One-machine, N-product-type, continuous-time scheduling with a common due date: a polynomially solvable case

The paper analyzes a manufacturing system made up of one-machine which produces N-product-types with controllable production rates in response to product demands. The demands are characterized by different amounts of each product-type to be produced and a common due date. The objective is to minimize inventory and backlog costs which are incurred when meeting the due date results in inventory surpluses and shortages. With the aid of the maximum principle, the continuous-time scheduling problem is studied as an optimal control model and is reduced to a combinatorial one, polynomially solvable when the costs are either "agreeableʹʹ or when the number of the non-agreeable costs is limited.