendor model, it is a feasible approach to get the risks assessment on the foundation of an optimal “critical point ratio” weighing against costs, and the target function is to make the risks prevention cost and risks response cost minimum. Besides, the weight of two costs, at the same time, is also the weight of two attitudes-risk averse and risk appetite. 3.1. Model foundation This model considers risks probability as a continuous variable. To assess the probability of a risk occurring, it introduces two types of costs to weigh against. That is called opportunity cost and disruption cost in this model. The former is the cost spends on preventing risks from happening, and the latter is the loss to response the consequences after risks occur. Assume a certain risk’s probability is stochastic and obeys a known distribution. Evaluate an occurrence probability of the risk is P. Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.613 - 192 -  If P is higher than the actual probability. That is to say, risk averse decision overestimates the risk giving rise to an overdone prevention and emergence action, which generates opportunity cost.  If P is lower than the actual probability. That is to say, risk appetite decision underestimates the risk binging about a potential disruption point in supply chains, which a liable to generate disruption cost. Assume a certain risk is named Ni. Its actual occurrence probability is r, obeying a distribution with density function ф(r), namely 0( ) 1 rr dr    (2) In one risk assessment process, its calculating probability is p. In order to get the optimal solution p*, define the two concerned cost in the first place. Opportunity Cost L When risks are overestimated (p≥r), opportunity cost happens and the loss is: (p - r)·L, so its expectation value is: 0·( ) ( ) pL p r r dr    (3) Disruption Cost C1 When risks are underestimated (p<r), disruption cost happens and its loss is: (r - p)·C1, so its expectation value is: 1( ) ( ) pC r p r dr    (4) 3.2. The optimal decision When a risk Ni and its calculated probability is p, combining the mentioned above(1) and(2), the total expectation losses are: 1 0 [ ( )] ( ) ( ) ( ) ( ) p p E C p L p r r dr C r p r dr        (5) Target function is min E[C(P)]. Here follows the differentiation method inference process of newsvendor model: Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.613 - 193 - When p is continuous variable, E[C(P)] is continuous function about p. 1 0 1 0 [ ( )] So, [ ( ) ( ) ( ) ( ) ] = ( ) ( ) p p p p dE C p d L p r r dr C r p r dr dp dp L r dr C r dr            (6) Let [ ( )]=0 dE C p dp (7) If 0 ( ) ( ) p r r dr   (8) Then 1( ) [1 ( )] 0L p C p      (9) and 1 1 () C pLC   (10) Therefore, p is solved from the arithmetic expression above, and be denoted as P*, then P* is the stationary point of E[C(P)]. And because 2 1 2 [ ( )] ( ) ( ) 0 d E C P L p C p dp     (11) It is clear that p* is the limited minimum point of E[C(P)], minimum point of the model. 3.3. Model analysis It can be inferred from the optimal decision: 1 * 1 () C pLC   (12) Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.613 - 194 - That the optimal assessment result towards some certain risks comprehensively affected by followings： Opportunity cost L This part of cost in reality reflects that manager is risk averse attitude, which means the loss of potential profits. Because of the averse of risk, manager takes vigorous prevention and emergence measures so as to be more defensive to disruptions in supply chain. Correspondingly, the overprotection needs more cost input, so the opportunity cost is come into being. This kind of cost is inversely proportional to the result p*. The higher some certain kinds of risks’ opportunity cost is, the lower their optimal assessment probability is. Disruption cost C1 When manager’s preference towards risk is risk appetite, the cost input to prevent risk from occurring is much more than the risk averse manager. But in contrast, there are more risk events happen, and can bring more disruption cost. The optimal risk assessment will be a tradeoff between the two types 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 2 () 2 1 ( ) , 2 , r re r           (13) Where is mean value, and  is standard deviation. 