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Towards coordination in robust supply networks
IFAC Conference on Manufacturing Modelling, IFAC Manufacturing IFAC Conference Conference on Manufacturing Modelling, Modelling, Management and on Control IFAC Conference on Manufacturing Modelling, Management and Control Management and Control June 28-30, 2016. Troyes, France Available online at www.sciencedirect.com Management and Control France June June 28-30, 28-30, 2016. 2016. Troyes, Troyes, France June 28-30, 2016. Troyes, France
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Towards robust Towards coordination coordination in robust supply supply in Towards coordination in robust supply networks networks networks
P´ eter Egri ∗∗∗ Botond K´ ad´ ar ∗∗∗ J´ ozsef V´ ancza ∗∗∗ P´ e ter Egri Botond K´ a d´ a rr ∗ J´ o zsef V´ a ncza ∗ P´ e ter Egri a d´ a J´ o zsef V´ a ∗ Botond K´ P´ eter Egri Botond K´ ad´ ar J´ ozsef V´ ancza ncza ∗ Fraunhofer Project Center for Production Management and ∗ ∗ Fraunhofer Project Center for Production Management and Project Center for Production Management and ∗ Fraunhofer Informatics, Institute for Computer Science and Control, Hungarian Fraunhofer Project for Production Management and Informatics, Institute for Center Computer Science and Control, Hungarian Informatics, Institute for Computer Science and Control, Hungarian Academy of Sciences, Kende u. 13-17, 1111 Budapest, Hungary Informatics, Institute forKende Computer Science and Control, Hungary Hungarian Academy of Sciences, u. 13-17, 1111 Budapest, Academy of Kende {egri,kadar,vancza}@sztaki.mta.hu) Academy (e-mail: of Sciences, Sciences, Kende u. u. 13-17, 13-17, 1111 1111 Budapest, Budapest, Hungary Hungary (e-mail: {egri,kadar,vancza}@sztaki.mta.hu) (e-mail: {egri,kadar,vancza}@sztaki.mta.hu) (e-mail: {egri,kadar,vancza}@sztaki.mta.hu) Abstract: Supply chains nowadays frequently face risks caused by increased environmental Abstract: Supply chains nowadays frequently face risks caused by increased environmental Abstract: Supply chains frequently risks by environmental volatility and performance inefficiency. In this face paper an caused integrated supply chain planning Abstract: Supply chains nowadays nowadays frequently face risks caused by increased increased environmental volatility and performance inefficiency. In this paper an integrated supply chain planning volatility and performance inefficiency. In this paper an integrated supply chain planning approach is suggested that combines the three aspects of optimisation, risk mitigation and volatility performance this aspects paper an supply planning approach and is suggested suggested that inefficiency. combines the theInthree three of integrated optimisation, risk chain mitigation and approach is that combines aspects of optimisation, risk mitigation and decentralisation. The goal ofcombines this paper isthree to outline theofresearch directions for industrially approach is suggested that the aspects optimisation, risk mitigation and decentralisation. The goal of this paper is to outline the research directions for industrially decentralisation. The goal of this paper is to outline the research directions for industrially relevant and applicable methods forpaper integrating robust and coordinated supply chain planning. decentralisation. The goal of this is to outline the research directions for industrially relevant and applicable methods for integrating robust and coordinated supply relevant and methods for robust coordinated supply chain chain planning. planning. relevant and applicable applicable methods forofintegrating integrating robust and and coordinated © 2016, IFAC (International Federation Automatic Control) Hosting by Elseviersupply Ltd. Allchain rightsplanning. reserved. Keywords: Supply chain, risk mitigation, robustness, coordination, inventory control Keywords: Supply chain, risk mitigation, robustness, coordination, inventory control Keywords: Keywords: Supply Supply chain, chain, risk risk mitigation, mitigation, robustness, robustness, coordination, coordination, inventory inventory control control 1. INTRODUCTION AND RELATED WORKS ence the supply chain operations, but they are extremely 1. INTRODUCTION INTRODUCTION AND RELATED RELATED WORKS ence the the supply supply chain chain operations, operations, but but they they are extremely extremely 1. ence hard to predict 2010). 1. INTRODUCTION AND AND RELATED WORKS WORKS ence supply (Simchi-Levi, chain operations, but they are are extremely hard the to predict predict (Simchi-Levi, 2010). hard to (Simchi-Levi, 2010). hard tocan predict (Simchi-Levi, Risks be categorised into2010). two types: predictable and Risks can can be be categorised categorised into into two two types: types: predictable predictable and and Risks Recently, supply chains have became more and more glob- unpredictable (Simchi-Levi, 2010). The predictable Risks can be categorised into two types: predictable risks and Recently, supply supply chains chains have have became became more more and and more more globglob- unpredictable unpredictable (Simchi-Levi, 2010). The predictable risks Recently, (Simchi-Levi, 2010). predictable alised andsupply lean so thathave theybecame can reduce operating quite frequent, thus they can The be forecasted forrisks exRecently, chains more their and more glob- are unpredictable (Simchi-Levi, 2010). The predictable risks alised and lean so that they can reduce their operating are quite quite frequent, frequent, thus thus they they can can be be forecasted forecasted for for exexalised and lean reduce their costs. However, thisthat hasthey alsocan decreased flexibility are ample by statistical methods. Such predictable types are alised and lean so so that they can reduce their their operating operating are quite frequent, thus they can be forecasted for excosts. However, this has also decreased their flexibility ample by statistical methods. Such predictable types are costs. However, this has also decreased their flexibility ample by statistical methods. Such predictable types are and increased their Several cases known the demand fluctuation or theSuch scrappredictable production.types On the costs. However, thisvulnerability. has also decreased their are flexibility ample by statistical methods. are and increased their vulnerability. Several cases are known the demand fluctuation or the scrap production. On the and increased their vulnerability. Several cases are known demand fluctuation the production. On when unexpected disturbances at any distant point their the other hand, unpredictable are rare (their probability and their vulnerability. Several cases are of known the fluctuation or orrisks the scrap scrap production. On the the whenincreased unexpected disturbances at any any distant point of their other otherdemand hand, unpredictable unpredictable risks are rare rare (their probability probability when unexpected disturbances at distant point of their hand, risks are (their supply chains could paralyse even large multinational comlow), butunpredictable if they happen, they have(their hugeprobability influence. when unexpected disturbances at any distant point of comtheir is other hand, risks are rare supply chains could paralyse even large multinational is low), low), but but if if they they happen, they they have have huge influence. influence. supply chains could paralyse even companies due to the lack of risk mitigation and uncoordinated Some recent natural disasters—such tsunami, supply chains could paralyse even large large multinational multinational com- is is low), but extreme if they happen, happen, they have huge hugeas panies due due to the the lack of risk risk mitigation mitigation and uncoordinated uncoordinated Some recent extreme natural disasters—such disasters—such as influence. tsunami, panies to lack of and Some recent extreme natural as tsunami, decision making. flood, volcano eruption, blizzard—, sudden changes in the panies due to the lack of risk mitigation and uncoordinated Some natural disasters—such as tsunami, decision making. making. flood, recent volcanoextreme eruption, blizzard—, sudden changes changes in the the decision flood, volcano eruption, blizzard—, sudden in economic conditions or political environment fall in decision making. flood, volcano eruption, blizzard—, sudden changes in this the The RobustPlaNet project aims at developing an inno- economic economic conditions or political environment fall in this conditions or political this The RobustPlaNet RobustPlaNet project project aims aims at at developing developing an an innoinno- category. An important metric of environment disruptions isfall the in TimeThe economic conditions or political environment fall in this vative business approach along with a supporting techcategory. An An important important metric metric of of disruptions disruptions is is the the TimeTimeThe projectalong aimswith at developing an innovativeRobustPlaNet business approach approach supporting tech- category. To-Repair (TTR), i.e., the timeof required for is the vative business along with aa supporting techcategory. An important metric disruptions theaffected Timenology that willapproach change the current rigid product-based To-Repair (TTR), i.e., the time required for the affected vative business along with a supporting techTo-Repair (TTR), i.e., the time required for the affected nology that that will will change change the the current current rigid rigid product-based product-based facility to return toi.e., full the capacity. nology To-Repair (TTR), time required for the affected business models into collaborative and robust production facility to return to full capacity. nology that will into change the current product-based to full business models collaborative andrigid robust production facility business models collaborative and production facility to to return return full capacity. capacity. networks able tointo timely deliver products services Considering risks to during the supply chain planning phase business models into collaborative and robust robustand production networks able to timely deliver products and services Considering risks risks during during the the supply supply chain chain planning planning phase phase networks able to timely deliver products and services Considering in very dynamic and unpredictable, global environments. can be carried out in several ways. One for example networks able to timely deliver products and services Considering risks the supply chaincan planning phase in very very dynamic dynamic and and unpredictable, unpredictable, global global environments. environments. can can be carried carried outduring in several several ways. One One can for example example in be out in ways. can for This approach will allow distributed supply networks to run several randomised simulations in order to example evaluate in very dynamicwill andallow unpredictable, can be carried out in several ways. One can for This approach distributedglobal supplyenvironments. networks to to run run several randomised simulations in order to evaluate This approach will allow distributed supply networks several randomised simulations in order to efficiently operate service levels in networks global marplan in a stochastic environment. is This approach willwith allowhigh distributed supply to arun several randomised simulations An in other order approach to evaluate evaluate efficiently operate with high service levels levels in