Scheduling parallel machines by the dynamic newsboy problem

This paper focuses on a dynamic, continuous-time generalization of the single period newsboy problem. Similar to the classical newsboy problem, the model may represent the inventory of an item that becomes obsolete quickly, spoils quickly, or has a future that is uncertain beyond a single period. The problem is characterized by a number of newsboys (machines) whose operations are organized and controlled in parallel. 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 production and surplus costs that are incurred at each time point along the period. We prove that this continuous-time problem can be reduced to a number of discrete-time problems which are determined by loose, balanced and pressing production conditions. As a result, a polynomial-time combinatorial algorithm is derived in order to find globally optimal solutions.