مشکل تعیین اندازه دسته تولید ایجاد شده : بررسی مدل ها و الگوریتم ها

Lot sizing is one of the most important and also one of the most difficult problems in production planning. This subject has been studied extensively in the literature. In this article, we consider single-level lot sizing problems, their variants and solution approaches. After introducing factors affecting formulation and the complexity of production planning problems, and introducing different variants of lot sizing and scheduling problems, we discuss single-level lot sizing problems, together with exact and heuristic approaches for their solution. We conclude with some suggestions for future research.

Production planning is an activity that considers the best use of production resources in order to satisfy production goals (satisfying production requirements and anticipating sales opportunities) over a certain period named the planning horizon. Production planning typically encompasses three time ranges for decision making: long-term, medium-term and short-term. In long-term planning usually the focus is on anticipating aggregate needs and involves such strategic decisions as product, equipment and process choices, facility location and design, and resource planning. Medium-term planning often involves making decisions on material requirements planning (MRP) and establishing production quantities or lot sizing over the planning period, so as to optimise some performance criteria such as minimising overall costs, while meeting demand requirements and satisfying existing capacity restrictions. In short-term planning, decisions usually involve day-to-day scheduling of operations such as job sequencing or control in a workshop. In this review the focus is on medium-term production planning and especially on single-level lot sizing decisions. Lot sizing decisions give rise to the problem of identifying when and how much of a product to produce such that setup, production and holding costs are minimised. Making the right decisions in lot sizing will affect directly the system performance and its productivity, which are important for a manufacturing firm's ability to compete in the market. Therefore, developing and improving solution procedures for lot sizing problems is very important. The applicability of these problems arises commonly in operations such as forging and casting and in industries which consist of a single production process, or where all production process can be considered as a single operation, such as some medical or chemical industries. After an introduction to lot sizing problems, this paper will focus on the capacitated lot sizing problem and will review the main contributions to this long standing but active research field focusing, particularly, on developments that have taken place since research was reviewed and compared in [1] and [2].

In this work, after a brief introduction in Section 1, in Section 2 we described factors which cause different variants of production planning problem and affect its complexity. The variants are discussed in Section 3, and in Section 4, among different variants, the single-level lot sizing problem, in both uncapacitated and capacitated cases is discussed. Basic formulations are presented and, based on different solution approaches, the literature and its classification is reviewed in detail. The focus has been more on the capacitated variant, termed CLSP in the literature. Although the traditional CLSP problem has been studied by many authors, looking for more efficient solution approaches is a challenging subject. Variants of the CLSP with complex setup and other variants which are more realistic and practical have received less attention in the literature. There has been little literature regarding problems such as CLSP with backlogging or with setup times and setup carry-over. Since these problems are NP-hard, fast and efficient heuristics are required. Also there is little literature for problems such as CLSP with single-family or multi-family joint setup, in both capacitated and uncapacitated cases. Developing heuristics with reasonable speed and solution quality for these kinds of problems is another interesting research area. Using some relatively new solution approaches such as tabu search, simulated annealing, and other meta-heuristics for solving CLSP is also another fruitful area of research. Such techniques have been shown to be effective for similar NP-hard problems.