Scheduling and optimal delivery time quotation for customers with time sensitive demand

In this research, we study a supply chain which consists of a firm and a set of customer groups, where the demand (order quantity) from each customer group depends on the quoted delivery time. The prices of the product are determined and different to each customer group. The firm's objective is to maximize the profit by quoting different delivery times for all customer groups. A mathematical model is developed, which is proved to be NP hard. Both a mixed integer programming (MIP) formulation and the branch-and-bound algorithm are proposed to study the moderate size of the problem. Also, a heuristic algorithm is developed which is able to obtain the optimal solution quickly in most of cases when customer size is less than 20.