Thi Le Hoa Vo, Daniel Thiel

Transcription

1 MITIGATING THE BULLWHIP EFFECT IN CASE OF CHAOTIC DEMAND Thi Le Hoa Vo, Daniel Thiel University of Nantes and E.N.I.T.I.A.A. Nantes, LEM LARGECIA Rue de la Géraudière BP 85 Nantes Cedex, France {thilehoa.vo, Abstract The Bullwhip Effect (BE) is an important phenomenon of demand oscillation and amplification causing inefficiencies in supply chain management. In this paper, we are interested in studying how to mitigate the BE when customer demand becomes chaotic. We will first of all present a system dynamics model to observe and analyse the BE through out the supply chain under chaotic demand. And then a sensitivity analysis will be realized to propose policies for moderating the BE in order to minimize the supply chain costs. We conclude by offering a deeper insight about the important role of feedback perception and lead time in the supply chain management. Keywords: Bullwhip Effect, chaotic demand, system dynamics. Introduction The Bullwhip Effect, one of the main causes of the production distribution supply chain inefficiency, is a phenomenon of order amplification resulted from the demand variability at each supply chain echelon (Lee et al., 997). This phenomenon is particularly brought forth by the inherent uncertainty in the system s operational environment such as the future demand uncertainty or the real lead time. It means that a small perturbation of the demand can bring about a «waterfall» exaggerated reaction at local level of inferior links and spread out the entire supply chain. It is worth to analyse this effect because it causes the following problems: In order to make up for the unpredictability of sale variation, the managers usually maintain amplified inventory levels. Even if the inventory levels are globally considerable in the entire supply chain, the problems of synchronisation between supply and demand at different stages sometime give rise to delivery issues. The BE amplifies not only the inventory levels but also logistics operating costs. In fact, there are lots of researches in the literature emphasizing on studying the BE in the supply chain and adjusting some important factors (demand pattern, lead time, time delay, demandinformation sharing, and ordering policy) to reduce this effect (Sterman, 989; Taylor, 999; Chen et al. 000; Shen, 00...) However, the application of these solutions for dealing with chaotic demand remains modest. In this paper, we are accordingly interested in studying how to reduce the BE when customer demand becomes chaotic. Our research objectives are: (i) to observe and analyse the BE through out the supply chain in case of chaotic demand, (ii) to propose policies to minimize the BE, and (iii) to provide a deeper insight of the important role of feedback perception and lead time in the supply chain management. Hence, we will firstly present a literature review of related works focusing on the BE analysis and some system dynamics applications in the BE. And then, we will use the system dynamics model of the Beer Game (Kirkwood, 00) basing on a simulation game developed in MIT: The Beer Distribution Game (BG) (Sterman, 989) to study the BE under a chaotic demand. Finally, a sensitivity analysis will be implemented allowing to define some adjustment policies to minimize the

2 MASHS 008, Créteil BE and the supply chain costs in this context. This paper will be concluded with some suggestions on the role of human behaviour in decisionmaking and lead time in supply chain management. Literature review. Bullwhip Effect In general, there are two principal BE causes: operational and behavioural causes. The operational causes can come from the structural characteristics of the supply chain that lead the rational agents to amplify the demand variability. For example, Lee et al. (997 divide these causes into four categories rising from different problems: demand forecasting updating, order batching, price fluctuations and rationing, shortage gaming. Chen et al. (000), SimchiLevi et al. (000) and Shen (00) also notice that independent local optimisation choices of each manager without global vision are one BE cause. The second category of behavioural causes introduced initially by Forrester (958, 96) and then detailed by Sterman (989) focuses on behavioural causes resulting in the instability of the supply chain. These causes principally come from rationality limits of the managers, in particular their blurred justification in feedback effects and their reaction delay. Additionally, there are other researches showing these cognitive restrictions (Croson and Donohue, 00). Moreover, Wu et al. (00) demonstrate that chaotic demand for liquid detergent exists at the interface of a manufacturer and its distributors. Kumara et al. (00) suggest that in a queuing model of supply chain logistics systems the behaviour of the system exhibits chaos. In addition, Lal and VillasBoas (998) show another type of chaotic demand caused by marketing and competition activities. In order to smooth out oscillations of the BE, it is required to understand what drives demand and supply patterns, information quality and cycle times compression. Among them, reducing demand variability is an efficient approach to reducing the BE as this variability causes the forecast error which in turn is the principal cause of the effect. On the other hand, shorter lead time not only reduce the BE, but also induce order smoothing by retailers. Supply chain lead time is made up of the delays in information processing and materials processing. MasonJones and Towill (000) refer this as two distinct lead time pipelines: the order information transfer pipeline, moving upstream from point of sale to raw material supplier and the product transfer downstream from raw material to customer. Longer lead times result in customer s replenishment planning systems raises, and usually, false demand for future supply coverage and demand variability is magnified (Sterman, 989, Steckel et al. 00). While decreasing the lead time between each level of the supply chain will aid in reducing the BE (Lee et al., 997; SimchiLevi et al. 000; de Treville et al., 00). The reduction of the overall supply chain lead time is treated with the utmost priority in contemporary supply chain management. This has resulted in rapid response manufacturing practices which are built on the concept of agile manufacturing seen as new dimension in SCM, often referred to as demand management.. BE system dynamics models Further to Forrester researches (958, 96) introducing the concept of BE, numerous recent publications are appeared. Sterman (989) suggests that the manager s insufficient understating of the supply chain dynamics and their nonoptimal order decisions will result in the BE. In order to improve this understanding, he proposes some solutions concerning feedback loops, time delays, and order policy. Lee et al. (997) find that the BE comes from the distortion of upstream and downstream demand information of the supply chain and the amplification of distortion variance. Hence, it is necessary to establish coordination within supply chain members by information flow of the production plan, stock control and delivery planning. Additionally, Anderson et al. (000) take into account demand forecasting, delivery delay reduction, and order and employment policies to avoid the amplification of demand volatility and its consequences on production, productivity, inventory and delivery delay. Chen et al. (000) or

