Multi-Item Capacitated Lot-Sizing Problem with Parallel Resources, Setups, Backorders and Overtime Decisions

In this paper we study the production planning problem, more precisely we address a lot sizing problem with parallel resources, setup times and costs and backorder costs. The aim of this work is to propose a mathematical operational planning model based on two work organization approaches: the first configuration in regular mode, the second configuration by using overtime with regular hours when demands are high. The developed models have been tested on a production unit in the textile domain industry. The results obtained have made it possible to draw up a work plan that is optimal in terms of cost and time for all the planning periods while ensuring demand satisfaction.