مشکل تعیین اندازه دسته تولید در ماشین کاغذ تحت روش تولید دوره ای

In this paper, we address the problem of defining the production campaigns on a paper machine. Each campaign is of a fixed duration (cycle time) and produces batches (lot sizes) of all or a set of the products. This paper presents a real case study discussing a specific lot sizing problem where a predetermined production sequence must be maintained. We propose a new approach where we compute first the cycle time by assuming constant demand, and then lot sizes are determined for each product within each cycle in order to satisfy demand. Finally, studying the context of a Canadian paper maker, we evaluate the impact of planning production under a cycling manner.

In a pulp and paper mill, the paper machine often represents the bottleneck resource and therefore requires an efficient production planning approach, optimizing resource utilization and minimizing setup and inventory costs. In this industry, production is often planned within campaigns of fixed duration, called the production cycle time in this paper. In these campaigns, production volumes (lot sizes) are planned to best meet forecasted or confirmed demand. Furthermore, the paper producer generally aims to set the production sequence from lighter weight to heavier weight paper. To face this complexity, plant managers often fix a cycle time t in which the different papers are produced in a specific and stable order. Hence, one of the objectives of the current study is to evaluate the impact of considering fixed cycle time on production costs and planning. The problem addressed in this paper is the production planning of n paper products on a capacitated paper machine within a horizon of T periods. For each period, capacity is limited and demand is deterministic (historic demand database). Demand must be satisfied without backlogs. The paper machine stops producing only for planned maintenance. This problem is known in the literature as a capacitated lot sizing problem with a particularity that the setup costs are sequence dependent and a predetermined production sequence must be maintained. The aim of this contribution is to define the optimum cycle time and lot sizes to produce for each planning period minimizing the sum of the fixed setup costs, the variable production costs and the inventory costs for the entire planning horizon while respecting demand and capacity constraints for each period. Validation of the proposed methodology is pursued studying the case of a Canadian paper producer. Its historical delivery database serves as demand for the experimentation. The impact of planning under a cyclic approach is also addressed. Let us proceed as follows. In Section 2, we first present the literature review related to the problem. Section 3 will then formally introduce the models describing the approach proposed to solve our real case problem. In the following section we give some experimental results obtained by testing our models on real data obtained from our partner so that we can evaluate their current practises. Section 5 provides concluding remarks.

In this paper we have proposed and validated a new approach which can define optimum cycle length as well as the optimal batch sizes to be produced in the case of several products, several periods, finite capacity, dynamic demand and when setup costs and times are sequence dependent. This concerns a real case study that we have done with a partner of the For@C Research Consortium, in the pulp and paper industry. For the studied company the sequence of producing different products on the machine is fixed and setup costs and times are known only for the predefined cycle. For further research, it will be interesting to complete data for the other setups in order to estimate the real gain of considering a cycle. In this article, we considered the minimum setup costs to evaluate this gain. Furthermore, we intend to broaden our work to include the just-in-time policy of flow management which requires the re-examination of several working hypotheses. Moreover, further investigation could interestingly extend our study by considering the case of the multiple machine lot sizing problem. It will be interesting for this purpose to think about another approach for modeling a fixed order for production sequence without considering a fixed cycle. Indeed, in cases where the cycle is too long and because of demand variability, we could be unable to satisfy demand as it occurs.