Multi-location production and delivery with job selection

We study a problem of coordinating multi-location production with limited delivery capability and the option to select jobs. Each job has to be completed and delivered to a central warehouse, or customer, before its due-date to avoid incurring a job-dependent penalty. A single vehicle, capable of carrying an unlimited number of jobs, is available to transport processed jobs to the warehouse. The traveling times to and from the different production sites and the delivery costs are location-dependent. We assume equal processing time jobs and location dependent production speed. We develop several properties of an optimal scheduling and delivery policy, and show that the problem can be solved by reduction to a
shortest-path problem in a corresponding network. The overall computational effort is O(n^(2m^2 + 4)log n) (where n and m are the number of jobs and the number of machines, respectively) by the application of the Directed Acyclic Graph (DAG) method. We test the algorithm numerically and show that the algorithm finds an optimal solution in reasonable time. For various special cases the computational effort reduces substantially.