Capacitated lot sizing with linked lots for general product structures in job shops

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.