Parallel-machine, multiple-product-type, continuous-time scheduling: Decomposable cases

This paper considers a manufacturing system where multiple-product-types are produced on a set of parallel machines. The production quantity for each product-type in a planning horizon is predetermined. However, the planning horizon is not fixed, and a cost must be paid for each unit of time in the horizon. Inventory holding costs are incurred due to storing products in the buffer placed after each machine. In addition, a production cost is incurred if a machine is not idle. Our objective is to schedule the production so that inventory, production, and planning horizon costs are minimized. With the aid of the maximum principle, this continuous-time scheduling problem is studied, and the conditions such that the problem can be decomposed into a set of well-structured, discrete-time sub-problems are derived. Consequently, several solvable cases are identified, and their corresponding polynomial-time algorithms are suggested.