Authors: Dmitry A. Ivanov, Boris V. Sokolov, Semyon A. Potryasaev
We present a new model and algorithm for optimal scheduling of a supply chain (SC) with multiple customers and suppliers. The formulation assumes that suppliers can dynamically allocate jobs and schedule their resources in a coordinated manner so that all the suppliers are equally utilized and jobs are accomplished without interruptions and scheduled subject to maximal customer service level and minimal delays. This problem is represented as a special case of the job shop scheduling problem with dynamically distributed jobs. The approach is based on a natural dynamic decomposition of the problem and its solution with the help of a modified form of continuous maximum principle blended with combinatorial optimization.