- Email: [email protected]
Order Crossovers in an Automotive Supply Chain
7th IFAC Conference on Manufacturing Modelling, Management, and Control International Federation of Automatic Control June 19-21, 2013. Saint Petersburg, Russia
Order Crossovers in an Automotive Supply Chain J. Riezebos University of Groningen, Faculty of Economics and Business, The Netherlands (Tel:+31503634853; e-mail:[email protected]). Abstract: Order crossovers occur when the delivery of orders is not in sequence with the issuing of orders. In automotive supply chains this may occur due to transportation mode choices, multiple suppliers, asynchronous capacity management at the suppliers, supply chain design choices, and speed differences in long supply chains. This study examines the problem that a Dutch first-tier supplier to the automotive industry in Europe faces when ordering items in Asia. Their information system and procurement procedures do not take the possibility of order crossovers into account. We have examined the consequences of neglecting these order crossovers with a situation where the occurrence of such order crossovers is used to advance the supply chain management and reduce the overall costs for the first-tier supplier. The difference between a non-crossover policy and our new model shows an average cost improvement of almost 6%. The proposed model is an extension of MRP ordering procedures and is build in an Excel spreadsheet.
has been neglected in this stream of literature, although it may play an important role in practice. This problem is denoted as order crossovers. An order crossover occurs if two orders do not arrive in the sequence in which they were issued. According to Riezebos (2006) we may distinguish between various types of order crossovers, depending on the underlying process that causes this phenomenon to occur. He distinguishes, amongst others, between random and expected order crossovers. In case of random order crossovers, stochastic fluctuations in lead times may sometimes cause a later order to arrive before an earlier issued order. In case of expected order crossovers, fluctuations in lead times are not random, but known in advance. These dynamic lead time changes are known at the moment of ordering. It is the latter type of order crossovers that may occur in responsiveness strategies that consider transportation mode changes.
1. INTRODUCTION Suppliers in automotive supply chains are under high pressure. Relatively small batches of high-quality parts are frequently delivered according to tight schedules in order to achieve a responsive supply chain. The responsiveness is important as the OEM’s face highly volatile customer behaviour. Their first tier suppliers should be able to deliver quickly when demanded, to chase the demand patterns faced by the OEM. However, they should also be as cost-efficient as possible. In order to reduce costs, parts are often bought in low cost countries and delivered through container transport over sea. This causes long supply lead times and reduces the responsiveness. Hence, these first-tier suppliers may have to use additional strategies to increase responsiveness when needed.
This paper will explore the occurrence of order crossovers in an automotive supply chain of a first-tier supplier to the automotive industry in Europe. The Dutch supplier orders items in Asia. We first examine whether their information system and procurement procedures do take the possibility of order crossovers into account. Next, we examine the consequences of neglecting these order crossovers with a situation where the occurrence of such order crossovers is used to advance the supply chain management and reduce the overall costs for the first tier supplier. The cost effect depends on the magnitude of the holding costs and transportation costs.
Two well-known strategies to increase the responsiveness focus on the supply network. First, using more than one second-tier supplier for the same component. (Minner, 2003) provides an excellent review of multiple-supplier inventory models, amongst which models that describe suppliers with different lead times. A major problem with this strategy is how to assure the same quality. Even in case the second-tier supplier has two plants (one located nearby the first-tier supplier, one located in a low cost country) and uses the same quality management system, parts may not be of the same quality. Therefore, the second strategy to increase responsiveness is frequently applied. That strategy selects a different transportation mode with a different expected speed and cost performance in case a quicker response is required. Transportation mode changes have also extensively been studied in literature (see e.g., Alp et al., 2003; Muharremoglu and Tsitsiklis, 2003). However, there is a very specific problem associated with transportation mode changes which 978-3-902823-35-9/2013 © IFAC
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10.3182/20130619-3-RU-3018.00249
2013 IFAC MIM June 19-21, 2013. Saint Petersburg, Russia
postpone the transportation mode decision. In this paper, we will use the model of Kiesmüller et al. (2005) as a reference model for studying the effect of order crossovers in automotive supply chains in case of transportation mode choices. Note that by taking the manufacturing time equal to zero, the model results in the classic model of transportation mode changes (where suppliers are assumed to deliver from stock).
2. LITERATURE REVIEW 2.1 Issues in modern supply chains Recent research on geographically dispersed supply chains (Lorentz et al., 2011) shows that the more geographically dispersed a supply network is, the more likely it is that structure-related development priorities will be chosen. Such structural development efforts aim to reduce uncertainty and to improve the reliability of the international supply chain.
2.3 Inventory order crossovers
Another reason for changes in modern supply chains are the developments in information technology and available intelligent systems to support decision making. A recent review of operations research literature (Crainic et al., 2009) shows that performance of intelligent freight-transportation systems improves due to enabling technologies, such as electronic data interchange, advanced decision-support software, and better control in fields such as vehicle operations, advanced fleet management, and city logistics.
In the field of inventory control, order crossovers were first identified by Hadley and Whitin (1963) as an anomalous effect that caused the regular mathematical models not to be applicable. They discussed the class of so-called random order crossovers (Riezebos, 2006), where orders change sequence due to random lead-time fluctuations. The two assumptions that are made in these models, i.e., no order crossings and at the same time independently distributed lead times are mutually contradictory. Since then, several schools of thoughts have emerged that either avoid, neglect or account for random order crossovers in inventory control and supply chain modelling. In Hayya et al. (2008) these schools are respectively labelled as the Zipkin school, the HadleyWhitin school, and the Zalkind school. Examples of recent papers in this class of inventory order crossovers are Hayya and Harrison (2010); Muharremoglu and Yang ( 2010); Hayya et al.(2011) and Srinivasan et al. (2011).
