Possible cost savings due to stock and demand pooling at a central warehouse cannot be realized, when distribution warehouses fulfill spare part requests by ...
Source Selection in Spare Part Supply K. Tracht1, M. Mederer2, D. Schneider1 Bremen Institute for Mechanical Engineering (bime), University of Bremen, Germany 2 2 m hycon, Oberolm, Germany
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Abstract Spare part supply for high-tech machines is realized with multi-echelon closed-loop supply chains, in which spare parts are repaired and put back into stock after removal from a broken machine. The failure rate of parts is Poisson distributed. Spare parts are kept in stock in distribution warehouses close to the operating locations of the machines and in one central warehouse, replenishing the distribution warehouses. A requested spare part can be delivered from different warehouses. The location of the source warehouse impacts delivery time to the customers and replenishment deliveries to distribution warehouses. This paper investigates strategies for selecting the part source. Keywords: logistics, simulation, maintenance
1 INTRODUCTION 1.1 Problem Statement Operators of high-tech machines need quick and reliable spare part supply, if an unexpected part failure occurs. For fast spare part supply, distribution warehouses, which are located close to the machines, hold stock. Each machine is assigned to the closest distribution warehouse and is provided with spare parts from that warehouse in case of part failure. After removal from the machine the broken spare part is sent to a repair shop, repaired and put back into stock of the central warehouse. Stock of the distribution warehouse is refilled by replenishment deliveries from a central warehouse. The system considered in this investigation is a two echelon closedloop supply chain for repairable items. Possible cost savings due to stock and demand pooling at a central warehouse cannot be realized, when distribution warehouses fulfill spare part requests by default. Delivering directly from the central warehouse without routing via a distribution warehouse furthermore reduces total transportation distances and times. Effects of delivering from the central warehouse are analyzed in this paper for a given set of minimum, suboptimal stock levels in the warehouses. Spare parts will only be delivered from the distribution warehouse, if transportation time from the central warehouse is too long to arrive at its destination before the due date. 1.2 Course of Investigation The literature review presents papers dealing with supply chains, stock allocation and lot sizing problems. The supply chain considered in this paper, the corresponding simulation model, and the utilized cost functions are introduced in the succeeding chapter. With the simulation model total costs of the supply chain for two different source selection strategies are compared. Results are summarized in the conclusion. 2 LITERATURE REVIEW Closed-loop and open loop supply chains including multiechelon problems have been investigated extensively. Güllü and Heijden present and compare optimal stock
allocation policies in multi-echelon supply chains [1][2]. Hjiaghaei-Keshteli and Sajadifar compare cost functions, assuming Poisson distributed demand, constant transportation times and three echelons [3]. They take into account transport delays. Graves finds that most of the stock should be stored at the distribution warehouses in the lower echelon [4]. Kalchschmidt, Zotteri, and Verganti investigate inventory management in a multiechelon supply chain, taking into account lumpy demand and providing solutions for different industrial sectors [5]. Kumar, Tiwari, and Babiceanu minimize supply chain costs by taking into account supply chain risks [6]. They consider costs for late shipments, exchange rates, custom delays, quality control problems, logistics and transport breakdowns. Gou and Liang develop a joint inventory model for an open loop reverse supply chain [7]. Jaruphongsa, Cetinkaya and Lee solve analytically a dynamic lot sizing problem under consideration of time windows and limited warehouse capacity [8]. Terzi and Cavalieri summarize reasons for using simulation models when analyzing closed-loop supply chains [9]. Tracht, Schneider, and Schuh improve performance by modelling the closed-loop supply chain as feedback control system and introducing trackpoints for information flow. [10] None of the publications, however, has considered priority rules when selecting a source warehouse in a multiechelon supply chain for repairable items. The lack of information on that topic was motivation for the work presented in this paper. 3 CLOSED-LOOP SUPPLY CHAIN The system under investigation is a closed-loop supply chain for quick and reliable spare part supply. It was set up to avoid extensive downtimes of the machines, when a part fails unexpectedly. The major elements of the supply chain are spare part stock, machines, and a repair shop for repairing spare parts that are removed from the machines.
