A model and polynomial algorithm for purchasing and repositioning containers

We study the management of containers in a logistic chain between a supplier and a manufacturer in a ramp-up scenario with deterministic non-decreasing demand. We consider a periodic review system with T periods of R time steps. The supplier sends full containers at every step and receives empty containers every period. To face demand increase, the manufacturer can purchase containers at a setup cost while the supplier can buy single-use disposables. We assume positive delivery times. We formulate our problem as a fixed-plus-linear-cost flow and solve it under a realistic assumption in O(R2·T4·log[R·T]2) time by adapting the Wagner-Within algorithm.