In the European automotive industry, relations between an OEM and its first-tier suppliers –whether they are geographically located in the same country or not– are known to be stable in order to allow them to focus on development and improvement (Ghijsen et al., 2010). However, OEMfirst-tier supplier relationships in the automotive industry differ from other buyer–supplier relationships with respect to power, dependence and the degree of collaboration. Therefore, research on the development of relations with suppliers at other tiers might result in different conclusions, due to the high pressure to perform in these supply chains.
The other main class of order crossovers, expected order crossovers, considers sequence changes that are known beforehand, i.e. at the decision moment. The underlying processes that cause the lead time differences to occur are known at some level of detail. Examples are to select either the standard or the high priority lead time offered by the supplier. When selecting the standard lead time, costs will be lower, but lead times will be longer as the freight transportation will be organised more efficiently, i.e. longer waiting or processing/transportation times before it arrives in its destination or more uncertainty/risk. See e.g. Ganeshan et al. (1999). Examples of recent papers that discuss this class of order crossovers are Muharremoglu and Yang (2010); Riezebos and Gaalman (2009) and Axsäter (2011).
2.2 Transportation mode changes A transportation mode change is just one possible method to achieve a lead time reduction. Problems with different lead times have been studied extensively. These differences may be modelled as the outcome of stochastic processes (i.e., uncertain lead times). Examples of papers in this area are Ramasesh et al. (1991) and Chen and Yu (2005). Others model these differences as dynamic processes. That allows for including knowledge on the expected lead time difference at the moment of issuing an order. See e.g., Jain et al. (2009); Muharremoglu and Tsitsiklis (2003); Riezebos and Gaalman (2009). With respect to transportation mode changes, most papers implicitly assume that the decision to use a specific mode of transport is taken at the moment of order issue (e.g., Blackburn, 2012). If the second-tier supplier delivers from stock, this is a realistic assumption. All activities that the supplier has to undertake, e.g. packaging, expedition, freight insurance, invoicing, customs, et cetera, depend on the knowledge of the transportation mode.
3. HANDLING ORDER CROSSOVERS IN AN AUTOMOTIVE SUPPLY CHAIN This case study describes the appearance of order crossovers in an automotive supply chain. The first-tier supplier of several OEMs in Europe (both car and truck manufacturers) has its global headquarter in the Netherlands. Focus of this study is on the truck segment of the company, where they produce hydraulic components. About 80% of their raw materials are supplied from companies located in Asia. Most of these products consist of steel, which makes the products relatively heavy. For economic reasons, long shipping lead times are preferred over higher transportation costs. However, due to the uncertain demand for some of their products, their inventory policy has to guarantee a specified customer service level, which causes high inventory costs.
However, in case of a second-tier supplier that has to undertake manufacturing tasks as well during the supply lead time, it may be not necessary to provide all information on the required transportation mode at the moment of order issue. Therefore, several papers (e.g., Jain et al. (2009); Kiesmüller et al. (2005)) have examined the possibility to
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The lead time of raw materials is larger than customers require. Lead times of raw materials can be up to 20 weeks.
before the items are available for shipment to the customer. That is the moment to decide on the amount Q1r Q0 r that will make use of the fast transportation mode with remaining lead time L1 . The remainder Q2 r Q0 r Q1r will use the slow transportation mode with remaining lead time L2 L1 .
For fast moving products with constant demand, these long lead times will not affect the customer service level that much, since a proper inventory policy is used to guarantee the required customer service level. Slow moving products with uncertain demand require more attention from management.
Kiesmüller et al. (2005) assume the review period R to be larger or equal to the longest replenishment lead-time for the item. However, in the automotive supply chain, and especially in our case study company, it is rather unrealistic to assume that orders for components are issued with a review period of 5 months. Therefore, we investigate more realistic options where the length of the review period is shorter than the total lead time.
Their current control policy has determined safety stock levels and batch sizes. However, while setting these parameters no attention has been given to the possibility of selecting another transportation mode for a part of the order whenever necessary. By selecting another transportation mode for a part of the order, e.g. by air instead of sea, lead times of some of the items are reduced, hence inventory levels increase, backorder levels decrease, and customer service level increases. The net cost effect is the sum of increased transportation costs, increased holding costs, and reduced backordering costs.
The sequence of events (Fig. 1) is that at the start of a review period delivery batches (if any) arrive, next an order will be issued, and demand for that period occurs, while in the meantime a transportation mode decision is being made, and deliveries take place accordingly.
The company uses fixed review periods, which are part of the contract (and hence negotiated) with the suppliers. At each review moment for each product a new order may be issued. The decision on a new order specifies the amount, quality, and moment of order delivery. We investigated whether postponing the transportation mode decision and reconsidering the review period decision could improve the cost performance of the company. In the following section, the methodology will be described. A dual supply model to analyse the performance effect of the transportation mode and order splitting decision is derived from the dual supply model by Kiesmüller et al. (2005) where the transportation mode decision is postponed until the supplier finished manufacturing the order.
Fig. 1: Sequence of events with long review period Now, Fig. 2 and 3 show example schemes if we have a review period shorter than the total lead time.