4. Example 4.1. Background and risks identification An enterprise wants to rebuild its supply chain network, in order to improve its performance and competitiveness. But as its limited resources and funds, it is necessary to evaluating the costs and benefits of each risk in its supply chain, and to rebuild the supply chain network from the most importance parts. Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.613 - 195 - Identification Details Symbol Supply risk lack of capacity N1 technology retardation N2 Poor credit N3 traffic inconvenience N4 natural disaster N5 Demand risk customer churn N6 lower prediction N7 demand fluctuations N8 Product risk manufacturing interrupt N9 product diversification N10 product substitution N11 stockpiling N12 Information risk system paralysis N13 communication outage N14 poor information N15 Finance risk exchange fluctuations N16 supplier bankruptcy N17 customer bankruptcy N18 Table 1. Supply Chain Risks Identification According to the identification of the supply chain risk, the enterprise classifies its risks into: supply risk, manufacture risk, demand risk, information risk and finance risk. Moreover, the enterprise analysis the above risks of supply chain in detail as the table 1. These are the factors of the supply chain network. The table 2 is parameters demonstration used in newsvendor model to assess supply chain disruption.identification Details Number Cost Profit Prevent cost Interrupt cost Risk obedient earnings Opportunity cost Supply risk lack of capacity N1 C01 C11 L01 L11 technology retardation N2 C02 C12 L02 L12 poor credit N3 C03 C13 L03 L13 traffic inconvenience N4 C04 C14 L04 L14 natural disaster N5 C05 C15 L05 L15 Demand risk customer churn N6 C06 C16 L06 L16 lower prediction N7 C07 C17 L07 L17 demand fluctuations N8 C08 C18 L08 L18 Product risk manufacturing interrupt N9 C09 C19 L09 L19 product diversification N10 C010 C110 L010 L110 product substitution N11 C011 C111 L011 L111 stockpiling N12 C012 C112 L012 L112 Information risk system paralysis N13 C013 C113 L013 L113 communication outage N14 C014 C114 L014 L114 poor information N15 C015 C115 L015 L115 Finance risk exchange fluctuations N16 C016 C116 L016 L116 supplier bankruptcy N17 C017 C117 L017 L117 customer bankruptcy N18 C018 C118 L018 L118 Table 2. Parameters Demonstration 4.2. The trade-off of the costs and profits We need evaluating the costs and profits according to the factors in table 1 of the Supply Chain Risks Identification, before we made trade-off analysis of the supply chain risk when rebuild the supply chain network. Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.613 - 196 - In the front of supply chain risk, manager must assess the probability of each factors and its cost, which are prevent cost and interrupt cost. And if manager is obedient to the supply chain risks, he can obtain revenue from it, which are risk obedient earnings and opportunity cost. When manager is obedient to the supply chain risk, he has to take risk of interrupt of supply chain. 4.3. Simulation Based on formula (12), we have： 1 0 1 0 1 () 2 ( ) C pC C L L      (14) For example of the N10, which is a factor of the supply chain risk, its cost and profit can be calculate from usual financial data. The prevent cost of N10 is 451800 RMB. The interrupt cost of N10 is 411100RMB. The risk obedient earnings of N10 is 26300RMB. The opportunity cost of N10 is 44900RMB. That is: C0=45.18, C1=41.11, L010=2.63, L110=4.49. Cost Profit Prevent cost Interrupt cost Risk obedient earnings Opportunity cost N10 45.18 41.11 2.63 4.49 Table 3. Parameters Demonstration of N10 So, we can calculate:  p*)=0.57 If P is subject to standard normal distribution, it can be seen that P * = 0.7157, this is the optimal evaluation to the risk of N10 by trade-off its cost and profit. Number Cost Profit Simulation results Prevent cost C0 Interrupt cost C1 Risk obedient earnings L0 Opportunity cost L1 N1 65.89 42.79 2.71 9.73 0.51 N2 27.47 57.99 1.59 8.71 0.89 N3 79.29 75.66 2.09 6.23 0.55 N4 53.28 63.45 7.16 8.34 0.74 N5 26.03 2.90 7.87 5.67 1.57 N6 98.02 1.45 5.10 0.66 0.02 N7 54.18 66.65 9.15 1.16 0.67 N8 58.07 14.35 1.52 5.44 0.25 N9 40.97 44.44 8.61 6.89 0.82 N10 97.80 55.38 7.94 2.58 0.42 N11 59.98 32.66 1.81 5.79 0.42 N12 62.97 27.96 1.33 7.22 0.38 N13 67.47 1.22 7.46 4.26 0.03 N14 12.02 11.41 1.21 2.61 0.72 N15 10.40 27.69 0.91 0.45 0.78 N16 68.34 33.09 9.18 6.06 0.47 N17 16.30 92.62 7.40 2.88 1.05 N18 40.31 33.71 2.69 9.59 0.68 Table 4. Calculation-result 1