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Figure 1: Two-echelon closed loop supply chain for repairable items. Figure 1 shows the two-echelon supply chain with a central warehouse and several distribution warehouses. The central warehouse (cw) receives the parts leaving the repair shop. Six distribution warehouses (dw) are located close to the machines, for quick spare parts supply in case of part failure. A requested spare part is delivered from the distribution warehouse, which is assigned to the requesting location. In case of a spare part request, the part is taken from stock of a distribution warehouse and shipped to the location of the broken machine. The part arriving from stock replaces the broken one in the machine. The broken part is sent to the repair shop, repaired, and put back into stock in the central warehouse. After delivery the distribution warehouse is replenished by the central warehouse to maintain minimum stock levels. If there is more than one replenishment request by the distribution warehouses, the oldest request will be served first. Allowing transshipments, the spare part will be delivered by the central warehouse or another distribution warehouse, if the assigned warehouse is out of stock. As delivery lead time from the central warehouse or other distribution warehouses to the requesting location is longer than from the assigned distribution warehouse, the spare part arrives at its destination too late. The spare part is loaned from a competitor during the transportation time of the part in order to avoid downtimes of the machines. It is returned as soon as it arrives at the distribution warehouse. These loan costs are called transport loan costs. The spare part is also loaned, if all the warehouses are out of stock. The spare part will be returned to the lender as soon as a repaired spare part from the shop arrives at the central warehouse. These loan costs are called inventory loan costs. In both cases loan costs are incurred daily, accumulating during the loan duration. Prioritizing the central warehouse, impacts inventory loan costs and transport loan costs. A comparison of this strategy to the initial setup is subject of investigation. 4 SIMULATION MODEL 4.1 Model Features A discrete event simulation model of the closed-loop supply chain with replenishments is utilized in order to analyze the effects of delivering from the central warehouse. Loan costs are calculated once a day, thus loaning only a few hours will incur costs for the whole day. Demand for the spare parts at the distribution warehouses
is Poisson distributed. Every warehouse holds minimum stock for supplying spare parts in emergency cases. The repair time in the repair shop is exponentially distributed. Transportation times between warehouses, to the machines and from and to the repair shop are taken into account and follow a triangular distribution. Total costs and service levels are used to evaluate supply chain performance. 4.2 Cost Functions The total costs ct, which are subject of investigation in this paper, consist of capital costs cc and loan costs cl.
ct = cc + cl
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The capital costs cc depend on the purchase price cp of a spare part, the number of spare parts in the supply chain np, and the depreciation pd. cc (c p , n p , pd )
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cc = capital costs cp = purchase price of spare part np = number of spare parts in the supply chain pd = depreciation The loan costs cl are a function of the purchasing price cp, the number of spare parts np, the demand d, and the transportation times tt. cl (c p , n p , d, t t )
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cl = loan costs d = demand tt = transportation time Loan costs are subdivided in inventory loan costs cli and transport loan costs clt, depending on whether the warehouses are of stock or the transportation time is too long.
cl = cli + clt
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Impacting parameters for both types of loan costs follow equation (3). Compared to the loan costs cl handling and transportation costs are negligible and will not be considered. 4.3 Service Level The service level is an indicator for supply chain performance, measuring the probability of a stock out. It equals the percentage of the requests that are fulfilled by stock in the warehouses. For example, if all the requests are served from stock, the service level is 100%. If all the warehouses are out of stock and the spare part has to be to be loaned, the service level is lowered. Spare parts that are in stock but arrive too late, causing a transport loan, do not impact the service level. 4.4 Source Selection In the initial setup spare part request are fulfilled by the assigned distribution warehouse. Delivering spare parts from the central warehouse as primary source can improve supply chain performance, by exploiting the pooling effect at the central warehouse and reducing total transportation times. The greater the number of requests per warehouse is, the fewer spare parts per request are necessary on average. Total transportation distances and times decrease, because every delivery from a distribution warehouse generates a replenishment delivery from the central warehouse. Delivering directly from the central warehouse is shorter than a detour via a distribution warehouse. When serving a request with urgent due date, delivering from the central warehouse can cause transportation
times that are too long to keep the due date. The part is delivered by the distribution warehouse, because of shorter transportation time. All distribution warehouses are taken into account, but usually only the closest distribution warehouse will be the one to deliver on time. With the simulation model introduced in the following the effects of prioritizing delivery from the central warehouse are analyzed. Using the distribution warehouse as primary source will be called scenario 1, using the central warehouse as primary source will be called scenario 2. Minimum stock levels at the warehouses impact total costs. For the analysis of both scenarios the same minimum stock levels at the warehouses are assumed. In both scenarios minimum stock levels are not cost optimal. Impact on supply chain performance and reduction of total costs can be expected, when optimizing stock levels in warehouses. This optimization is beyond the scope of this work and will be focus of further research activities.