4. EXAMINING THE EFFECT OF ORDER CROSSOVERS
Order Transportation mode size decision decision
Fast delivery
Slow delivery
4.1 Mathematical model pipeline inventory
In our model we assume that there are two different transportation modes, a fast mode with deterministic lead time L1 and per unit transportation cost c1 , and a slow mode with lead time L2 and per unit transportation cost c2 . The total lead time of an order also includes a constant manufacturing lead time L0 . The demand per time unit Dt is a non-negative random variable. The demand distribution is assumed to be stationary with known mean μ and variance σ2. Demand in disjoint intervals is independently distributed and unsatisfied demand is backordered.
Q0r+1
Q1r Q0r
Q0r+2
Q1r+1
Q2r
Q2r+1 time
0
L0
L0 + L1
R L0 + L2 R+L0
R+L0+L1
2R
R+L0+L2
R
Fig. 2: Example if review period < total lead time Fig. 2 shows a temporary increase of pipeline inventory. There are no order crossovers.
The first-tier supplier reviews the inventory periodically and sends during the rth review period an order of size Q0r to the second-tier supplier. The length of the review period R is assumed to be constant and to be an integer multiple of the chosen time unit t with in total T time units per year. After issuing Q0r a constant amount of time L0 elapses due to manufacturing, packaging and other handling activities
Fig. 3 Order crossovers 77
2013 IFAC MIM June 19-21, 2013. Saint Petersburg, Russia
mode system, which reduces average holding costs in the system. How much lower depends on the cost difference between the slow and fast transportation mode. If there would be no cost difference at all, it should only have to cover demand uncertainty in the interval t nR, t R L0 L2 .
Fig. 3 has a much smaller review period (equal to L0 . We see that the next two ordering decisions have to be taken while nothing has yet arrived. Orders arrive at the moments L0 L1 ; R L0 L1 ; L0 L2 ; R L0 L2 . Therefore, an order crossover takes place. The decision moment for the third arrival was at time L0 , while the decision moment for the second arrival was later, namely at time R L0 . Therefore, these orders cross, a phenomenon which has huge implications for the management of the inventory, as it will occur in every replenishment cycle. Moreover, the total number of order crossovers in a replenishment cycle depends on the length of R, L0 , L1 , and L2 .
The advantage of the availability of a fast transportation mode therefore translates to no demand uncertainty to cope with in the safety stock during a period of length nR. Hence the maximal savings on safety stock are SS k
R L0 L2 R L0 L2 nR , where k is
the parameter for the service level, and the standard deviation of demand per period of length t. The savings on safety stock translate to a yearly holding cost reduction ( hSS ). These savings are higher in case the length of the review period decreases, the lead time difference between slow and fast transportation increases, the standard deviation of demand increases, or the required service level increases.
In order to examine this configuration, we develop a mathematical model. Assume that at time t we are at the start of a review period and we have to decide upon the order size Q0 r . Define Ipt , the inventory position at time t , as the total amount of inventory available for demand satisfaction during the interval t , t L0 L2 . Define Ilt as the inventory
Note that the transportation costs do not necessarily increase, as we only need to use fast transportation mode in case of an exceptional large demand during the first nR periods, i.e. t nR 1 only if demand exceeded SS E Di SS nR . i t
level at time t , where the inventory level may be negative (back order case). Then we have: m L L2 Ipt Ilt i 1 Q0,t iR with m 0 . R
t nR 1 So Q1, nR min Q0, nR , max 0, Dt SS nR , as we i t cannot have more delivered through a fast transport than that we ordered during that review period.
All orders that have been issued before t mR have already arrived in stock (both the slow and fast transportation mode) at or before time t . So we have an expression for the number of orders that have not yet been delivered. Then: n L L1 Q0 r Q1, r i SS ( R L0 L2 ) Ipt with n 2 R i 1 where SS is the safety stock that on average should be available in stock on the moment the slow transport arrives. The new orders have to cover the difference in what we need to have just before the arrival of the next slow transport t R L0 L2 and what we actually will have available due to already issued orders.
4.2 Numerical analysis In order to examine the effect of order crossovers in a twolevel supply chain with postponement of the choice for one of the two available transportation modes, we have set up a simulation study using data from the first-tier supplier. Four items are analysed. Two are so called ‘cylinder bases’. The other two items are ‘reservoirs’, which are needed for the housing of the pump system. We analysed the effect of crossovers and postponing the transportation mode decision until the supplier finished manufacturing. The mean and variance of demand were calculated based on historical data.
The remarkable thing in this formula is that it provides an expression for the number n of crossover orders that will arrive before the next slow transport will arrive. The decision maker should balance the cost of ordering now (and the possibility to involve slow transport with associated lower transportation and holding costs) or ordering in any of the future review periods (up to n) and using fast transportation mode for these orders. This affects the safety stock level required at the moment of arrival of a slow order.
The service level factor that we used was k 1.96 , which would correspond with a cycle service level of 95% in case of normally distributed demand. Holding costs h 25% * P are charged as an annual carrying charge of the price P . Table 1. Item data
In a single transportation mode system, the safety stock guarantees a specified service level by covering for uncertainty in demand during the whole interval t , t R L0 L2 . Due to the option to use the nth fast
Item 1 2 3 4
moving order (i.e. the order that is being issued at time t nR ) to correct for possibly higher demand than expected, the safety stock may be lower than in a single transportation
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Price € 4.11 7.92 2.31 2.28
Weight kg/item 0.81 0.45 0.52 0.52
c1 €/kg 4.91 4.91 4.03 3.20
c2 €/kg 1.55 1.55 0.65 0.25
μ per wk 4.6 4.8 43.1 51.3
σ per wk 12.3 11.0 121.1 101.0
2013 IFAC MIM June 19-21, 2013. Saint Petersburg, Russia
108 items, with a SS equal to 18. The next thing to notice is the behaviour of the system when such a large demand has occurred. In Fig. 4, it takes 18 weeks before an order that is issued to compensate for the large demand has arrived. In Fig. 5, all three orders that have been issued before the large demand occurred and for which the transportation mode has not yet been set will be delivered by air to achieve an inventory level as near as possible to the required safety stock level. This adds transportation costs, but safeguards against backorders, something which has to be avoided in automotive supply chains.
