Multi-item dynamic production–distribution planning in process industries with divergent finishing stages

This paper examines a multi-item dynamic production–distribution planning problem between a manufacturing location and a distribution center. Transportation costs between the manufacturing location and the distribution center offer economies of scale and can be represented by general piecewise linear functions. The production system at the manufacturing location is a serial process with a multiple parallel machines bottleneck stage and divergent finishing stages. A predetermined production sequence must be maintained on the bottleneck machines. A tight mixed-integer programming model of the production process is proposed, as well as three different formulations to represent general piecewise linear functions. These formulations are then used to develop three equivalent mathematical programming models of the manufacturer–distributor flow planning problem. Valid inequalities to strengthen these formulations are proposed and the strategy of adding extra 0–1 variables to improve the branching process is examined. Tests are performed to compare the computational efficiency of these models. Finally, it is shown that by adding valid inequalities and extra 0–1 variables, major computational improvements can be achieved.