Optimizing production and transportation in a commit-to-delivery business mode

In problems involving the simultaneous optimization of production and transportation, the requirement that an order can only be shipped once its production has been completed is a natural one. One example is a problem of optimizing shipping costs subject to a production capacity constraint studied recently by Stecke and Zhao. Here we present an integer programming formulation for the case in which only completed orders can be shipped that leads to very tight dual bounds and enables one to solve instances of significant size to optimality.