برنامه ریزی تولید سلسله مراتبی قوی برای سیستم تولید دو مرحله ای

In this paper, we propose a robust hierarchical production planning approach for a two-stage real world capacitated production system operating in an uncertain environment. The first stage of the system produces a set of semi-finished products having relatively stable annual demands, and the second finishing stage produces finished products having highly variable weekly demands. The fixed production setup costs incurred at the first stage are considerably high. Fixed production setup costs incurred at the second stage are fairly small compared to those of the first stage. We propose an integrated hierarchical planning model, where semi-finished products from the first stage (i.e. the aggregate level) are disaggregated into finished products to be produced in the second stage (i.e. the operational level). As a result of the relatively stable demands and the high setup costs experienced at the first stage, a cyclical aggregate planning model is proposed for production planning at the upper level of the hierarchical plan. Based on this aggregate plan, a modified periodic review policy is then proposed for production planning at the lower level. Finally, a coupling plan, linking the two planning levels, is proposed to ensure the feasibility of the disaggregation process at every period.

The two-stage production system discussed in this paper is a real world production process having some particular features which, if taken into account in the planning process, may unequivocally lead to effective production plans. The first stage of the production system produces some 200 different semi-finished products which are either shipped directly in this current status to other manufacturers or processed further in the second stage to produce some 10,000 different finished products. Therefore, production plans developed for the first stage can naturally be considered as aggregate production plans (i.e. the aggregate level), which can subsequently be disaggregated to provide plans for the second stage (i.e. the operational level). The first special feature of the production system is that fixed production setup costs experienced at the first stage are significantly higher than those experienced at the second stage. This fact differs from the usual hierarchical production planning processes which consider that fixed costs at the aggregate level are negligible and take these costs into account only at the detailed level (i.e. the operational level). In addition, as it is often the case in almost all manufacturing systems, it is difficult to accurately forecast finished product demands. This is what usually makes aggregate plans less effective in practice. The second special feature is related to the fact that demands of the semi-finished products are relatively stable, due to the strong position of the manufacturers in the semi-finished product market. Moreover, the variability of the finished product demands can be approximated by looking back into the past demand realizations. The main objective of this research is to develop a robust hierarchical production planning approach for the two-stage production system, which explicitly considers those special features during the planning process. The production planning approach also takes the variability of finished product demands into account, which consequently generates plans for the whole system that are robust (i.e. less sensitive to the demand variability). The proposed planning approach is based on the hierarchical production planning approach presented by Bitran and Hax (1977), which benefits are well-established in the literature (see also Bitran et al., 1981 and Bitran et al., 1982). In a typical hierarchical production planning model, the objective is mainly to decompose a large and complex planning problem into less complex planning sub-problems resulting in consistent aggregate and master production schedules. In the production system at hand, the fact that demands of semi-finished products are relatively stable suggests that, even though demands of the finished products are random, planning at the level of semi-finished products may have some stabilizing effect on the aggregate production planning of the whole system. The remainder of this paper is organized as follows. Section 2 provides a brief review of the literature. In Section 3, we describe and formulate the two-stage production planning problem. Section 4 presents and discusses an alternative robust planning approach. Section 5 provides an extensive analysis of the approaches and presents related computational results. Finally, some concluding remarks are given in Section 6.

The common hierarchical production planning approaches typically consider holding costs at the aggregate level and setup costs at the detailed level. This is, however, not the case for the aggregation–disaggregation approach pursued for the two-stage capacitated production process discussed in this paper. The first stage is considered as the aggregate level and the second stage as the detailed level. The fact that the setup costs in the first stage (i.e. the aggregate level) are significantly higher than the setup costs incurred in the second stage (i.e. the detailed level) is explicitly taken into account during the planning process. Demands of semi-finished products in the first stage are relatively stable; therefore a cyclical planning model is proposed. The resulting plan is then used as a basis for the production planning in the second stage. A coupling plan linking the aggregate and the detailed level is proposed based on the group demands (using the ABC rule). For this coupling plan, an anticipative strategy is proposed based on a modified chase strategy, where each production is augmented with an “extra quantity”. These extra quantities are intended to anticipate the deterministic part of future group demand which is represented by the lower bound of group demand for the remaining periods before the next semi-finished production. It is not meant to cover the variability of the demand as in the “safety stock” strategy. The robustness and consistency conditions are ensured as long as the extra quantities never exceed the sum of lower bound demand for all remaining periods before the next production of semi-finished products. The modified periodic review is used for the finished product planning, where the available production for each group is fairly shared among the finished products within the group. The modified policy gives a robust (stable) performance in terms of service levels because the coupling plan consistently guarantees the availability of the semi-finished products during the cycle time. The performance (i.e. the total costs and the service level) of the revised base policy depends on the capacity and deteriorates when the capacity is very limited. The modified policy, in the other hand, shows some robustness in term of service levels. The total cost of the modified policy is only 5% higher in the case of limited capacity than that in the unlimited capacity. Future research is directed toward the search for a better disaggregation procedure besides the proportional share between finished products. It is also of our interest to seek a proper approach if the aggregate demand is stochastic.