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0 20 21 22 23 24 25 26 27 28 29 30 number of spare parts np [pcs] capital costs transport loan costs inventory loan costs Figure 3: Costs of scenario 2. Figure 2 shows capital costs, inventory loan costs, and transport loan costs, depending on the number of spare parts np of scenario 1. For loan costs and capital costs only mean values are given, omitting confidence intervals for simplicity. The confidence interval for total costs ct, using a 95 % confidence coefficient, is displayed at the top of every bar. The top of each bar equals the expected mean value of total costs ct. Increasing np, capital costs cc rise and inventory loan costs lower. Transport loan cost slightly decrease with growing np. Minimum mean total cost at the given minimum stock levels are realized with np=28. Figure 3 shows the mean costs of the different cost types over np of scenario 2. Total costs, inventory loan costs, and transport loan cost are very similar to the values of Figure 2. The minimum total cost at the given setting of minimum stock levels is incurred with np=27 spare parts. A comparison of both scenarios is given in Figure 4, displaying costs for scenario 1 at the left hand bar and for scenario 2 at the right hand bar for each value of np. Similar to the figures above the bars equal the mean expected values, and the confidence interval is given for total costs ct only. The service level, whose scale is on the ordinate to the right, is displayed for every np and both scenarios. The corresponding confidence interval also uses a 95 % confidence coefficient. While np23 total cost ct for scenario 2 are lower. Comparing the total cost optima of each scenario, total costs can be reduced by up to 6%, using the central warehouse as primary source.
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SIMULATION RESULTS 80 60 40 20 0 20 21 22 23 24 25 26 27 28 29 30 number of spare parts np [pcs] capital costs transport loan costs inventory loan costs Figure 2: Costs of scenario 1.
A maintenance, repair and overhaul provider of the aviation industry supplies the historical demand level for an electronic aircraft device of the years 2008 and 2009 as input data to the simulation model. The presented results show the effects of two different strategies of source selection for an example of not cost optimal minimum stock levels at the warehouses. Every simulation run is repeated 30 times to generate reliable confidence intervals. To allow for settling of transient effects, measuring of total costs ct and service levels is started on January 01, 2009 one year after simulation start.
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Figure 4: Costs and service level of scenarios 1 and 2.
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Transport loan costs ctl are lower in scenario 2 for every number np of spare parts in the system. Delivering spare parts from the central warehouse, if transportation time is shorter than the remaining time to the due date, fewer spare parts are provided by the distribution warehouse. When requesting a spare part at the distribution warehouse, the probability of stock out is lower, because the majority of the request before was fulfilled by the central warehouse. As fewer spare parts have to be provided by the central warehouse because of a stock out at the distribution warehouse, the transport loan costs, because a spare part from the central warehouse does not arrive on time, decrease. The inventory loan costs are greater in scenario 2 for all np. As fewer parts require transport loans, fewer parts are available in total to fulfill requests, raising probability for stock outs and corresponding inventory loan costs. The sum of inventory loan costs and transport loan costs is lower for scenario 2, if np>23. For the same reason service levels in scenario 2 are slightly lower for np26 spare part stock is sufficient to serve almost every request. Overlapping confidence intervals require further investigation for statistically significant distinction of service levels. Total costs ct of scenario 2 are either equal or lower than in scenario 1. The greater np, the greater is the reduction of total costs by providing requested spare parts from the central warehouse. Prioritizing the central warehouse for delivery, more spare part remain at the distribution warehouses, raising the probability of a spare part in stock in a distribution warehouse. An urgent request with little remaining time until the due date can more likely be fulfilled from a distribution warehouse.