In accordance with the company data, manufacturing lead time L0 =10 weeks, fast transportation L1 =2 weeks and slow transportation L2 =8 weeks. Hence the total replenishment lead time is 18 weeks. We used two different lengths for the review period R (2 and 16 weeks) in order to show the performance effect of these lengths on the transportation and holding costs as well as on the inventory levels. Note that at a review period length of 16 weeks no order crossovers occur, while at a review period length of 2 weeks three orders will cross.
From the results in Table 2 the effect of including order crossovers becomes clear. The first three items clearly benefit from this policy, with cost improvements between 7.7% and 11.8%. The last item faces a cost increase of 4.4%. Its air transportation cost has increased a lot due to a very high demand in one of the first periods. The holding costs decrease drastically for all four items due to the reduced safety stock requirements.
Table 1 shows that the transportation costs are charged per kilogram, but differ per item due to negotiations with the transportation company. Before we show the results for all four items, we present in Fig. 4 and 5 an overview of item one’s inventory position and inventory level for the two review period lengths.
The model has been implemented in a Microsoft Excel worksheet. It is an extension of regular MRP ordering, as it includes an additional row for the fast transportation mode decision on Q1 , L0 periods after the Q0 decision has been taken. Based on the entries in this row, the delivery schedule is modified, showing an (additional) arrival of Q1 with an offset time of L1 periods ahead and the remaining Q0 Q1 with the regular offset time of L2 , counting from the moment the transportation mode decision is taken.
Fig. 4 Inventory position (upper) and level (lower) R=16
5. CONCLUSIONS Based on our analysis of the transportation mode policy in this automotive supply chain, we have suggested a new model to determine the order quantities as well as the part of the batch that should be send through a more expensive and faster transportation mode. This policy makes use of the occurrence of order crossovers. The analysis of four items has shown that on average there is a cost improvement of almost 6%, but this includes a possibility for a cost increase.
Fig. 5 Inventory position (upper) and level (lower) R=2 Table 2. Results
Item 1 2 3 4
R
SS Total c1
Total c2
Total h
Grand % Cost total improve
16 141 0 585.8 305.2 891.0 2 108 121.5 494.8 205.9 822.1 16 126 0 301.9 607.6 909.4 2 96 216.6 197.1 425.7 839.3 16 1372 0 1256.5 1712.4 2969.0 2 1052 149.9 1351.8 1116.0 2617.7 16 1155 0 645.5 1551.7 2197.2 2 886 686.1 586.8 1010.8 2293.7
Future research should extend our model to include the costbenefit analysis of using fast or slow transportation costs in the determination of the safety stock level. Up to now, the safety stock calculation only considers service level requirements (or back order cost) versus holding cost, but the difference between the transportation costs might be included as well. Moreover, additional periodic inventory models could be considered.
7.8% 7.7% 11.8% -4.4%
ACKNOWLEDGEMENT I would like to thank Roy Bouwhuis for his help in performing this study.
The first thing to notice in Fig. 4 and 5 is that demand for item one is lumpy. In some periods there is no usage at all, while in other periods demand can be five times as high as the mean demand. The safety stock is therefore quite high. For the long review period, safety stock is calculated as 141 items, while for the short review period, the safety stock is 79
2013 IFAC MIM June 19-21, 2013. Saint Petersburg, Russia
REFERENCES Alp, O., Erkip, N.K., Güllü, R., 2003. Outsourcing Logistics: Designing Transportation Contracts Between a Manufacturer and a Transporter. Transportation Science, 37 (1), 23–39.
Jain, A., Groenevelt, H., Rudi, N., 2009. Continuous Review Inventory Model with Dynamic Choice of Two Freight Modes with Fixed Costs. Manufacturing & Service Operations Management, 12 (1), 120–139.
Axsäter, S., 2011. Inventory control when the lead-time changes. Production and Operations Management, 20 (1), 72–80.
Kiesmüller, G., Kok, A. de, Fransoo, J.C., 2005. Transportation mode selection with positive manufacturing lead time. Transportation Research Part E: Logistics and Transportation Review, 41 (6), 511– 530.
Blackburn, J., 2012. Valuing time in supply chains: Establishing limits of time-based competition. Journal of Operations Management, 30 (5), 396–405.
Lorentz, H., Solakivi, T., Töyli, J., Ojala, L., 2011. Supply chain development priorities of manufacturing firms: empirical findings from a Finnish national survey. International Journal of Logistics Research and Applications, 14 (5), 351–365.
Chen, F., Yu, B., 2005. Quantifying the Value of Leadtime Information in a Single-Location Inventory System. Manufacturing & Service Operations Management, 7 (2), 144–151.
Minner, S., 2003. Multiple-supplier inventory models in supply chain management: A review. International Journal of Production Economics, 81-82, 265–279.
Crainic, T.G., Gendreau, M., Potvin, J.-Y., 2009. Intelligent freight-transportation systems: Assessment and the contribution of operations research. Transportation Research Part C: Emerging Technologies, 17 (6), 541– 557.
