A possibilistic programming approach for capacitated lot-sizing problem in mixed assembly shops

This paper develops a fuzzy multi-objective linear programme (FMOLP) model for solving the bi-objective capacitated lot-sizing problem (CLSP). The proposed model attempts to simultaneously minimise total cost consist of total production variation cost, inventory cost, backlog cost and total setup cost while maximising the resource utilisation. According to the structure of the mixed assembly shops, a multi-product model with multi-item that should be produced during multi-level has been designed. Based on the vagueness and imprecision of the real case, the production, holding and backorder costs and demand of the products were considered as fuzzy number that have their membership function during planning horizon in each period. An interactive fuzzy solution method is developed by combining a number of efficient solution algorithms from the recent literature in order to solve the proposed possibilistic model. In order to demonstrate the significance and applicability of the proposed model as well as the usefulness of the proposed solution approach, numerical experiments are conducted and the results are provided.