Two-product two-region production and transportation models

Abstract

A deterministic production and transportation planning problem is considered over a finite time horizon for two products that can be produced in each of two regions. Each region employs its own facility to supply the demands for two products. Demands for product 2 in one region can be satisfied either by its own production or transportation from another region, while no transportation between two regions is allowed for product 1. Production and transportation costs are assumed to be nondecreasing and concave. Backlogging is not allowed. The objective is to find the schedule of production and transportation in each region by which the total cost over the horizon is minimized. Using a network flow approach, we develop a dynamic programming algorithm that can find an optimal policy. The model is extended to the case in which capacity bounds on transportation are allowed.