Muharremoglu, A., Tsitsiklis, J.N., 2003. Dynamic Leadtime Management in Supply Chains. Working paper, Graduate School of Business, Columbia University, New York.
Ganeshan, R., Tyworth, J.E., Guo, Y., 1999. Dual sourced supply chains: the discount supplier option. Transportation Research Part E: Logistics and Transportation Review, 35 (1), 11–23.
Muharremoglu, A., Yang, N., 2010. Inventory management with an exogenous supply process. Operations Research, 58 (1), 111–129.
Ghijsen, P.W.T., Semeijn, J., Ernstson, S., 2010. Supplier satisfaction and commitment: The role of influence strategies and supplier development. Journal of Purchasing and Supply Management, 16 (1), 17–26.
Ramasesh, R. V, Ord, J.K., Hayya, J.C., Pan, A., 1991. Sole versus dual sourcing in stochastic lead-time (s,Q) inventory models. Management Science, 37 (4), 428– 443.
Hadley, G., Whitin, T.M., 1963. Analysis of inventory systems, Englewood Cliffs: Prentice-Hall.
Riezebos, J., 2006. Inventory order crossovers. International Journal of Production Economics, 104 (2), 666–675.
Hayya, J.C., Bagchi, U., Kim, J., Sun, D., 2008. On static stochastic order crossover. International Journal of Production Economics, 114 (1), 404–413.
Riezebos, J., Gaalman, G.J.C., 2009. A single-item inventory model for expected inventory order crossovers. International Journal of Production Economics, 121 (2), 601–609.
Hayya, J.C., Harrison, T.P., 2010. A mirror-image lead time inventory model. International Journal of Production Research, 48 (15), 4483–4499.
Srinivasan, M., Novack, R., Thomas, D., 2011. Optimal and approximate policies for inventory systems with order crossover. Journal of Business Logistics, 32 (2), 180– 193.
Hayya, J.C., Harrison, T.P., He, X.J., 2011. The impact of stochastic lead time reduction on inventory cost under order crossover. European Journal of Operational Research, 211 (2), 274–281.
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Order Crossovers in an Automotive Supply Chain J. Riezebos University of Groningen, Faculty of Economics and Business, The Netherlands (Tel:+31503634853; e-mail:[email protected]). Abstract: Order crossovers occur when the delivery of orders is not in sequence with the issuing of orders. In automotive supply chains this may occur due to transportation mode choices, multiple suppliers, asynchronous capacity management at the suppliers, supply chain design choices, and speed differences in long supply chains. This study examines the problem that a Dutch first-tier supplier to the automotive industry in Europe faces when ordering items in Asia. Their information system and procurement procedures do not take the possibility of order crossovers into account. We have examined the consequences of neglecting these order crossovers with a situation where the occurrence of such order crossovers is used to advance the supply chain management and reduce the overall costs for the first-tier supplier. The difference between a non-crossover policy and our new model shows an average cost improvement of almost 6%. The proposed model is an extension of MRP ordering procedures and is build in an Excel spreadsheet.
has been neglected in this stream of literature, although it may play an important role in practice. This problem is denoted as order crossovers. An order crossover occurs if two orders do not arrive in the sequence in which they were issued. According to Riezebos (2006) we may distinguish between various types of order crossovers, depending on the underlying process that causes this phenomenon to occur. He distinguishes, amongst others, between random and expected order crossovers. In case of random order crossovers, stochastic fluctuations in lead times may sometimes cause a later order to arrive before an earlier issued order. In case of expected order crossovers, fluctuations in lead times are not random, but known in advance. These dynamic lead time changes are known at the moment of ordering. It is the latter type of order crossovers that may occur in responsiveness strategies that consider transportation mode changes.
1. INTRODUCTION Suppliers in automotive supply chains are under high pressure. Relatively small batches of high-quality parts are frequently delivered according to tight schedules in order to achieve a responsive supply chain. The responsiveness is important as the OEM’s face highly volatile customer behaviour. Their first tier suppliers should be able to deliver quickly when demanded, to chase the demand patterns faced by the OEM. However, they should also be as cost-efficient as possible. In order to reduce costs, parts are often bought in low cost countries and delivered through container transport over sea. This causes long supply lead times and reduces the responsiveness. Hence, these first-tier suppliers may have to use additional strategies to increase responsiveness when needed.
This paper will explore the occurrence of order crossovers in an automotive supply chain of a first-tier supplier to the automotive industry in Europe. The Dutch supplier orders items in Asia. We first examine whether their information system and procurement procedures do take the possibility of order crossovers into account. Next, we examine the consequences of neglecting these order crossovers with a situation where the occurrence of such order crossovers is used to advance the supply chain management and reduce the overall costs for the first tier supplier. The cost effect depends on the magnitude of the holding costs and transportation costs.
Two well-known strategies to increase the responsiveness focus on the supply network. First, using more than one second-tier supplier for the same component. (Minner, 2003) provides an excellent review of multiple-supplier inventory models, amongst which models that describe suppliers with different lead times. A major problem with this strategy is how to assure the same quality. Even in case the second-tier supplier has two plants (one located nearby the first-tier supplier, one located in a low cost country) and uses the same quality management system, parts may not be of the same quality. Therefore, the second strategy to increase responsiveness is frequently applied. That strategy selects a different transportation mode with a different expected speed and cost performance in case a quicker response is required. Transportation mode changes have also extensively been studied in literature (see e.g., Alp et al., 2003; Muharremoglu and Tsitsiklis, 2003). However, there is a very specific problem associated with transportation mode changes which 978-3-902823-35-9/2013 © IFAC
75
10.3182/20130619-3-RU-3018.00249
2013 IFAC MIM June 19-21, 2013. Saint Petersburg, Russia
postpone the transportation mode decision. In this paper, we will use the model of Kiesmüller et al. (2005) as a reference model for studying the effect of order crossovers in automotive supply chains in case of transportation mode choices. Note that by taking the manufacturing time equal to zero, the model results in the classic model of transportation mode changes (where suppliers are assumed to deliver from stock).
