Determining $(k)$-Most Demanding Products with Maximum Expected Number of Total Customers

In this paper, a problem of production plans, named k-most demanding products ($(k)$-MDP) discovering, is formulated. Given a set of customers demanding a certain type of products with multiple attributes, a set of existing products of the type, a set of candidate products that can be offered by a company, and a positive integer $(k)$, we want to help the company to select $(k)$ products from the candidate products such that the expected number of the total customers for the $(k)$ products is maximized. We show the problem is NP-hard when the number of attributes for a product is 3 or more. One greedy algorithm is proposed to find approximate solution for the problem. We also attempt to find the optimal solution of the problem by estimating the upper bound of the expected number of the total customers for a set of $(k)$ candidate products for reducing the search space of the optimal solution. An exact algorithm is then provided to find the optimal solution of the problem by using this pruning strategy. The experiment results demonstrate that both the efficiency and memory requirement of the exact algorithm are comparable to those for the greedy algorithm, and the greedy algorithm is well scalable with respect to $(k)$.