global global marmara plan plan in aa stochastic stochastic environment. An other approach is efficiently operate with high service in ato in environment. An other approach is kets characterised by demand and levels variant uncertainty, include the uncertainty into the planning model and efficiently operate with high service in global maratoplan in a the stochastic environment. other approach is kets characterised characterised by by demand demand and and variant variant uncertainty, uncertainty, to include uncertainty into the the An planning model and and kets include the uncertainty into planning model and an environment exposed to disruptive events. In this apply a stochastic programming to solve it. and Yet kets characterised demand variantevents. uncertainty, to include the uncertainty into approach the planning model and an an environmentbyexposed exposed to and disruptive In this this apply apply a stochastic programming approach to solve it. Yet and environment to disruptive events. In aa stochastic approach to it. Yet paper investigate the theoretical background, as In wellthis as another possibility programming is the scenario generation, which and anwe exposed to disruptive events. apply stochastic approach to solve solve it.does Yet paper weenvironment investigate the the theoretical background, as well well as as another another possibility programming is the the scenario scenario generation, which does paper we investigate theoretical as possibility is generation, which does the applicability andthe integrability ofbackground, robust supply chain not require a stochastic model, but instead a number paper we investigate theoretical background, as well as another possibility is the scenario generation, which does the applicability and integrability of robust supply chain not require require aa stochastic stochastic model, model, but but instead instead aa number number the applicability and of planning and coordination methods. of alternative scenarios of possible in the the applicability and integrability integrability of robust robust supply supply chain chain not not require a stochastic model, but disruptions instead a number planning and coordination coordination methods. of alternative alternative scenarios of of possible disruptions in the the planning and methods. of scenarios possible disruptions in system. Furthermore, robust optimization approaches planning and coordination methods. of alternative scenarios of possible disruptions in aim the There are numerous risk factors in supply chain planning. system. system. Furthermore, Furthermore, robust robust optimization optimization approaches approaches aim aim There are numerous risk factors in supply chain planning. at finding such solutions that also perform well if their There are numerous risk factors in supply chain planning. system. Furthermore, robust optimization approaches aim One ofare thenumerous most frequently studied type chain is theplanning. demand at at finding finding such such solutions solutions that that also also perform perform well well if if their There risk factors in supply One of of the the most most frequently frequently studied type is is the the demand demand uncertain varythat in predefined intervals. One studied type at finding parameters such solutions also perform well if their their variation and obsolescence. The demand for athe product is uncertain uncertain parameters vary in predefined intervals. One of the most frequently studied type is demand parameters vary in predefined intervals. variation and and obsolescence. obsolescence. The The demand demand for for aa product product is is uncertain parameters vary in predefined intervals. variation not only fluctuating, but can even permanently cease, e.g., variation and obsolescence. for a cease, product is In RobustPlaNet we define robustness as the ability of a not only fluctuating, fluctuating, but can canThe evendemand permanently e.g., In RobustPlaNet RobustPlaNet we we define define robustness robustness as as the the ability ability of of aa not only but even cease, in case the development anpermanently improved substituting system to providewe thedefine desired output even in ability presence not onlyof fluctuating, but can of even permanently cease, e.g., e.g., In In RobustPlaNet robustness as the of of a in case of the development of an improved substituting system to provide the desired output even in presence of in case of the development of an improved substituting system to provide the desired output even in presence of product. Inthe order to avoid unnecessary excess substituting inventories, internal and external disturbances. Both uncertainties in in case of development of an improved system to provide the desired output even in presence of product. In order to avoid unnecessary excess inventories, internal and external disturbances. Both uncertainties in product. In to excess and disturbances. in the ramp-down phase of theunnecessary products should beinventories, considered internal the environment and partial failure Both of theuncertainties system should product. In order order to avoid avoid excess internal and external external disturbances. in the ramp-down ramp-down phase of the theunnecessary products should should beinventories, considered the the environment environment and partial partial failure Both of the theuncertainties system should should the phase of products be considered and failure of system separately and planned with special care. An other probbe considered in order to call the system robust. A possible the ramp-down phase of with the products should beother considered the environment and partial failure of the system should separately and planned special care. An probbe considered considered in in order order to to call call the the system robust. robust. A A possible possible separately and with care. other lem is the supply time uncertainty: shortages can be metric for supply chaintorobustness is therobust. Time-To-Survive separately and planned planned with special specialmaterial care. An An other probprobbe considered in order call the system system A possible lem is is the the supply supply time uncertainty: uncertainty: material shortages can metric metric for supply supply chain robustness robustness is the the Time-To-Survive Time-To-Survive lem time material shortages can for chain is occur also due to supplier fault, transportation problems, which waschain proposed by Simchi-Levi et al. (2015). lem is also the supply uncertainty: material shortages can (TTS), metric supply robustness is the Time-To-Survive occur due to to time supplier fault, transportation transportation problems, (TTS),for which was proposed proposed by Simchi-Levi Simchi-Levi et al. al. (2015). (2015). occur also due supplier problems, which was by et quality problems, to name afault, few. Furthermore, there is also (TTS), The TTS of a facility in a supply chain is the time that occur also due to supplier fault, transportation problems, (TTS), which was proposed by Simchi-Levi et al. (2015). quality problems, problems, to to name name aa few. few. Furthermore, Furthermore, there there is is also also The The TTS of a facility in a supply chain is the time that quality TTS of aaservice facility in aacan supply chain is the time that production uncertainty due to machine breakdowns and the customer level be maintained if the facility quality problems, to name a few. Furthermore, there is also The TTS of facility in supply chain is the time that production uncertainty due to machine breakdowns and the customer service level can be maintained if the facility production uncertainty due to machine breakdowns and customer service maintained the facility personnel absence that can production. Finally, and dis- the is disrupted, and the level TTS can of a be supply chain isif the minimal production uncertainty duedelay to machine breakdowns the customer service level can be maintained if the facility personnel absence that can delay production. Finally, disis disrupted, disrupted, and and the the TTS TTS of of aa supply supply chain chain is the the minimal personnel that delay Finally, disasters and absence other unforeseen natural disasters, TTS of its facilities link).chain is personnel that can can events—e.g., delay production. production. Finally, dis- is is disrupted, and the(the TTSweakest of a supply is the minimal minimal asters and and absence other unforeseen unforeseen events—e.g., natural disasters, TTS of its its facilities facilities (the weakest link). asters other events—e.g., natural disasters, TTS of (the weakest link). terrorist attacks, political instability—considerably influasters andattacks, other unforeseen events—e.g., natural disasters, terrorist political instability—considerably instability—considerably influ- TTS of its facilities (the weakest link). terrorist attacks, political influterrorist attacks, political instability—considerably influCopyright © 2016, 2016 IFAC 41 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 41 Copyright ©under 2016 responsibility IFAC 41 Control. Peer review of International Federation of Automatic Copyright © 2016 IFAC 41 10.1016/j.ifacol.2016.07.547
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There are several planning decisions in supply chains that influence the robustness. For supplier selection, when the decision is made for the long term, single sourcing is very vulnerable. Instead, frequently dual (or even multiple) sourcing is applied—c.f., 2-flexibility from SimchiLevi et al. (2015). The place and level of the inventories are also essential for the robust planning. For example, storing large amount of finished goods might provide safeguards against supply problems, but this is usually a quite expensive solution. Sometimes production capacity buffers and flexibility might be necessary in order to adapt to the increased demand and avoidance of bottlenecks, but this decreases the resource utilization. Logistic decisions— such as choosing the applied ordering policies, frequencies, order quantities and transportation modes—also affect the vulnerability towards disruptions. Further decisions can also indirectly influence robustness, such as the applied forecasting method or the product and part pricing.
Optimization
Risk mitigation
Autonomous systems
Fig. 1. Related research fields ods for integrating robust and coordinated supply chain planning. This paper focuses on the logistic optimization and disregards other related supplementary approaches of the project such as production optimization (Gyulai et al., 2014), lead-time reduction or required information and communication technology.
Numerous practical approaches have been proposed for supply chain risk mitigation focusing on the previously mentioned decision problems, see e.g., Tang (2006) or a recent literature review by Ho et al. (2015). Two of the most well-studied strategies are holding protective inventory and increasing process flexibility. Holding additional inventory is a straightforward way to hedge against disruptions: if the inventory is high enough to cover the demand for the duration of TTR of the disrupted facility, then it will not affect the service level, thus the supply chain can be considered robust. Note that the necessary protective inventory depends only on the TTR, thus the long leadtimes of some suppliers do not increase the required inventory. Unfortunately, holding sufficient buffers can still be very expensive.