2. LITERATURE REVIEW 2.1 Issues in modern supply chains Recent research on geographically dispersed supply chains (Lorentz et al., 2011) shows that the more geographically dispersed a supply network is, the more likely it is that structure-related development priorities will be chosen. Such structural development efforts aim to reduce uncertainty and to improve the reliability of the international supply chain.
2.3 Inventory order crossovers
Another reason for changes in modern supply chains are the developments in information technology and available intelligent systems to support decision making. A recent review of operations research literature (Crainic et al., 2009) shows that performance of intelligent freight-transportation systems improves due to enabling technologies, such as electronic data interchange, advanced decision-support software, and better control in fields such as vehicle operations, advanced fleet management, and city logistics.
In the field of inventory control, order crossovers were first identified by Hadley and Whitin (1963) as an anomalous effect that caused the regular mathematical models not to be applicable. They discussed the class of so-called random order crossovers (Riezebos, 2006), where orders change sequence due to random lead-time fluctuations. The two assumptions that are made in these models, i.e., no order crossings and at the same time independently distributed lead times are mutually contradictory. Since then, several schools of thoughts have emerged that either avoid, neglect or account for random order crossovers in inventory control and supply chain modelling. In Hayya et al. (2008) these schools are respectively labelled as the Zipkin school, the HadleyWhitin school, and the Zalkind school. Examples of recent papers in this class of inventory order crossovers are Hayya and Harrison (2010); Muharremoglu and Yang ( 2010); Hayya et al.(2011) and Srinivasan et al. (2011).
In the European automotive industry, relations between an OEM and its first-tier suppliers –whether they are geographically located in the same country or not– are known to be stable in order to allow them to focus on development and improvement (Ghijsen et al., 2010). However, OEMfirst-tier supplier relationships in the automotive industry differ from other buyer–supplier relationships with respect to power, dependence and the degree of collaboration. Therefore, research on the development of relations with suppliers at other tiers might result in different conclusions, due to the high pressure to perform in these supply chains.
The other main class of order crossovers, expected order crossovers, considers sequence changes that are known beforehand, i.e. at the decision moment. The underlying processes that cause the lead time differences to occur are known at some level of detail. Examples are to select either the standard or the high priority lead time offered by the supplier. When selecting the standard lead time, costs will be lower, but lead times will be longer as the freight transportation will be organised more efficiently, i.e. longer waiting or processing/transportation times before it arrives in its destination or more uncertainty/risk. See e.g. Ganeshan et al. (1999). Examples of recent papers that discuss this class of order crossovers are Muharremoglu and Yang (2010); Riezebos and Gaalman (2009) and Axsäter (2011).
2.2 Transportation mode changes A transportation mode change is just one possible method to achieve a lead time reduction. Problems with different lead times have been studied extensively. These differences may be modelled as the outcome of stochastic processes (i.e., uncertain lead times). Examples of papers in this area are Ramasesh et al. (1991) and Chen and Yu (2005). Others model these differences as dynamic processes. That allows for including knowledge on the expected lead time difference at the moment of issuing an order. See e.g., Jain et al. (2009); Muharremoglu and Tsitsiklis (2003); Riezebos and Gaalman (2009). With respect to transportation mode changes, most papers implicitly assume that the decision to use a specific mode of transport is taken at the moment of order issue (e.g., Blackburn, 2012). If the second-tier supplier delivers from stock, this is a realistic assumption. All activities that the supplier has to undertake, e.g. packaging, expedition, freight insurance, invoicing, customs, et cetera, depend on the knowledge of the transportation mode.
3. HANDLING ORDER CROSSOVERS IN AN AUTOMOTIVE SUPPLY CHAIN This case study describes the appearance of order crossovers in an automotive supply chain. The first-tier supplier of several OEMs in Europe (both car and truck manufacturers) has its global headquarter in the Netherlands. Focus of this study is on the truck segment of the company, where they produce hydraulic components. About 80% of their raw materials are supplied from companies located in Asia. Most of these products consist of steel, which makes the products relatively heavy. For economic reasons, long shipping lead times are preferred over higher transportation costs. However, due to the uncertain demand for some of their products, their inventory policy has to guarantee a specified customer service level, which causes high inventory costs.
However, in case of a second-tier supplier that has to undertake manufacturing tasks as well during the supply lead time, it may be not necessary to provide all information on the required transportation mode at the moment of order issue. Therefore, several papers (e.g., Jain et al. (2009); Kiesmüller et al. (2005)) have examined the possibility to
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The lead time of raw materials is larger than customers require. Lead times of raw materials can be up to 20 weeks.
before the items are available for shipment to the customer. That is the moment to decide on the amount Q1r Q0 r that will make use of the fast transportation mode with remaining lead time L1 . The remainder Q2 r Q0 r Q1r will use the slow transportation mode with remaining lead time L2 L1 .
For fast moving products with constant demand, these long lead times will not affect the customer service level that much, since a proper inventory policy is used to guarantee the required customer service level. Slow moving products with uncertain demand require more attention from management.
