Rolling schedule approaches for supply chain operations planning

J.M. Spitter

Research output: ThesisPhd Thesis 1 (Research TU/e / Graduation TU/e)

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Supply Chain Operations Planning (SCOP) involves the determination of an extensive production plan for a network of manufacturing and distribution entities within and across organizations. The production plan consist of order release decisions that allocate materials and resources in order to transform these materials into (intermediate) products. We use the word item for both materials, intermediate products, and end-products. Furthermore, we consider arbitrary supply chains, i.e. the products produced by the supply chain as a whole and sold to customers consist of multiple items, where each item may in turn consists of multiple items and where each item may be used in multiple items as well. The aim of SCOP is not only to obtain a feasible production plan, but the plan must be determined such that pre-specified customer service levels are met while minimizing cost. To obtain optimal production plans we use a linear programming (LP) model. The reason we use an LP model is twofold. First, LP models can easily be incorporated in existing Advanced Planning Systems (APS). Second, while the multi-echelon inventory concept can only be used for uncapacitated supply chains and some special cases of capacitated supply chains, capacity constraints but also other restrictions can easily added to LP models. In former mathematical programming (MP) models, the needed capacity was allocated at a fixed time offset. This time offset was indicated by fixed or minimum lead times. By the introduction of planned lead times with multi-period capacity allocation, an additional degree of freedom is created, namely the timing of capacity allocation during the planned lead time. When using the LP model in a rolling schedule context, timing the capacity allocation properly can reduce the inventory cost. Although the number of studies on MP models for solving the SCOP or related problems are carried out by various researchers is enormous, only a few of these studies use a rolling schedule. Production plans are only calculated for a fixed time horizon based on the forecast of customers demand. However, since customer demand is uncertain, we emphasize the use of a rolling schedule. This implies that a production plan, based on sales forecasts, is calculated for a time interval (0; T], but only executed for the first period. At time 1, the actual demand of the first period is known, and the inventory status of the consumer products are adjusted according the actual demand. For time interval (1; T + 1], a new production plan is calculated. In this thesis, we studied the proposed LP strategy with planned lead times in a rolling schedule setting whereby we focused on the following topics: ² timing of production within the planned lead time, ² factors influencing the optimal planned lead time, ² early availability of produced items, i.e. availability of items before the end of their planned lead time, and ² balanced material allocation. In the first three studies we explore the possibilities of using planned lead times. In the first study, timing of production, we compare the situation whereby released items are produced as soon as there is available capacity with the situation whereby released items are produced as late as possible within the planned lead time. If items are produced as soon as possible, there is more capacity left for future production. Since we work with uncertain customer demand whereby demand may be larger than expected, this capacity might be very useful. A drawback of production as soon as possible are the additional work-in-process cost. The results of simulation studies show that if the utilization rates of resources and/or the variation in demand are high, producing early is better. However this is only the case if the added value between the concerned item and the end item is high. The second study deals with factors influencing the optimal planned lead time. From queuing theory it is already known that the variance in demand and the utilization rate of the resources determine the waiting time. More variation and/or higher utilization rates give longer waiting times. Since lead times consist for a large part of waiting time, these two factors most probably also influence the length of the optimal planned lead time. For a set of representative supply chain structures we showed that this was indeed the case. With longer planned lead times, the flexibility in capacity allocation is higher. Additional flexibility gives lower safety stocks, but longer planned lead times also means more work-in-process. Hence, an important third factor which influence the optimal planned lead time is the holding costs structure. When using planned lead times, early produced items have to wait the remainder of their planned lead time. This seems contradictory, especially if these items are necessary to avoid or reduce backorders. Therefore we adapt the standard LP model in two ways. In the first model, items are made available for succeeding production steps directly after they are produced. And in the second model, produced items are only made available for succeeding production steps if they are needed to avoid or reduce backorders. Experiments showed that the first model does not improve the performance of the standard LP strategy. The advantages of planned lead times longer than one period are nullified by early availability of produced items. The second model indeed improves the performance of the standard LP strategy, but only when the planned lead times are optimal or longer. Comparing the introduced LP strategy with a so-called synchronized base stock policy under the assumption of infinite capacity, it turned out that the LP strategy is outperformed by the base stock policy. In order to obtain a better performance, we Summary 121 added linear allocation rules to the LP model. With these allocation rules shortages of child items are divided among the parent items using a predefined allocation fraction. A second way of balanced allocation of child items is obtained by replacing the linear objective function by a quadratic one. The results of a well-chosen set of experiments showed that although the synchronized base stock policy also outperforms the adjusted LP strategies, the difference in performance is small. Hence, the adjusted LP strategies are good alternatives for large, capacitated supply chain structures which cannot be solved by synchronized base stock policies. Comparing the model with linear allocation rules with the model with quadratic objective function, the preference is given to the latter model. This model does not only give the lowest inventory costs, it also has the shortest computation time. Furthermore, this model can easily be implemented and solved by existing software. Summarizing the main results of this thesis, we conclude that deterministic LP models can be used to solve the SCOP problem with stochastic demand by using the LP model in a rolling schedule concept. By using optimal planned lead times with multiperiod capacity allocation, early production during the planned lead times, and early availability of needed produced items before the end of the planned lead time, we can decrease the inventory costs. The costs can also be reduced by using allocation strategies to allocate shortages among parent items proportionally. Especially the results for the model with quadratic objective function are promising.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Industrial Engineering and Innovation Sciences
  • de Kok, A.G. (Ton), Promotor
  • Fransoo, Jan C., Promotor
  • Dellaert, Nico P., Copromotor
Award date25 Apr 2005
Place of PublicationEindhoven
Print ISBNs90-386-0021-6
Publication statusPublished - 2005


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