Multiple Plants Capacitated Lot Sizing and Scheduling with Sequence-Dependent Setup Costs

Abstract

Production planning is a crucial activity for companies to satisfy customers demand while minimizing cost. The objective of this research is to optimize the production planning and scheduling decisions of companies in petrochemical industry field. A Mixed-Integer Linear Programming (MILP) model is developed for the capacitated lot sizing and scheduling problem with sequence dependent setup costs; that considers the chain of multiple suppliers, affiliates, warehouses and customers. Different grades can be produced by each affiliate, and a changeover cost occurs when changing the production from one grade to another. The model integrates scheduling and lot-sizing decisions with the logistics functions of transportation and warehousing. In particular, it provides answers to questions regarding the amount of each raw material to be purchased from each supplier, sequence of production plans, inventory levels, and warehouse selection to satisfy orders. Petrochemical companies usually own several joint-ventures and centrally prepare the affiliates' production plans for the upcoming periods; their current planning procedures do not consider the overall costs in their supply-chain. The developed model will integrate their raw material costs, production and sequencing costs, inventory costs and transportation costs from the supplier side across the supply-chain to the customer side. The problem under study is considered an NP-Hard problem due to its complexity and size; therefore, a three stage heuristic was developed which provided good quality solutions with an acceptable computational time. The first stage of the heuristic works on reducing the complexity of the model by removing the sequencing decisions; where the resulting model decides only the size of lots for each affiliate. In the second and third stages, an iterative process is done to reduce the total setup and total holding costs while restoring the sequencing decisions. The heuristic was applied on different problem instances of different sizes and the reported results were within a range of 0.09% - 2.0% away from optimality. The development of the Mixed-Integer Linear Programming and the Three Stage Heuristic is the main contribution of this research.