2. INDUSTRIAL MOTIVATION The setting of this case study is illustrated on Fig. 2. This supply chain produces electromechanical drives and its studied part consists of four stakeholders: the distribution centre (DC), the manufacturer, the inventory hub (IH) and a supplier of parts. The task of the DC is to provide the required electromechanical drives for the customers. In order to do this, it needs to make long-term (2-3 years) demand forecast aggregating across several customer areas and maintain appropriate finished good stock to satisfy the prompt demands. The manufacturer has to provide the required finished goods for the DC. Since the manufacturing process takes in average 50 days, the production is planned for the medium term, i.e., a few months ahead. For providing flexibility for production planning, some finished good buffer is held also at the manufacturer.
The process flexibility on the other hand, means introducing redundancy to the supply chain, e.g., when a plant or production line can build different types of products, thus the demand can be satisfied from different sources. Increasing flexibility can also be costly, and in addition, it also requires additional capacities: if there is no excess capacities in the system, the work cannot be redistributed in case of disturbances.
A required part for the manufacturing is supplied by a factory located in the Far East, which has a very long production time–approximately 8 months—, therefore their production has to be started quite in advance. In the studied case, the supplier is an external company operating in a Make-To-Order (MTO) manner, thus it is the responsibility of the manufacturer to give long-term orders based on demand forecasts. Note that such long leadtime suppliers are also typical in the European automotive industry (Zapp et al., 2012).
Simchi-Levi et al. (2015) suggests that protective inventory and process flexibility should be combined in order to provide sufficient robustness but also keep costs as low as possible. They point out that the probability of some supply chain risk are very difficult to estimate, furthermore, the resulted stochastic models are computationally rarely tractable. Therefore they suggest using a robust optimization approach by defining uncertainty sets for the uncertain parameters. They also suggest considering the worst-case possibility that helps identifying the vulnerabilities of a supply chain.
The transportation from the supplier to the IH also takes rather long time. The default transportation mode is by ship which takes 2.5 months, therefore the transportation also has to be planned in advance. In case of unexpected shortage however, a faster transportation alternative by plane can be chosen. By using air transportation the duration can be reduced to 3 weeks, but due to its high cost, only applied in emergency situations.
As we have just seen, robust supply chain planning is located at the intersection of optimisation and risk mitigation. Similarly, the supply chain coordination is at the intersection of (distributed) optimisation and autonomous systems. This idea is illustrated on Fig. 1. Considering robust planning and coordination together in supply chains is still a relatively unexplored research field (Lu et al., 2015). The goal of this paper is to outline the research directions for industrially relevant and applicable meth-
Since the inventory space at the manufacturing site is limited, the storage of the parts between the supplier and the manufacturer takes place at an IH. The IH is located close to the manufacturing site managed by an external service provider collaborating with the manufacturer. Besides the storage of the parts, the IH is responsible for choosing the transportation mode from the supplier and providing the 42
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43
Long-term order Long-term forecast, short term demand
Inventory level
Prod. status
Supplier
Information flow
Manufacturer
Inventory Hub
Material flow
Distribution Centre
Fig. 2. Supply chain of the case study required parts for the manufacturer, who only maintains a small inventory of parts.
θi ∈ { 1, 2, 3, . . . }—which covers the demand for Ti time. Fig. 4 illustrates the expected inventory positions for the first two stages, i.e., the inventory level plus the ordered items.
The primary key performance indicators (KPIs) for the supply chain are delivery time (for low-runner customised products), quality and customer satisfaction (on-time delivery for high-runner standardised products). Note that these KPIs measure the performance of the whole supply chain and disregard the viewpoint of the different stakeholders described above. Therefore further KPIs should be used—such as cost, inventory level, number of reconfigurations/setups, required investments, resource utilization— in order to measure the performance and efficiency of the whole chain as well as its members. Since the survey conducted in the project pointed out that the logistic (inventory and transportation) costs are very high compared to the manufacturing expenses, the goal of this study is to provide an approach for optimizing these costs while maintaining robustness and the required service level towards the end-customers.
3.1 Computing the reorder point The reorder point should be determined in such a way that it would cover the demand until the order arrives, i.e., the demand during the lead-time. According to Simchi-Levi et al. (2000), the reorder point is the average demand during the lead-time plus a safety stock to handle the uncertainty in the demand. Assuming √ normal distribution, this yields si = µLi + F −1 (α)σ Li , where F is the cumulative standard normal distribution and α is the required service level. 3.2 Computing the order quantities Traditionally, supply chain decisions are made in a hierarchical manner: the first stage decides its optimal Q1 order quantity, then makes its orders. After that the second stage makes its decisions, and so on, upwards the supply chain. We call this decomposed planning. While this approach is very simple and easy to implement, the problem with it is that a decision introduces constraints to the upstream planning, which may cause additional costs, and eventually inefficiency in the overall supply chain (Egri et al., 2011).
3. PROBLEM FORMULATION In this section we formulate a model for the above described logistic optimization problem. For the long-term we assume static demand, but the approach remains similar in the dynamic case, too. We consider a serial supply chain with n stages, where the nodes represent inventories and the links between them are either production or transportation operations. Inventory can be held at each node with different hi unit holding costs. The market demand is stochastic with mean µ and expected value σ, but the Li lead-times between the nodes are deterministic. We also consider that the production and transportation incurs Ki fixed costs. The studied supply chain in this formulation is illustrated on Fig. 3.
Instead of the decomposed planning, we apply a multiechelon model for considering the average cost of the whole supply chain: n hi µ(Ti − Ti−1 ) Ki , (1) + C(T1 , . . . , Tn ) = Ti 2 i=1 where T0 = 0. When i = 1, this yields the cost used in the EOQ model; while for i > 1, the terms reflect to the inventory shape in the right side of Fig. 4.
Since there are fixed costs involved, we cannot use the basestock model as in Egri (2012). Instead, we assume the first stage considers continuous stochastic demand, therefore applies the standard (s, Q) policy with the Economic Order Quantity (EOQ) model (Harris, 1913). Accordingly, it determines the s1 level of reorder point, and as the inventory position drops to s1 , orders Q1 products—which covers the demand approximately for T1 = µ/Q1 time.
Then we have the following optimization problem: min C(T1 , . . . , Tn )
(2)
s.t. Ti = θi Ti−1
According to the model of Muckstadt and Roundy (1993), the other stages (stage i) take the order quantity from the previous stage (Qi−1 ), and use dynamic lot sizing method together with safety stocks. This results in reorder point si and order quantity Qi —which equals to θi Qi−1 for some
Ti ≥ 0
T0 = 0 θi ∈ { 1, 2, 3, . . . } 43
i ∈ { 2, . . . , n }
(3)
i ∈ { 1, . . . , n }
(4)
i ∈ { 1, . . . , n }
(6)
(5)
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Supplier production + Transportation
L4, K4
Transportation
IH
L3, K3
h4
Production
L2, K2
MP
h3
Transportation
L1, K1
MF
h2
DC
h1
Fig. 3. Example supply chain model for the case studied (IH: inventory hub, MP: manufacturer’s part inventory, MF: manufacturer’s finished goods inventory, DC: distribution centre) Inventory
Inventory T1
T1
Q1
T2
Q1
Q 2 - Q1
s2
s1 Time
Time
Fig. 4. Expected inventory positions of stages 1 and 2 demand fluctuation. The model described in the previous subsections therefore helps to estimate the medium-term costs assuming different supply chain configurations, hence it also supports the strategic level decision making.
This is a non-convex mixed integer nonlinear programming (MINLP) problem, whose exact solution is hard to compute, therefore usually an approximation algorithm is used (Muckstadt and Roundy, 1993). After having the quasioptimal Ti values, the order quantities can be straightforwardly computed with Qi = µTi . Note that in case of dynamic demand forecast, the algorithm of Zangwill (1969) can be applied for solving the multi-echelon lotsizing problem.
Since the possibilities of process flexibility in our use case are limited, we focus here on determining the required protective inventories for providing robustness. For each edge i in the supply chain model we have to determine T T Ri , i.e., the time within edge i can be recovered after a disruption. Similarly to the reorder point, the protective inventory at the end of edge i can be computed with √ the following formula: µT T Ri + F −1 (α)σ T T Ri , which is used as a safety buffer until edge i is recovered.
3.3 Determining the transportation mode As we have seen, the transportation between the supplier and the IH has two possibilities: by water or by air. Choosing the latter drastically reduces the lead-time, which results in lower reorder point, but in higher fixed cost. These two alternatives result in two instances of the optimization problem formulated above, which can be solved separately and compared according the different KPIs.
Note that the protective inventory at the IH should consider only the TTR of the supplier, since in case of a shipment failure, there is an alternative transportation mode. Without the possibility of the air transportation, the maximum TTR of the supplier and the shipment should have been taken into account instead.
In practice, the difference between the costs of water and air transportation is so huge, that the IH chooses water shipment whenever possible. Therefore the longer and cheaper transportation mode is considered in the above optimization. However, the quicker transportation mode can be used as a protection tool against shortages: whenever the IH observes that increased demand shall cause stockout, it can change the transportation of the already ordered and produced parts in order to speed up supply.