6 CONCLUSION This paper presents an analysis of selecting a spare parts supplying source in a closed-loop two-echelon supply chain for repairable items with suboptimal minimum stock levels. The results are generated with a discrete event simulation model of the supply chain. In scenario 1 spare parts are delivered from the assigned distribution warehouse. In scenario 2 spare parts are delivered from the central warehouse, if the transportation time is shorter than the remaining time before the due date. Minimum stock levels at the warehouses are equal in both scenarios and not cost optimal. Comparison of the scenarios shows that at the number of spare parts np with lowest costs in each scenario cost savings of up to 6 % can be realized by scenario 2. The lowest total costs are incurred with np=28 in scenario 1 and np=27 in scenario 2. At these values for np service levels are almost equal in both scenarios. Changing the priority rules when selecting a source warehouse, impacts total costs. The model of the closedloop supply chain with an example for not cost optimal minimum stock levels shows that total costs are lower, if spare parts are delivered from a central warehouse, when keeping the delivery date. Further improvement of supply chain performance and reduction of total costs are expected, when optimizing minimum stock levels at the warehouses. An analysis of the source selection strategy with cost optimal stock levels will be subject of future research activities.
7 ACKNOWLEDGEMENTS The results presented in this paper were developed in the research project dLP – dynamic LRU planning (03CL02H). dLP is part of the Aviation Cluster Metropolitan Region Hamburg funded by the German Federal Ministry of Education and Research (BMBF). 8 REFERENCES [1] Güllü R, Erkip N, 2003, Optimal Allocation Policies in a Two-Echelon Inventory Problem with fixed Shipment Cost, International Journal of Production Economics, 46-47, p. 311-321. [2] van der Heijden, M.C., Diks, E.B., de Kok, A.G., 1997, Stock Allocation in General Multi-Echelon Distribution Systems with (R, S) Order-up-toPolicies, International Journal of Production Economics, 49:2, p.157-174. [3] Hijiaghaei-Keshteli, M., Sajadifar, S. M., 2010, Deriving the cost function for a class of threeechelon inventory system with N-retailers and onefor-one ordering policy, The International Journal of Advanced Manufacturing Technology, 50:1, p. 343352. [4] Graves, S., 1996, A Multiechelon Inventory Model with Fixed Replenishment Intervals, Management Science, Vol. 42, No. 1, pp. 1-18. [5] Kalchschmidt, M., Zotteri, G., Verganti, R., 2003, Inventory Management in a Multi-Echelon Spare Parts Supply Chain, International Journal of Production Economics, p. 81-82. [6] Kumar, S., Tiwari, M., Babiceanu, R., 2009, Minimisation of Supply Chain Costs with embedded Risk Using Computational Intelligence Approaches, International Journal of Production Research, 48:13, p. 3717-3739. [7] Gou, Q., Liang, L. Huang, Z. Xu, C., 2008, A Joint Inventory Model for an Open-Loop Reverse Supply Chain, International Journal of Production Economics, p. 28-42. [8] Jaruphongsa, W. Cetinkaya, S., Lee, C., Warehouse Space Capacity and Delivery Time Window Considerations in Dynamic Lot-Sizing for a Simple Supply Chain, International Journal of Production Economics, 2004, p. 169-180. [9] Terzi, S., Cavalieri, S., 2004, Simulation in the Supply Chain Context: a Survey, Computers in Industry, 53: 3-16. [10] Tracht, K., Schneider, D. Schuh, P., 2010, A Feedback Control System for Spare Parts Logistic Networks in the Field of Civil Aviation, 7th CIRP International Conference on Intelligent Computation in Manufacturing Engineering, ICME 10.
