A new formulation for a variant of the Capacitated Lot Sizing and Scheduling Problem with Sequence Dependent setup costs and times: Single machine, multiple products and periods

We present in this paper a new formulation of the Capacitated Lot sizing and Scheduling Problem with Sequence Dependent set up cost and times (CLSPSD) problem, well known as an NP-Hard problem. We formulate the problem as a non linear model and use it to modify a lot sizing problem described in literature and applied to a real-life problem of a Canadian paper maker where the paper machine represents the bottleneck resource and consequently requires an efficient production planning approach optimizing resource utilization and minimizing production, setup and inventory costs. In these previous works, the dependency of the costs and times with the production sequences is not thoroughly dealt with. We prove that by really treating the problem of determining the production sequences, we handle to considerably reduce the supply chain total cost. This cost includes production costs, inventory holding costs, start up and setup costs. The reduction in the total cost varies from 6 to 52% when setup costs vary from 20% to 200% of inventory holding costs.