4. COORDINATION As we have previously seen, the main objective for the supply chain relates to the customer satisfaction. In this aspect, similar results can be provided by completely different plans. For example, the service level can be guaranteed by high end-product inventories, or by investing into new, high speed production equipment, or by ensuring fast replenishment by using air transportation. Even though all of these might provide the required service level, and their costs might be similar, these costs are distributed differently between the stakeholders.
3.4 Designing for robustness In the previous subsections we have introduced a planning framework which can be applied for supporting mediumand short-term supply chain decisions assuming a given chain. We have considered uncertain demand and determined the necessary safety stocks to hedge against the
Coordination considers the supply chain planning as a distributed decision making problem. Generally, a coordination mechanism aims at aligning the objectives of the different stakeholders with the global supply chain objective. Therefore we now overview the decisions and costs 44
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cooperative game theory. Calculating the Shapley value however usually involves solving a series of mathematical programming problems, thus might be practically inappropriate when the number of the participants is large.
of the stakeholders of our case study. (Since the supplier is an external company not involved in the project, we enumerate only the other participants.) Table 1. The decentralised setting IH Manuf.
DC
Decision transportation mode transportation schedule long-term orders production plan min/max part inventory transportation to DC forecasts short-term orders
45
4.2 Coordination by mechanism design
Cost inventory transportation production transportation to DC inventory
In case of incomplete information—e.g., when some information (such as the private cost parameters) are not known by all the stakeholders—mechanism design can help in the coordination. For example, the Vickrey-ClarkeGroves (VCG) mechanism has been designed to inspire the individual participants to share their private information truthfully, and applies a similar concept of marginal contribution as the Shapley value. In Egri (2012) VCG mechanisms were used to coordinate inventory decisions in a supply chain where the inventory holding costs and the lead-times were private information of the corresponding decision makers—but there was assumed to be no fixed costs.
inventory forecasting
It can be seen that the decisions not only affect the decision makers, but the other stakeholders, too. For example, if the manufacturer orders too much products, that causes high inventory levels (and costs) at the IH; on the other hand, if the ordered quantity is not enough to cover the demand, the IH might have to use the expensive air transportation in order to speed up the supply. The aim of coordination mechanisms is to guarantee that the autonomous decision makers follow the globally optimal supply plan and to fairly redistribute the occurred costs among the collaborating stakeholders. Sometimes achieving the exact optimal solution is not realistic, thus in a weaker sense, coordination should result in Pareto-improvement compared to some baseline plan, such as the decomposed solution (see Section 3.2). The applied tools for achieving coordination usually include novel business models, special contracts (e.g., buyback) and sharing the benefit of the cooperation with specialized payment schemes (Gao, 2015).
Although VCG mechanisms result in globally optimal plans even with autonomous decision makers and private information, they have some properties that make them difficult to apply in the practice of supply chain coordination: • Usually an independent entity is required to collect all information and do the planning. • An external budget is needed for the mechanism. • When the optimization is done by an approximation algorithm—as it was suggested above for the multiechelon inventory planning—the VCG does not provide the appropriate incentive to cooperate. When the private information are statistical distributions of random variables which can be later evaluated with their realized values—for example in case of demand forecasts— then information elicitation mechanisms can be applied which avoid the above mentioned drawbacks of VCG. For example, Egri (2015) presents such a model, which in supply networks leads to the widespread practical ideas of vendor managed inventory (VMI) and risk pooling.
4.1 Decision support for coordination In this project we aim at the analysis of the distributed optimization in order to support negotiation among the stakeholders. For this reason, we suggest generating different supply chain scenarios and compute the resulted costs, inventory levels, resource utilizations and other local KPIs for each stages. This helps quantifying how much compensation is needed for the stakeholders to change their behaviour. For example, with appropriate quantity discounts a buyer can be inspired to increase the order quantities, i.e., the discount helps to partially redistribute the benefit—caused by the increased order quantity—from the supplier to the buyer.
Another approach is to apply an iterative mechanism, which may not result in globally optimal solution, but can improve efficiency compared to a baseline solution, e.g., the decomposed planning solution. Such model was presented in Egri et al. (2011), where adjacent stages in the chain applied a feedback mechanism called dynamic supply loop with benefit balancing in order to provide a possibility of collaboratively improving supply chain planning considering standard ERP lot-sizing policies. A similar coordination model was compared to different other solutions—namely the decomposed (non-cooperative), the integrated (cooperative) and the bilevel—in Kov´ acs et al. (2013). While the previously mentioned models provide only one feedback loop and relatively simple planning problems, there are also multi-step iterative mechanisms for collaborative planning tasks (Albrecht, 2010).
In addition, one can also take the total cost of these different plans. Specifically, if we compare the optimal solution of the (non-cooperative) decomposed decision model and the (cooperative) multi-echelon decision model described above, we can get the so-called Price of Anarchy (PoA) that measures how much benefit can be gained from cooperation (Nisan et al., 2007). Similarly, one can compare non-robust plans and plans with different levels of robustness. This measures the price of robustness and that who pays this price according to the given plan.
5. CASE STUDY
Eventually, the fair redistribution of the benefit can be based on the contribution to the supply chain, which can be measured applying the Shapley value concept of the
In this section we illustrate the above described analysis considering one of the industrial partners in the project 45
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THK Japan-France illustration
Egri, P. (2012). Safety stock placement in non-cooperative supply chains. In Proc. of the ECAI 2012 Workshop on Artificial Intelligence and Logistics, 31–36. Egri, P., D¨oring, A., Timm, T., and V´ancza, J. (2011). Collaborative planning with benefit balancing in dynamic supply loops. CIRP Journal of Manufacturing Science and Technology, 4(3), 226–233. Egri, P. (2015). Information elicitation for aggregate demand prediction with costly forecasting. Autonomous Agents and Multi-Agent Systems, in print. Gao, L. (2015). Collaborative forecasting, inventory hedging and contract coordination in dynamic supply risk management. European Journal of Operational Research, 245(1), 133–145. Gyulai, D., K´ad´ar, B., Kov´acs, A., and Monostori, L. (2014). Capacity management for assembly systems with dedicated and reconfigurable resources. CIRP Annals - Manufacturing Technology, 63(1), 457–460. Harris, F.W. (1913). How many parts to make at once. Factory: The Magazine of Management, 10(2), 135–136, 152. Ho, W., Zheng, T., Yildiz, H., and Talluri, S. (2015). Supply chain risk management: a literature review. International Journal of Production Research, 53(16), 5031–5069. Kov´acs, A., Egri, P., Kis, T., and V´ancza, J. (2013). Inventory control in supply chains: Alternative approaches to a two-stage lot-sizing problem. International Journal of Production Economics, 143(2), 385 – 394. Lu, M., Sethi, S., and Yan, H. (2015). Robustness of supply chain coordination contracts: Taxonomy, examples, and structural results. Available at http://dx.doi.org/10.2139/ssrn.1864548. Muckstadt, J. and Roundy, R.O. (1993). Analysis of multistage production systems. In S. Graves, A.R. Kan, and P. Zipkin (eds.), Logistics of production and inventory, volume 4 of Handbooks in Operations Research and Management Science, 59–131. Elsevier. ´ and Vazirani, Nisan, N., Roughgarden, T., Tardos, E., V.V. (eds.) (2007). Algorithmic Game Theory. Cambridge University Press. Simchi-Levi, D. (2010). Operation Rules – Delivering Customer Value through Flexible Operations. MIT Press. Simchi-Levi, D., Kaminsky, P., and Simchi-Levi, E. (2000). Designing and managing the supply chain: Concepts, strategies, and cases. McGraw – Hill. Simchi-Levi, D., Wang, H., and Wei, Y. (2015). Increasing supply chain robustness through process flexibility and inventory. Available at http://dx.doi.org/10.2139/ssrn.2433175. Tang, C.S. (2006). Perspectives in supply chain risk management. International Journal of Production Economics, 103(2), 451–488. Zangwill, W.I. (1969). A backlogging model and a multiechelon model of a dynamic economic lot size production system-a network approach. Man. Sci., 15(9), 506–527. Zapp, M., Forster, C., Verl, A., and Bauernhansl, T. (2012). A reference model for collaborative capacity planning between automotive and semiconductor industry. Procedia CIRP, 3, 155–160.