Kiesmüller et al. (2005) assume the review period R to be larger or equal to the longest replenishment lead-time for the item. However, in the automotive supply chain, and especially in our case study company, it is rather unrealistic to assume that orders for components are issued with a review period of 5 months. Therefore, we investigate more realistic options where the length of the review period is shorter than the total lead time.
Their current control policy has determined safety stock levels and batch sizes. However, while setting these parameters no attention has been given to the possibility of selecting another transportation mode for a part of the order whenever necessary. By selecting another transportation mode for a part of the order, e.g. by air instead of sea, lead times of some of the items are reduced, hence inventory levels increase, backorder levels decrease, and customer service level increases. The net cost effect is the sum of increased transportation costs, increased holding costs, and reduced backordering costs.
The sequence of events (Fig. 1) is that at the start of a review period delivery batches (if any) arrive, next an order will be issued, and demand for that period occurs, while in the meantime a transportation mode decision is being made, and deliveries take place accordingly.
The company uses fixed review periods, which are part of the contract (and hence negotiated) with the suppliers. At each review moment for each product a new order may be issued. The decision on a new order specifies the amount, quality, and moment of order delivery. We investigated whether postponing the transportation mode decision and reconsidering the review period decision could improve the cost performance of the company. In the following section, the methodology will be described. A dual supply model to analyse the performance effect of the transportation mode and order splitting decision is derived from the dual supply model by Kiesmüller et al. (2005) where the transportation mode decision is postponed until the supplier finished manufacturing the order.
Fig. 1: Sequence of events with long review period Now, Fig. 2 and 3 show example schemes if we have a review period shorter than the total lead time.
4. EXAMINING THE EFFECT OF ORDER CROSSOVERS
Order Transportation mode size decision decision
Fast delivery
Slow delivery
4.1 Mathematical model pipeline inventory
In our model we assume that there are two different transportation modes, a fast mode with deterministic lead time L1 and per unit transportation cost c1 , and a slow mode with lead time L2 and per unit transportation cost c2 . The total lead time of an order also includes a constant manufacturing lead time L0 . The demand per time unit Dt is a non-negative random variable. The demand distribution is assumed to be stationary with known mean μ and variance σ2. Demand in disjoint intervals is independently distributed and unsatisfied demand is backordered.
Q0r+1
Q1r Q0r
Q0r+2
Q1r+1
Q2r
Q2r+1 time
0
L0
L0 + L1
R L0 + L2 R+L0
R+L0+L1
2R
R+L0+L2
R
Fig. 2: Example if review period < total lead time Fig. 2 shows a temporary increase of pipeline inventory. There are no order crossovers.
The first-tier supplier reviews the inventory periodically and sends during the rth review period an order of size Q0r to the second-tier supplier. The length of the review period R is assumed to be constant and to be an integer multiple of the chosen time unit t with in total T time units per year. After issuing Q0r a constant amount of time L0 elapses due to manufacturing, packaging and other handling activities
Fig. 3 Order crossovers 77
2013 IFAC MIM June 19-21, 2013. Saint Petersburg, Russia
mode system, which reduces average holding costs in the system. How much lower depends on the cost difference between the slow and fast transportation mode. If there would be no cost difference at all, it should only have to cover demand uncertainty in the interval t nR, t R L0 L2 .
Fig. 3 has a much smaller review period (equal to L0 . We see that the next two ordering decisions have to be taken while nothing has yet arrived. Orders arrive at the moments L0 L1 ; R L0 L1 ; L0 L2 ; R L0 L2 . Therefore, an order crossover takes place. The decision moment for the third arrival was at time L0 , while the decision moment for the second arrival was later, namely at time R L0 . Therefore, these orders cross, a phenomenon which has huge implications for the management of the inventory, as it will occur in every replenishment cycle. Moreover, the total number of order crossovers in a replenishment cycle depends on the length of R, L0 , L1 , and L2 .
The advantage of the availability of a fast transportation mode therefore translates to no demand uncertainty to cope with in the safety stock during a period of length nR. Hence the maximal savings on safety stock are SS k
R L0 L2 R L0 L2 nR , where k is
the parameter for the service level, and the standard deviation of demand per period of length t. The savings on safety stock translate to a yearly holding cost reduction ( hSS ). These savings are higher in case the length of the review period decreases, the lead time difference between slow and fast transportation increases, the standard deviation of demand increases, or the required service level increases.
In order to examine this configuration, we develop a mathematical model. Assume that at time t we are at the start of a review period and we have to decide upon the order size Q0 r . Define Ipt , the inventory position at time t , as the total amount of inventory available for demand satisfaction during the interval t , t L0 L2 . Define Ilt as the inventory
Note that the transportation costs do not necessarily increase, as we only need to use fast transportation mode in case of an exceptional large demand during the first nR periods, i.e. t nR 1 only if demand exceeded SS E Di SS nR . i t
level at time t , where the inventory level may be negative (back order case). Then we have: m L L2 Ipt Ilt i 1 Q0,t iR with m 0 . R
t nR 1 So Q1, nR min Q0, nR , max 0, Dt SS nR , as we i t cannot have more delivered through a fast transport than that we ordered during that review period.
All orders that have been issued before t mR have already arrived in stock (both the slow and fast transportation mode) at or before time t . So we have an expression for the number of orders that have not yet been delivered. Then: n L L1 Q0 r Q1, r i SS ( R L0 L2 ) Ipt with n 2 R i 1 where SS is the safety stock that on average should be available in stock on the moment the slow transport arrives. The new orders have to cover the difference in what we need to have just before the arrival of the next slow transport t R L0 L2 and what we actually will have available due to already issued orders.
