A study on the scheduling problem of goods pictures in an online store

An integer programming model is given to deal with the problem that an online store wants to arrange the display time of goods pictures within the given scheduling horizon and space in order to maximize its profits. In this model, two characters that goods pictures have effect on demands and there are no inventories in many online stores are considered. It is explained that the problem discussed is equivalent to a special multiple-choice knapsack problem, so a dynamic programming algorithm with a complexity of pseudo polynomial time is provided; the properties of the objective function are studied, a greedy-like heuristic algorithm based on them with a complexity of polynomial time is proposed, and an example is given to demonstrate that the greedy-like heuristic method is effective.