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Fig. 5. Comparison of alternative supply chain configurations and one of its suppliers from the Far East. We have performed numerical analysis comparing two scenarios: (i) continue purchasing from this supplier or (ii) switch to a European supplier providing higher component prices. Fig. 5 shows the estimated difference in the purchasing cost—which is paid by the manufacturer—and the logistic costs—which is paid by the IH for a specific component. It can be seen that the savings in the logistic cost surpass the effect of the increased purchasing cost, therefore it is beneficial to change despite being disadvantageous to the manufacturer. In order to motivate the manufacturer, the IH should offer a compensation by sharing its benefit determined by the numerical study. A further possible scenario could be to apply a dual sourcing and therefore increasing process flexibility. This would necessitate additional qualitative risk analysis besides considering costs, i.e., whether the potential risks of purchasing from the FarPage East 1 surpass the benefit of having an alternative supplier or not. 6. CONCLUSIONS In this paper we have outlined a research agenda for integrating robust planning and coordination in supply chains. We have presented a case study of an industrial supply chain, concentrating on the long lead-time supplier which is one of the most serious sources of difficulties. We have focused on inventory optimization taking specifically robustness into account and also illustrated possible coordination approaches that consider the supply chain stakeholders as autonomous decision makers. As for future work, we will develop a multiagent simulation tool for decision support integrated into the RobustPlaNet cockpit. ACKNOWLEDGEMENTS This work has been supported by the European Union 7th Framework Programme Project No. NMP 2013-609087, Shock-robust Design of Plants and their Supply Chain Networks (RobustPlaNet) and by the Hungarian Scientific Research Fund (OTKA), Grant No. 113038. REFERENCES Albrecht, M. (2010). Supply Chain Coordination Mechanisms – New Approaches for Collaborative Planning. Springer-Verlag, Berlin Heidelberg. 46
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Towards robust Towards coordination coordination in robust supply supply in Towards coordination in robust supply networks networks networks
P´ eter Egri ∗∗∗ Botond K´ ad´ ar ∗∗∗ J´ ozsef V´ ancza ∗∗∗ P´ e ter Egri Botond K´ a d´ a rr ∗ J´ o zsef V´ a ncza ∗ P´ e ter Egri a d´ a J´ o zsef V´ a ∗ Botond K´ P´ eter Egri Botond K´ ad´ ar J´ ozsef V´ ancza ncza ∗ Fraunhofer Project Center for Production Management and ∗ ∗ Fraunhofer Project Center for Production Management and Project Center for Production Management and ∗ Fraunhofer Informatics, Institute for Computer Science and Control, Hungarian Fraunhofer Project for Production Management and Informatics, Institute for Center Computer Science and Control, Hungarian Informatics, Institute for Computer Science and Control, Hungarian Academy of Sciences, Kende u. 13-17, 1111 Budapest, Hungary Informatics, Institute forKende Computer Science and Control, Hungary Hungarian Academy of Sciences, u. 13-17, 1111 Budapest, Academy of Kende {egri,kadar,vancza}@sztaki.mta.hu) Academy (e-mail: of Sciences, Sciences, Kende u. u. 13-17, 13-17, 1111 1111 Budapest, Budapest, Hungary Hungary (e-mail: {egri,kadar,vancza}@sztaki.mta.hu) (e-mail: {egri,kadar,vancza}@sztaki.mta.hu) (e-mail: {egri,kadar,vancza}@sztaki.mta.hu) Abstract: Supply chains nowadays frequently face risks caused by increased environmental Abstract: Supply chains nowadays frequently face risks caused by increased environmental Abstract: Supply chains frequently risks by environmental volatility and performance inefficiency. In this face paper an caused integrated supply chain planning Abstract: Supply chains nowadays nowadays frequently face risks caused by increased increased environmental volatility and performance inefficiency. In this paper an integrated supply chain planning volatility and performance inefficiency. In this paper an integrated supply chain planning approach is suggested that combines the three aspects of optimisation, risk mitigation and volatility performance this aspects paper an supply planning approach and is suggested suggested that inefficiency. combines the theInthree three of integrated optimisation, risk chain mitigation and approach is that combines aspects of optimisation, risk mitigation and decentralisation. The goal ofcombines this paper isthree to outline theofresearch directions for industrially approach is suggested that the aspects optimisation, risk mitigation and decentralisation. The goal of this paper is to outline the research directions for industrially decentralisation. The goal of this paper is to outline the research directions for industrially relevant and applicable methods forpaper integrating robust and coordinated supply chain planning. decentralisation. The goal of this is to outline the research directions for industrially relevant and applicable methods for integrating robust and coordinated supply relevant and methods for robust coordinated supply chain chain planning. planning. relevant and applicable applicable methods forofintegrating integrating robust and and coordinated © 2016, IFAC (International Federation Automatic Control) Hosting by Elseviersupply Ltd. Allchain rightsplanning. reserved. Keywords: Supply chain, risk mitigation, robustness, coordination, inventory control Keywords: Supply chain, risk mitigation, robustness, coordination, inventory control Keywords: Keywords: Supply Supply chain, chain, risk risk mitigation, mitigation, robustness, robustness, coordination, coordination, inventory inventory control control 1. INTRODUCTION AND RELATED WORKS ence the supply chain operations, but they are extremely 1. INTRODUCTION INTRODUCTION AND RELATED RELATED WORKS ence the the supply supply chain chain operations, operations, but but they they are extremely extremely 1. ence hard to predict 2010). 1. 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Several cases are known the demand fluctuation or the scrap production. On the and increased their vulnerability. Several cases are known demand fluctuation the production. On when unexpected disturbances at any distant point their the other hand, unpredictable are rare (their probability and their vulnerability. Several cases are of known the fluctuation or orrisks the scrap scrap production. On the the whenincreased unexpected disturbances at any any distant point of their other otherdemand hand, unpredictable unpredictable risks are rare rare (their probability probability when unexpected disturbances at distant point of their hand, risks are (their supply chains could paralyse even large multinational comlow), butunpredictable if they happen, they have(their hugeprobability influence. when unexpected disturbances at any distant point of comtheir is other hand, risks are rare supply chains could paralyse even large multinational is low), low), but but if if they they happen, they they have have huge influence. influence. supply chains could paralyse even companies due to the lack of risk mitigation and uncoordinated Some recent natural disasters—such tsunami, supply chains could paralyse even large large multinational multinational com- is is low), but extreme if they happen, happen, they have huge hugeas panies due due to the the lack of risk risk mitigation mitigation and uncoordinated uncoordinated Some recent extreme natural disasters—such disasters—such as influence. tsunami, panies to lack of and Some recent extreme natural as tsunami, decision making. flood, volcano eruption, blizzard—, sudden changes in the panies due to the lack of risk mitigation and uncoordinated Some natural disasters—such as tsunami, decision making. making. flood, recent volcanoextreme eruption, blizzard—, sudden changes changes in the the decision flood, volcano eruption, blizzard—, sudden in economic conditions or political environment fall in decision making. flood, volcano eruption, blizzard—, sudden changes in this the The RobustPlaNet project aims at developing an inno- economic economic conditions or political environment fall in this conditions or political this The RobustPlaNet RobustPlaNet project project aims aims at at developing developing an an innoinno- category. An important metric of environment disruptions isfall the in TimeThe economic conditions or political environment fall in this vative business approach along with a supporting techcategory. An An important important metric metric of of disruptions disruptions is is the the TimeTimeThe projectalong aimswith at developing an innovativeRobustPlaNet business approach approach supporting tech- category. To-Repair (TTR), i.e., the timeof required for is the vative business along with aa supporting techcategory. An important metric disruptions theaffected Timenology that willapproach change the current rigid product-based To-Repair (TTR), i.e., the time required for the affected vative business along with a supporting techTo-Repair (TTR), i.e., the time required for the affected nology that that will will change change the the current current rigid rigid product-based product-based facility to return toi.e., full the capacity. nology To-Repair (TTR), time required for the affected business models into collaborative and robust production facility to return to full capacity. nology that will into change the current product-based to full business models collaborative andrigid robust production facility business models collaborative and production facility to to return return full capacity. capacity. networks able tointo timely deliver products services Considering risks to during the supply chain planning phase business models into collaborative and robust robustand production networks able to timely deliver products and services Considering risks risks during during the the supply supply chain chain planning planning phase phase networks able to timely deliver products and services Considering in very dynamic and unpredictable, global environments. can be carried out in several ways. One for example networks able to timely deliver products and services Considering risks the supply chaincan planning phase in very very dynamic dynamic and and unpredictable, unpredictable, global global environments. environments. can can be carried carried outduring in several several ways. One One can for example example in be out in ways. can for This approach will allow distributed supply networks to run several randomised simulations in order to example evaluate in very dynamicwill andallow unpredictable, can be carried out in several ways. One can for This approach distributedglobal supplyenvironments. networks to to run run several randomised simulations in order to evaluate This approach will allow distributed supply networks several randomised simulations in order to efficiently operate service levels in networks global marplan in a stochastic environment. is This approach willwith allowhigh distributed supply to arun several randomised simulations An in other order approach to evaluate evaluate efficiently operate with high service levels levels in global global marmara plan plan in aa stochastic stochastic environment. An other approach is efficiently operate with high service in ato in environment. An other approach is kets characterised by demand and levels variant uncertainty, include the uncertainty into the planning model and efficiently operate with high service in global maratoplan in a the stochastic environment. other approach is kets characterised characterised by by demand demand and and variant variant uncertainty, uncertainty, to include uncertainty into the the An planning model and and kets include the uncertainty into planning model and an environment exposed to disruptive events. In this apply a stochastic programming to solve it. and Yet kets characterised demand