4.2 Numerical analysis In order to examine the effect of order crossovers in a twolevel supply chain with postponement of the choice for one of the two available transportation modes, we have set up a simulation study using data from the first-tier supplier. Four items are analysed. Two are so called ‘cylinder bases’. The other two items are ‘reservoirs’, which are needed for the housing of the pump system. We analysed the effect of crossovers and postponing the transportation mode decision until the supplier finished manufacturing. The mean and variance of demand were calculated based on historical data.
The remarkable thing in this formula is that it provides an expression for the number n of crossover orders that will arrive before the next slow transport will arrive. The decision maker should balance the cost of ordering now (and the possibility to involve slow transport with associated lower transportation and holding costs) or ordering in any of the future review periods (up to n) and using fast transportation mode for these orders. This affects the safety stock level required at the moment of arrival of a slow order.
The service level factor that we used was k 1.96 , which would correspond with a cycle service level of 95% in case of normally distributed demand. Holding costs h 25% * P are charged as an annual carrying charge of the price P . Table 1. Item data
In a single transportation mode system, the safety stock guarantees a specified service level by covering for uncertainty in demand during the whole interval t , t R L0 L2 . Due to the option to use the nth fast
Item 1 2 3 4
moving order (i.e. the order that is being issued at time t nR ) to correct for possibly higher demand than expected, the safety stock may be lower than in a single transportation
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Price € 4.11 7.92 2.31 2.28
Weight kg/item 0.81 0.45 0.52 0.52
c1 €/kg 4.91 4.91 4.03 3.20
c2 €/kg 1.55 1.55 0.65 0.25
μ per wk 4.6 4.8 43.1 51.3
σ per wk 12.3 11.0 121.1 101.0
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108 items, with a SS equal to 18. The next thing to notice is the behaviour of the system when such a large demand has occurred. In Fig. 4, it takes 18 weeks before an order that is issued to compensate for the large demand has arrived. In Fig. 5, all three orders that have been issued before the large demand occurred and for which the transportation mode has not yet been set will be delivered by air to achieve an inventory level as near as possible to the required safety stock level. This adds transportation costs, but safeguards against backorders, something which has to be avoided in automotive supply chains.
In accordance with the company data, manufacturing lead time L0 =10 weeks, fast transportation L1 =2 weeks and slow transportation L2 =8 weeks. Hence the total replenishment lead time is 18 weeks. We used two different lengths for the review period R (2 and 16 weeks) in order to show the performance effect of these lengths on the transportation and holding costs as well as on the inventory levels. Note that at a review period length of 16 weeks no order crossovers occur, while at a review period length of 2 weeks three orders will cross.
From the results in Table 2 the effect of including order crossovers becomes clear. The first three items clearly benefit from this policy, with cost improvements between 7.7% and 11.8%. The last item faces a cost increase of 4.4%. Its air transportation cost has increased a lot due to a very high demand in one of the first periods. The holding costs decrease drastically for all four items due to the reduced safety stock requirements.
Table 1 shows that the transportation costs are charged per kilogram, but differ per item due to negotiations with the transportation company. Before we show the results for all four items, we present in Fig. 4 and 5 an overview of item one’s inventory position and inventory level for the two review period lengths.
The model has been implemented in a Microsoft Excel worksheet. It is an extension of regular MRP ordering, as it includes an additional row for the fast transportation mode decision on Q1 , L0 periods after the Q0 decision has been taken. Based on the entries in this row, the delivery schedule is modified, showing an (additional) arrival of Q1 with an offset time of L1 periods ahead and the remaining Q0 Q1 with the regular offset time of L2 , counting from the moment the transportation mode decision is taken.
Fig. 4 Inventory position (upper) and level (lower) R=16
5. CONCLUSIONS Based on our analysis of the transportation mode policy in this automotive supply chain, we have suggested a new model to determine the order quantities as well as the part of the batch that should be send through a more expensive and faster transportation mode. This policy makes use of the occurrence of order crossovers. The analysis of four items has shown that on average there is a cost improvement of almost 6%, but this includes a possibility for a cost increase.
Fig. 5 Inventory position (upper) and level (lower) R=2 Table 2. Results
Item 1 2 3 4
R
SS Total c1
Total c2
Total h
Grand % Cost total improve
16 141 0 585.8 305.2 891.0 2 108 121.5 494.8 205.9 822.1 16 126 0 301.9 607.6 909.4 2 96 216.6 197.1 425.7 839.3 16 1372 0 1256.5 1712.4 2969.0 2 1052 149.9 1351.8 1116.0 2617.7 16 1155 0 645.5 1551.7 2197.2 2 886 686.1 586.8 1010.8 2293.7
Future research should extend our model to include the costbenefit analysis of using fast or slow transportation costs in the determination of the safety stock level. Up to now, the safety stock calculation only considers service level requirements (or back order cost) versus holding cost, but the difference between the transportation costs might be included as well. Moreover, additional periodic inventory models could be considered.
7.8% 7.7% 11.8% -4.4%
ACKNOWLEDGEMENT I would like to thank Roy Bouwhuis for his help in performing this study.
The first thing to notice in Fig. 4 and 5 is that demand for item one is lumpy. In some periods there is no usage at all, while in other periods demand can be five times as high as the mean demand. The safety stock is therefore quite high. For the long review period, safety stock is calculated as 141 items, while for the short review period, the safety stock is 79
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