Parallel machine, capacitated lot-sizing and scheduling for the pipe-insulation industry

We develop a solution procedure for a production problem that involves the optimal lot-sizing and scheduling of multiple products on parallel machines over a long planning horizon. The objective is to determine the product assignment, production quantities, and production sequence on each machine in order to meet demand and maximise the total production amount in a given planning horizon. We study this problem in the context of the manufacturing of pipe insulation, in which multiple features have to be considered simultaneously. The solution procedure combines mathematical programming and a post-processing sequencing heuristic. We also develop a procedure to determine safety stock levels and use Monte Carlo simulation to assess the risk associated with inventory shortages due to stochastic production rates. Computational tests are performed on both real and artificially-generated data.