variantevents. uncertainty, to include the uncertainty into approach the planning model and an an environmentbyexposed exposed to and disruptive In this this apply apply a stochastic programming approach to solve it. Yet and environment to disruptive events. In aa stochastic approach to it. Yet paper investigate the theoretical background, as In wellthis as another possibility programming is the scenario generation, which and anwe exposed to disruptive events. apply stochastic approach to solve solve it.does Yet paper weenvironment investigate the the theoretical background, as well well as as another another possibility programming is the the scenario scenario generation, which does paper we investigate theoretical as possibility is generation, which does the applicability andthe integrability ofbackground, robust supply chain not require a stochastic model, but instead a number paper we investigate theoretical background, as well as another possibility is the scenario generation, which does the applicability and integrability of robust supply chain not require require aa stochastic stochastic model, model, but but instead instead aa number number the applicability and of planning and coordination methods. of alternative scenarios of possible in the the applicability and integrability integrability of robust robust supply supply chain chain not not require a stochastic model, but disruptions instead a number planning and coordination coordination methods. of alternative alternative scenarios of of possible disruptions in the the planning and methods. of scenarios possible disruptions in system. Furthermore, robust optimization approaches planning and coordination methods. of alternative scenarios of possible disruptions in aim the There are numerous risk factors in supply chain planning. system. system. Furthermore, Furthermore, robust robust optimization optimization approaches approaches aim aim There are numerous risk factors in supply chain planning. at finding such solutions that also perform well if their There are numerous risk factors in supply chain planning. system. Furthermore, robust optimization approaches aim One ofare thenumerous most frequently studied type chain is theplanning. demand at at finding finding such such solutions solutions that that also also perform perform well well if if their There risk factors in supply One of of the the most most frequently frequently studied type is is the the demand demand uncertain varythat in predefined intervals. One studied type at finding parameters such solutions also perform well if their their variation and obsolescence. The demand for athe product is uncertain uncertain parameters vary in predefined intervals. One of the most frequently studied type is demand parameters vary in predefined intervals. variation and and obsolescence. obsolescence. The The demand demand for for aa product product is is uncertain parameters vary in predefined intervals. variation not only fluctuating, but can even permanently cease, e.g., variation and obsolescence. for a cease, product is In RobustPlaNet we define robustness as the ability of a not only fluctuating, fluctuating, but can canThe evendemand permanently e.g., In RobustPlaNet RobustPlaNet we we define define robustness robustness as as the the ability ability of of aa not only but even cease, in case the development anpermanently improved substituting system to providewe thedefine desired output even in ability presence not onlyof fluctuating, but can of even permanently cease, e.g., e.g., In In RobustPlaNet robustness as the of of a in case of the development of an improved substituting system to provide the desired output even in presence of in case of the development of an improved substituting system to provide the desired output even in presence of product. Inthe order to avoid unnecessary excess substituting inventories, internal and external disturbances. Both uncertainties in in case of development of an improved system to provide the desired output even in presence of product. In order to avoid unnecessary excess inventories, internal and external disturbances. Both uncertainties in product. In to excess and disturbances. in the ramp-down phase of theunnecessary products should beinventories, considered internal the environment and partial failure Both of theuncertainties system should product. In order order to avoid avoid excess internal and external external disturbances. in the ramp-down ramp-down phase of the theunnecessary products should should beinventories, considered the the environment environment and partial partial failure Both of the theuncertainties system should should the phase of products be considered and failure of system separately and planned with special care. An other probbe considered in order to call the system robust. A possible the ramp-down phase of with the products should beother considered the environment and partial failure of the system should separately and planned special care. An probbe considered considered in in order order to to call call the the system robust. robust. A A possible possible separately and with care. other lem is the supply time uncertainty: shortages can be metric for supply chaintorobustness is therobust. Time-To-Survive separately and planned planned with special specialmaterial care. An An other probprobbe considered in order call the system system A possible lem is is the the supply supply time uncertainty: uncertainty: material shortages can metric metric for supply supply chain robustness robustness is the the Time-To-Survive Time-To-Survive lem time material shortages can for chain is occur also due to supplier fault, transportation problems, which waschain proposed by Simchi-Levi et al. (2015). lem is also the supply uncertainty: material shortages can (TTS), metric supply robustness is the Time-To-Survive occur due to to time supplier fault, transportation transportation problems, (TTS),for which was proposed proposed by Simchi-Levi Simchi-Levi et al. al. (2015). (2015). occur also due supplier problems, which was by et quality problems, to name afault, few. Furthermore, there is also (TTS), The TTS of a facility in a supply chain is the time that occur also due to supplier fault, transportation problems, (TTS), which was proposed by Simchi-Levi et al. (2015). quality problems, problems, to to name name aa few. few. Furthermore, Furthermore, there there is is also also The The TTS of a facility in a supply chain is the time that quality TTS of aaservice facility in aacan supply chain is the time that production uncertainty due to machine breakdowns and the customer level be maintained if the facility quality problems, to name a few. Furthermore, there is also The TTS of facility in supply chain is the time that production uncertainty due to machine breakdowns and the customer service level can be maintained if the facility production uncertainty due to machine breakdowns and customer service maintained the facility personnel absence that can production. Finally, and dis- the is disrupted, and the level TTS can of a be supply chain isif the minimal production uncertainty duedelay to machine breakdowns the customer service level can be maintained if the facility personnel absence that can delay production. Finally, disis disrupted, disrupted, and and the the TTS TTS of of aa supply supply chain chain is the the minimal personnel that delay Finally, disasters and absence other unforeseen natural disasters, TTS of its facilities link).chain is personnel that can can events—e.g., delay production. production. Finally, dis- is is disrupted, and the(the TTSweakest of a supply is the minimal minimal asters and and absence other unforeseen unforeseen events—e.g., natural disasters, TTS of its its facilities facilities (the weakest link). asters other events—e.g., natural disasters, TTS of (the weakest link). terrorist attacks, political instability—considerably influasters andattacks, other unforeseen events—e.g., natural disasters, terrorist political instability—considerably instability—considerably influ- TTS of its facilities (the weakest link). terrorist attacks, political influterrorist attacks, political instability—considerably influCopyright © 2016, 2016 IFAC 41 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 41 Copyright ©under 2016 responsibility IFAC 41 Control. Peer review of International Federation of Automatic Copyright © 2016 IFAC 41 10.1016/j.ifacol.2016.07.547
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There are several planning decisions in supply chains that influence the robustness. For supplier selection, when the decision is made for the long term, single sourcing is very vulnerable. Instead, frequently dual (or even multiple) sourcing is applied—c.f., 2-flexibility from SimchiLevi et al. (2015). The place and level of the inventories are also essential for the robust planning. For example, storing large amount of finished goods might provide safeguards against supply problems, but this is usually a quite expensive solution. Sometimes production capacity buffers and flexibility might be necessary in order to adapt to the increased demand and avoidance of bottlenecks, but this decreases the resource utilization. Logistic decisions— such as choosing the applied ordering policies, frequencies, order quantities and transportation modes—also affect the vulnerability towards disruptions. Further decisions can also indirectly influence robustness, such as the applied forecasting method or the product and part pricing.
Optimization
Risk mitigation
Autonomous systems
Fig. 1. Related research fields ods for integrating robust and coordinated supply chain planning. This paper focuses on the logistic optimization and disregards other related supplementary approaches of the project such as production optimization (Gyulai et al., 2014), lead-time reduction or required information and communication technology.
Numerous practical approaches have been proposed for supply chain risk mitigation focusing on the previously mentioned decision problems, see e.g., Tang (2006) or a recent literature review by Ho et al. (2015). Two of the most well-studied strategies are holding protective inventory and increasing process flexibility. Holding additional inventory is a straightforward way to hedge against disruptions: if the inventory is high enough to cover the demand for the duration of TTR of the disrupted facility, then it will not affect the service level, thus the supply chain can be considered robust. Note that the necessary protective inventory depends only on the TTR, thus the long leadtimes of some suppliers do not increase the required inventory. Unfortunately, holding sufficient buffers can still be very expensive.
2. INDUSTRIAL MOTIVATION The setting of this case study is illustrated on Fig. 2. This supply chain produces electromechanical drives and its studied part consists of four stakeholders: the distribution centre (DC), the manufacturer, the inventory hub (IH) and a supplier of parts. The task of the DC is to provide the required electromechanical drives for the customers. In order to do this, it needs to make long-term (2-3 years) demand forecast aggregating across several customer areas and maintain appropriate finished good stock to satisfy the prompt demands. The manufacturer has to provide the required finished goods for the DC. Since the manufacturing process takes in average 50 days, the production is planned for the medium term, i.e., a few months ahead. For providing flexibility for production planning, some finished good buffer is held also at the manufacturer.
The process flexibility on the other hand, means introducing redundancy to the supply chain, e.g., when a plant or production line can build different types of products, thus the demand can be satisfied from different sources. Increasing flexibility can also be costly, and in addition, it also requires additional capacities: if there is no excess capacities in the system, the work cannot be redistributed in case of disturbances.