3 Mitigating the Bullwhip Effect in case of Chaotic Demand Daganzo (005) focus on demandinformation sharing and demand forecasting to restrict the upstream amplification of the supply chain. Moreover, the excessive reaction to order backlog is also a BE cause (Oliva and Gonçalves, 006). To solve this problem, the authors propose using all available information of stock level and order backlog in order to have a global vision that allows a coherent estimation in decisionmaking processes. Model design In this section, we will show the Beer Game model (Sterman, 989) of the threeechelon supply chain inventories and flows realised in Ithink software: Producer (S 0 ), Supplier (S ), and Supplier (S ). In the following figure, the influence diagram represents the causal relations between different variables at each echelon of the supply chain. Stock supplier (S) Order S Order S Stock producer S0 Order backlog S Order backlog S Order S0 Order backlog S0 Production Stock supplier (S) Demand Figure. Stockflow Beer Game diagram On this diagram, the polarity of each arrow indicates the direction of change that a change in the cause induces in the effect. It demonstrates that the orders and the order backlog at each supply chain level increase when the demand increases because of production and delivery delays. It means that the final orders placed to the producer S 0 are significant higher than the ones in the supplier S. In the diagram, there are three control loops of homeostatic type. Following this representation, we build a simulation model that allows us to understand the supply chain dynamics. The figure represents the model structure of the supply chain. Dema nd Coef A Order Coef B S Coef A Smooth Coef B S Coef A S0 Order sent Order Order sent Order sent Order Order sent Supply Supply Supply Backlog rate S Cost Inventory Inventory Supply Supply Inventory Supply Sale rate Backlog Receipt Sale rate Receipt Backlog Sale rate Receipt Backlog Coef B Backlog rate S Backlog rate S0 Cos Inventory S0 Inventory S Inventory S Backlog Backlog Backlog Receipt Figure. The BG supply chain structure A positive sign indicates change in the same direction while a negative sign indicates change in the opposite direction.

4 MASHS 008, Créteil The simulation starts at time t = 0. Each group of players makes one decision of how many cases of beer to order and then delivery to the client each week. At each supply chain level, the inventory level at time t is presented by: Inventory(t) = Inventory (t dt) (Receipt_rate Sale_rate) * dt INIT Inventory = 00 And the order backlog level at time t is: Backlog(t) = Backlog(t dt) (Backlog_rate) * dt INIT Backlog = 0 In general, the order placed in the upstream supplier is: O(t) = max(0, D O (t)) Where D O (t) is the decided order rate based on three factors : The forecasting level: FL The gap between actual and desired inventory: AI The gap between actual and desired supply level: AS D O (t) = LI(t) AI(t) AD(t) It means that: D O (t) = Forecasting Actual inventory gap Actual shipment level gap Or Order_placed_S0 = MAX(0,SMTH(Order_sent_S,Smooth_time)Coef_A*(00(Inventory_S0 Backlog_S0)Coef_B*Supply_S0)) D O (t) = Forecasting Coef A*(00(Inventorybacklog)(t))Coef B*S(t) Where : S(t) : Actual shipment level gap: S(t) = S(t) O(t) i(t) Desired inventory: I * = 00 Coef A (stock adjustment parameter): the fraction of the discrepancy ordered each period. Coef B (supply line adjustment parameter): the fraction of the supply line taken into account by the deciders. The cumulative total cost of all the sectors of the supply chain includes backlog order cost ($/case) and inventory cost ($0.5/case), and is formulated: Cost (t) = Cost (t) (*(Backlog S Backlog S Backlog S0) 0.5 (Inventory S Inventory S Inventory S0))*dt INIT Cost = 0 We have realized the simulation in Ithink software with one period of time of 500 weeks. The chaotic demand (see figure ) is formulated basing on the following differential equation: dx = 0.75x [.x] with x(t=0) = Demand. Demand Order placed S Order placed S Order placed S Figure. Chaotic customer demand Figure. Order placed rates evolutions at each level of the supply chain

