اندازه یابی با مقادیر زیاد ظرفیت سازی شده برای سازه های محصول کلی در تولید کارگاهی

In this paper, we propose a mixed integer programming (MIP) model for a multi-level multi resource capacitated lot sizing and scheduling problem with a set of constraints to track dependent demand balances, that is, the amount left over after allocating the available inventory to the dependent demands. A part of this leftover amount may be kept as a reservation quantity to meet dependent demands of the following period under capacity restrictions. These constraints are necessary because we assume independent demands as well as dependent demands for all items in the product structure. They also are used to tighten the domain of on hand and backorder inventory levels. Although we allow backorders for independent demands only, this is not possible for dependent demands as backorders will disturb the whole demand balance of the product structure. Determination of setup costs is a crucial task when developing lot sizing and scheduling models, especially in a capacitated manufacturing environment with backorders. In this respect, the capacitated lot sizing with linked lot sizes (CLSPL) model we formulate needs not to consider setup costs to avoid unnecessary setups thanks to the new set of constraints, and to obtain feasible lot sizes and schedules. Finally, a numerical example and computational results in a job shop environment are also given, and future research directions are provided.

Determining setup costs is not only a crucial work but, most of the time, somewhat arbitrary for manufacturing firms. This generally results in suboptimal solutions due to a trade-off between other cost elements such as holding and backorder costs. Hence, an approach that does not require setup cost minimization may overcome difficulties manufacturing companies face in estimating relevant costs. On the other hand, late delivery is a fact of life in manufacturing firms as different orders compete for the same capacitated resources, unless some measures such as overtime and outsourcing are taken in advance. In this paper, we present an improved CLSPL framework with a main research objective of eliminating setup minimization requirement to avoid unnecessary setups. New set of constraints presented here could easily be applied to small time bucket models with a minor modification. Although we abolish the need to specifically define setup minimization in the objective function, setups could be penalized, especially, when setup costs and times are considered to be more important than other cost elements. Meanwhile, we show in this paper that this penalization is not essential to acquire a feasible plan. If backorders are allowed for all items of the bill of materials in a capacitated production environment, then it should be such that the dependent demand structure must not be disturbed. In this respect, we formulate a set of new constraints to protect dependent demand structure. These constraints also set a new upper bound for backordered inventory that are tighter than what is adopted in literature. The developed model is applied to a job shop manufacturing environment with a general type product structure. CPLEX 9.0 is used to solve the MIP programming model. Since the goal of this paper is to develop a new framework for CLSPL, other solution approaches that are more efficient than the exact optimization are not considered in this paper. However, a study to develop a level-by-level decomposition heuristic is still in progress. In a future study, a mathematical programming model can be reformulated to include a sequence dependent setup option. Since the proposed model assumes that a resource can process just one item at a time, it could be extended by adapting parallel resources. Various supply alternatives, i.e., outsourcing and purchasing, could also be investigated. The structure of the model developed in this paper is flexible enough to accommodate these new supply alternatives. Relaxing the assumption of deterministic demand and/or processing time and capacity assumptions may also be considered in a future study. Finally the model can be modified such that instead of providing fixed manufacturing lead times, lead times can be computed dynamically for each order, which is an ongoing research.