A required part for the manufacturing is supplied by a factory located in the Far East, which has a very long production time–approximately 8 months—, therefore their production has to be started quite in advance. In the studied case, the supplier is an external company operating in a Make-To-Order (MTO) manner, thus it is the responsibility of the manufacturer to give long-term orders based on demand forecasts. Note that such long leadtime suppliers are also typical in the European automotive industry (Zapp et al., 2012).
Simchi-Levi et al. (2015) suggests that protective inventory and process flexibility should be combined in order to provide sufficient robustness but also keep costs as low as possible. They point out that the probability of some supply chain risk are very difficult to estimate, furthermore, the resulted stochastic models are computationally rarely tractable. Therefore they suggest using a robust optimization approach by defining uncertainty sets for the uncertain parameters. They also suggest considering the worst-case possibility that helps identifying the vulnerabilities of a supply chain.
The transportation from the supplier to the IH also takes rather long time. The default transportation mode is by ship which takes 2.5 months, therefore the transportation also has to be planned in advance. In case of unexpected shortage however, a faster transportation alternative by plane can be chosen. By using air transportation the duration can be reduced to 3 weeks, but due to its high cost, only applied in emergency situations.
As we have just seen, robust supply chain planning is located at the intersection of optimisation and risk mitigation. Similarly, the supply chain coordination is at the intersection of (distributed) optimisation and autonomous systems. This idea is illustrated on Fig. 1. Considering robust planning and coordination together in supply chains is still a relatively unexplored research field (Lu et al., 2015). The goal of this paper is to outline the research directions for industrially relevant and applicable meth-
Since the inventory space at the manufacturing site is limited, the storage of the parts between the supplier and the manufacturer takes place at an IH. The IH is located close to the manufacturing site managed by an external service provider collaborating with the manufacturer. Besides the storage of the parts, the IH is responsible for choosing the transportation mode from the supplier and providing the 42
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43
Long-term order Long-term forecast, short term demand
Inventory level
Prod. status
Supplier
Information flow
Manufacturer
Inventory Hub
Material flow
Distribution Centre
Fig. 2. Supply chain of the case study required parts for the manufacturer, who only maintains a small inventory of parts.
θi ∈ { 1, 2, 3, . . . }—which covers the demand for Ti time. Fig. 4 illustrates the expected inventory positions for the first two stages, i.e., the inventory level plus the ordered items.
The primary key performance indicators (KPIs) for the supply chain are delivery time (for low-runner customised products), quality and customer satisfaction (on-time delivery for high-runner standardised products). Note that these KPIs measure the performance of the whole supply chain and disregard the viewpoint of the different stakeholders described above. Therefore further KPIs should be used—such as cost, inventory level, number of reconfigurations/setups, required investments, resource utilization— in order to measure the performance and efficiency of the whole chain as well as its members. Since the survey conducted in the project pointed out that the logistic (inventory and transportation) costs are very high compared to the manufacturing expenses, the goal of this study is to provide an approach for optimizing these costs while maintaining robustness and the required service level towards the end-customers.
3.1 Computing the reorder point The reorder point should be determined in such a way that it would cover the demand until the order arrives, i.e., the demand during the lead-time. According to Simchi-Levi et al. (2000), the reorder point is the average demand during the lead-time plus a safety stock to handle the uncertainty in the demand. Assuming √ normal distribution, this yields si = µLi + F −1 (α)σ Li , where F is the cumulative standard normal distribution and α is the required service level. 3.2 Computing the order quantities Traditionally, supply chain decisions are made in a hierarchical manner: the first stage decides its optimal Q1 order quantity, then makes its orders. After that the second stage makes its decisions, and so on, upwards the supply chain. We call this decomposed planning. While this approach is very simple and easy to implement, the problem with it is that a decision introduces constraints to the upstream planning, which may cause additional costs, and eventually inefficiency in the overall supply chain (Egri et al., 2011).
3. PROBLEM FORMULATION In this section we formulate a model for the above described logistic optimization problem. For the long-term we assume static demand, but the approach remains similar in the dynamic case, too. We consider a serial supply chain with n stages, where the nodes represent inventories and the links between them are either production or transportation operations. Inventory can be held at each node with different hi unit holding costs. The market demand is stochastic with mean µ and expected value σ, but the Li lead-times between the nodes are deterministic. We also consider that the production and transportation incurs Ki fixed costs. The studied supply chain in this formulation is illustrated on Fig. 3.
Instead of the decomposed planning, we apply a multiechelon model for considering the average cost of the whole supply chain: n hi µ(Ti − Ti−1 ) Ki , (1) + C(T1 , . . . , Tn ) = Ti 2 i=1 where T0 = 0. When i = 1, this yields the cost used in the EOQ model; while for i > 1, the terms reflect to the inventory shape in the right side of Fig. 4.
Since there are fixed costs involved, we cannot use the basestock model as in Egri (2012). Instead, we assume the first stage considers continuous stochastic demand, therefore applies the standard (s, Q) policy with the Economic Order Quantity (EOQ) model (Harris, 1913). Accordingly, it determines the s1 level of reorder point, and as the inventory position drops to s1 , orders Q1 products—which covers the demand approximately for T1 = µ/Q1 time.
Then we have the following optimization problem: min C(T1 , . . . , Tn )
(2)
s.t. Ti = θi Ti−1
According to the model of Muckstadt and Roundy (1993), the other stages (stage i) take the order quantity from the previous stage (Qi−1 ), and use dynamic lot sizing method together with safety stocks. This results in reorder point si and order quantity Qi —which equals to θi Qi−1 for some
Ti ≥ 0
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i ∈ { 2, . . . , n }
(3)
i ∈ { 1, . . . , n }
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i ∈ { 1, . . . , n }
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Supplier production + Transportation
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Transportation
IH
L3, K3
h4
Production
L2, K2
MP
h3
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L1, K1
MF
h2
DC
h1
Fig. 3. Example supply chain model for the case studied (IH: inventory hub, MP: manufacturer’s part inventory, MF: manufacturer’s finished goods inventory, DC: distribution centre) Inventory
Inventory T1
T1
Q1
T2
Q1
Q 2 - Q1
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Fig. 4. Expected inventory positions of stages 1 and 2 demand fluctuation. The model described in the previous subsections therefore helps to estimate the medium-term costs assuming different supply chain configurations, hence it also supports the strategic level decision making.
This is a non-convex mixed integer nonlinear programming (MINLP) problem, whose exact solution is hard to compute, therefore usually an approximation algorithm is used (Muckstadt and Roundy, 1993). After having the quasioptimal Ti values, the order quantities can be straightforwardly computed with Qi = µTi . Note that in case of dynamic demand forecast, the algorithm of Zangwill (1969) can be applied for solving the multi-echelon lotsizing problem.
Since the possibilities of process flexibility in our use case are limited, we focus here on determining the required protective inventories for providing robustness. For each edge i in the supply chain model we have to determine T T Ri , i.e., the time within edge i can be recovered after a disruption. Similarly to the reorder point, the protective inventory at the end of edge i can be computed with √ the following formula: µT T Ri + F −1 (α)σ T T Ri , which is used as a safety buffer until edge i is recovered.
3.3 Determining the transportation mode As we have seen, the transportation between the supplier and the IH has two possibilities: by water or by air. Choosing the latter drastically reduces the lead-time, which results in lower reorder point, but in higher fixed cost. These two alternatives result in two instances of the optimization problem formulated above, which can be solved separately and compared according the different KPIs.
Note that the protective inventory at the IH should consider only the TTR of the supplier, since in case of a shipment failure, there is an alternative transportation mode. Without the possibility of the air transportation, the maximum TTR of the supplier and the shipment should have been taken into account instead.
In practice, the difference between the costs of water and air transportation is so huge, that the IH chooses water shipment whenever possible. Therefore the longer and cheaper transportation mode is considered in the above optimization. However, the quicker transportation mode can be used as a protection tool against shortages: whenever the IH observes that increased demand shall cause stockout, it can change the transportation of the already ordered and produced parts in order to speed up supply.
4. COORDINATION As we have previously seen, the main objective for the supply chain relates to the customer satisfaction. In this aspect, similar results can be provided by completely different plans. For example, the service level can be guaranteed by high end-product inventories, or by investing into new, high speed production equipment, or by ensuring fast replenishment by using air transportation. Even though all of these might provide the required service level, and their costs might be similar, these costs are distributed differently between the stakeholders.
3.4 Designing for robustness In the previous subsections we have introduced a planning framework which can be applied for supporting mediumand short-term supply chain decisions assuming a given chain. We have considered uncertain demand and determined the necessary safety stocks to hedge against the
Coordination considers the supply chain planning as a distributed decision making problem. Generally, a coordination mechanism aims at aligning the objectives of the different stakeholders with the global supply chain objective. Therefore we now overview the decisions and costs 44
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cooperative game theory. Calculating the Shapley value however usually involves solving a series of mathematical programming problems, thus might be practically inappropriate when the number of the participants is large.
of the stakeholders of our case study. (Since the supplier is an external company not involved in the project, we enumerate only the other participants.) Table 1. The decentralised setting IH Manuf.
