Multi-stage newsboy problem: A dynamic model

The newsboy problem is a well-known operations research model. Its various extensions have been applied to managing capacity and evaluating advanced orders in manufacturing, retail and service industries. This paper focuses on a dynamic, continuous-time generalization of the single-period newsboy problem. The problem is characterized by a number of the newsboys whose operations are organized and controlled in sequential stages. The objective is to minimize shortage and surplus costs occurring at the end of the period as in the classical newsboy problem, as well as intermediate surplus costs incurring at each time point along the period. We prove that this continuous-time problem can be reduced to a number of discrete-time problems. On this basis, a polynomial-time combinatorial algorithm is derived to find globally optimal solution when the system satisfies a certain capacity condition.