5 Mitigating the Bullwhip Effect in case of Chaotic Demand As we can see in this figure, the chaotic demand produces the chaos and BE at all stages of the supply chain. For example, at 7 th day, the demand is 9.05 beer cases but the order rate placed at Supplier S is.9 cases, at Supplier S is.5 cases, and at Producer S0 is.5 cases. At 5 st day, the demand decreases to 6.8 cases but the order placed at Supplier S remains.5 cases and at Producer S0 is 7.5 cases except the order placed at Supplier S is downed to 9.76 cases. The perturbation affected by the chaotic demand repeats all the simulation time and leads to an increase in the cumulative total cost for all sectors of $9, after 500 weeks as shown in the following figure: Costs Figure 5. The cumulative total cost of the supply chain Remark: We also examine our model by simulating the demand with Uniform Distribution law (U(min, max) = U(6.,.)) and Normal Distribution law (N(λ,σ) = N (9.,.5)) and then compare the simulation results with Chaotic Demand case (see Appendix.) The simulation will be run during 5,000 weeks and demonstrate that when the demand is varied following Uniform and Normal Distribution Laws, the system is stabilized and there is no BE after a period of time but this is not the case of Chaotic Demand. This can be explained that when the demand is uniformly or normally distributed, the supply chain deciders can be able to initiate change to adjust the orders in accordance with the demand variations. On the other hand, when the demand becomes chaotic, the supply chain turns to disturbed, having a chaotic behaviour, and cannot find itself the balance. Sensitivity analysis In this model, there are two important adjustment parameters and two time delays that significantly affect the system behaviour: Stock adjustment Supply line adjustment Order sent delay at each level Receipt delay at each level of the supply chain In order to study the role of these parameters in mitigating the BE and consequently reducing the supply chain cost, and to find out the best combination policy, we will implement a sensitivity analysis by varying the value of these parameters as shown below. At the first time, the value of one parameter will be varied while remaining the value of the others; we obtain some results as follows: Stock adjustment parameter (0<A ) Costs 7,57,686 9,765,79,70

6 MASHS 008, Créteil Supply line adjustment parameter(0<b ) Costs,86 9,765 9,9 9,7 0,08 Order sent delay at each level (days) Costs 5,9,59 9,765,797,87 Receipt delay at each level (days) Costs,0,509 9,765 6,5 7, The results show that there is no general trend for all the parameters to reduce the cost. For example, a small increase (from 0.05 to 0.5) in stock adjustment parameter can reduce the costs but a bigger increase (from 0.05 to 0.5) can augment the costs. There is the same movement for the other parameters. Therefore, we recognize that the system behaviour is really sensitive to the changes of these parameters. We then observe some combination between the four parameters values to point out the best adjustment policy for minimizing the cumulative costs. We found that when the value of stock adjustment parameter is 0.5, supply line adjustment parameter is 0.7, order sent delay is and receipt delay is, there are almost no BE and the cumulative costs are minimized to $5,76.5 as shown below: Demand Order placed S Order placed S Order placed S Figure 6. Mitigating the BE with the adjustment factors Figure 7. Decreasing in the cumulative total cost with the mitigated BE 5 Conclusion Basing on the simulation results, we recognize that a chaotic demand leads to a chaotic behaviour to all of the supply chain stages and this behaviour is extremely sensitive to the changes in adjustment factors. These adjustment factors can contribute to the amplification of the BE and the instability of the supply chain. However, one successful combination of the parameters values including more accurate perception of order and supply line information and shorter lead time of information and material can moderate the BE and reduce the total cost for the supply chain. This finding confirms the importance of human behaviour and lead time factors that need to be taken into account in the supply chain management.

7 Mitigating the Bullwhip Effect in case of Chaotic Demand Appendix Demand Order placed S Order placed S Order placed S Figure 8. Order placed rates evolutions at each level under Chaotic Demand Demand Order placed S Order placed S Order placed S Figure 9. Order placed rates evolutions at each level under Uniform Distribution Demand Order placed S Order placed S Order placed S Figure 0. Order placed rates evolutions at each level under Normal Distribution References [] Anderson, E.G.; Fine C.H.; and Parker G.G. (000). Upstream volatility in the supply chain: the machine tool industry as a case study, POMS Series in Technology and Operations Management, Teaching Supply Chain Management, USA, vol. 9, p. 96.

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