DC
Decision transportation mode transportation schedule long-term orders production plan min/max part inventory transportation to DC forecasts short-term orders
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4.2 Coordination by mechanism design
Cost inventory transportation production transportation to DC inventory
In case of incomplete information—e.g., when some information (such as the private cost parameters) are not known by all the stakeholders—mechanism design can help in the coordination. For example, the Vickrey-ClarkeGroves (VCG) mechanism has been designed to inspire the individual participants to share their private information truthfully, and applies a similar concept of marginal contribution as the Shapley value. In Egri (2012) VCG mechanisms were used to coordinate inventory decisions in a supply chain where the inventory holding costs and the lead-times were private information of the corresponding decision makers—but there was assumed to be no fixed costs.
inventory forecasting
It can be seen that the decisions not only affect the decision makers, but the other stakeholders, too. For example, if the manufacturer orders too much products, that causes high inventory levels (and costs) at the IH; on the other hand, if the ordered quantity is not enough to cover the demand, the IH might have to use the expensive air transportation in order to speed up the supply. The aim of coordination mechanisms is to guarantee that the autonomous decision makers follow the globally optimal supply plan and to fairly redistribute the occurred costs among the collaborating stakeholders. Sometimes achieving the exact optimal solution is not realistic, thus in a weaker sense, coordination should result in Pareto-improvement compared to some baseline plan, such as the decomposed solution (see Section 3.2). The applied tools for achieving coordination usually include novel business models, special contracts (e.g., buyback) and sharing the benefit of the cooperation with specialized payment schemes (Gao, 2015).
Although VCG mechanisms result in globally optimal plans even with autonomous decision makers and private information, they have some properties that make them difficult to apply in the practice of supply chain coordination: • Usually an independent entity is required to collect all information and do the planning. • An external budget is needed for the mechanism. • When the optimization is done by an approximation algorithm—as it was suggested above for the multiechelon inventory planning—the VCG does not provide the appropriate incentive to cooperate. When the private information are statistical distributions of random variables which can be later evaluated with their realized values—for example in case of demand forecasts— then information elicitation mechanisms can be applied which avoid the above mentioned drawbacks of VCG. For example, Egri (2015) presents such a model, which in supply networks leads to the widespread practical ideas of vendor managed inventory (VMI) and risk pooling.
4.1 Decision support for coordination In this project we aim at the analysis of the distributed optimization in order to support negotiation among the stakeholders. For this reason, we suggest generating different supply chain scenarios and compute the resulted costs, inventory levels, resource utilizations and other local KPIs for each stages. This helps quantifying how much compensation is needed for the stakeholders to change their behaviour. For example, with appropriate quantity discounts a buyer can be inspired to increase the order quantities, i.e., the discount helps to partially redistribute the benefit—caused by the increased order quantity—from the supplier to the buyer.
Another approach is to apply an iterative mechanism, which may not result in globally optimal solution, but can improve efficiency compared to a baseline solution, e.g., the decomposed planning solution. Such model was presented in Egri et al. (2011), where adjacent stages in the chain applied a feedback mechanism called dynamic supply loop with benefit balancing in order to provide a possibility of collaboratively improving supply chain planning considering standard ERP lot-sizing policies. A similar coordination model was compared to different other solutions—namely the decomposed (non-cooperative), the integrated (cooperative) and the bilevel—in Kov´ acs et al. (2013). While the previously mentioned models provide only one feedback loop and relatively simple planning problems, there are also multi-step iterative mechanisms for collaborative planning tasks (Albrecht, 2010).
In addition, one can also take the total cost of these different plans. Specifically, if we compare the optimal solution of the (non-cooperative) decomposed decision model and the (cooperative) multi-echelon decision model described above, we can get the so-called Price of Anarchy (PoA) that measures how much benefit can be gained from cooperation (Nisan et al., 2007). Similarly, one can compare non-robust plans and plans with different levels of robustness. This measures the price of robustness and that who pays this price according to the given plan.
5. CASE STUDY
Eventually, the fair redistribution of the benefit can be based on the contribution to the supply chain, which can be measured applying the Shapley value concept of the
In this section we illustrate the above described analysis considering one of the industrial partners in the project 45
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THK Japan-France illustration
Egri, P. (2012). Safety stock placement in non-cooperative supply chains. In Proc. of the ECAI 2012 Workshop on Artificial Intelligence and Logistics, 31–36. Egri, P., D¨oring, A., Timm, T., and V´ancza, J. (2011). Collaborative planning with benefit balancing in dynamic supply loops. CIRP Journal of Manufacturing Science and Technology, 4(3), 226–233. Egri, P. (2015). Information elicitation for aggregate demand prediction with costly forecasting. Autonomous Agents and Multi-Agent Systems, in print. Gao, L. (2015). Collaborative forecasting, inventory hedging and contract coordination in dynamic supply risk management. European Journal of Operational Research, 245(1), 133–145. Gyulai, D., K´ad´ar, B., Kov´acs, A., and Monostori, L. (2014). Capacity management for assembly systems with dedicated and reconfigurable resources. CIRP Annals - Manufacturing Technology, 63(1), 457–460. Harris, F.W. (1913). How many parts to make at once. Factory: The Magazine of Management, 10(2), 135–136, 152. Ho, W., Zheng, T., Yildiz, H., and Talluri, S. (2015). Supply chain risk management: a literature review. International Journal of Production Research, 53(16), 5031–5069. Kov´acs, A., Egri, P., Kis, T., and V´ancza, J. (2013). Inventory control in supply chains: Alternative approaches to a two-stage lot-sizing problem. International Journal of Production Economics, 143(2), 385 – 394. Lu, M., Sethi, S., and Yan, H. (2015). Robustness of supply chain coordination contracts: Taxonomy, examples, and structural results. Available at http://dx.doi.org/10.2139/ssrn.1864548. Muckstadt, J. and Roundy, R.O. (1993). Analysis of multistage production systems. In S. Graves, A.R. Kan, and P. Zipkin (eds.), Logistics of production and inventory, volume 4 of Handbooks in Operations Research and Management Science, 59–131. Elsevier. ´ and Vazirani, Nisan, N., Roughgarden, T., Tardos, E., V.V. (eds.) (2007). Algorithmic Game Theory. Cambridge University Press. Simchi-Levi, D. (2010). Operation Rules – Delivering Customer Value through Flexible Operations. MIT Press. Simchi-Levi, D., Kaminsky, P., and Simchi-Levi, E. (2000). Designing and managing the supply chain: Concepts, strategies, and cases. McGraw – Hill. Simchi-Levi, D., Wang, H., and Wei, Y. (2015). Increasing supply chain robustness through process flexibility and inventory. Available at http://dx.doi.org/10.2139/ssrn.2433175. Tang, C.S. (2006). Perspectives in supply chain risk management. International Journal of Production Economics, 103(2), 451–488. Zangwill, W.I. (1969). A backlogging model and a multiechelon model of a dynamic economic lot size production system-a network approach. Man. Sci., 15(9), 506–527. Zapp, M., Forster, C., Verl, A., and Bauernhansl, T. (2012). A reference model for collaborative capacity planning between automotive and semiconductor industry. Procedia CIRP, 3, 155–160.
15,000 10,000 Cost difference
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Fig. 5. Comparison of alternative supply chain configurations and one of its suppliers from the Far East. We have performed numerical analysis comparing two scenarios: (i) continue purchasing from this supplier or (ii) switch to a European supplier providing higher component prices. Fig. 5 shows the estimated difference in the purchasing cost—which is paid by the manufacturer—and the logistic costs—which is paid by the IH for a specific component. It can be seen that the savings in the logistic cost surpass the effect of the increased purchasing cost, therefore it is beneficial to change despite being disadvantageous to the manufacturer. In order to motivate the manufacturer, the IH should offer a compensation by sharing its benefit determined by the numerical study. A further possible scenario could be to apply a dual sourcing and therefore increasing process flexibility. This would necessitate additional qualitative risk analysis besides considering costs, i.e., whether the potential risks of purchasing from the FarPage East 1 surpass the benefit of having an alternative supplier or not. 6. CONCLUSIONS In this paper we have outlined a research agenda for integrating robust planning and coordination in supply chains. We have presented a case study of an industrial supply chain, concentrating on the long lead-time supplier which is one of the most serious sources of difficulties. We have focused on inventory optimization taking specifically robustness into account and also illustrated possible coordination approaches that consider the supply chain stakeholders as autonomous decision makers. As for future work, we will develop a multiagent simulation tool for decision support integrated into the RobustPlaNet cockpit. ACKNOWLEDGEMENTS This work has been supported by the European Union 7th Framework Programme Project No. NMP 2013-609087, Shock-robust Design of Plants and their Supply Chain Networks (RobustPlaNet) and by the Hungarian Scientific Research Fund (OTKA), Grant No. 113038. REFERENCES Albrecht, M. (2010). Supply Chain Coordination Mechanisms – New Approaches for Collaborative Planning. Springer-Verlag, Berlin Heidelberg. 46