A Zero-Inventory Production-Distribution Problem with Time-Window Constraints

In this paper, we study a sub-problem of integrated production and distribution for a perishable product that cannot be inventoried. The manufacturing facility has a limited production rate, and the delivery truck has a non-negligible traveling time between locations. The order in which customers may receive deliveries is fixed. Each customer requests a delivery quantity and a time window for receiving the delivery. Since the production facility and the shipping trucks are limited resources, not all the customers may receive the delivery within their specified time windows. The problem is then to choose a subset of customers from the given sequence to receive the deliveries to maximize the amount of demand satisfied without violating the product lifetime, the production capacity, and the delivery time window constraints. The general version of the problem is NP-hard even with relaxed time windows and instantaneous truck traveling time. We analyze the properties of this problem and show the conditions under which optimality is achieved. A greedy heuristic is proposed based on this analysis. Empirical observations on the error gaps achieved by this heuristic are reported. (