Optimal price and delivery time quotation with production scheduling for make-to-order manufacturing - Jin, Xianfei (2012)
Customers have varying requirements on price and delivery time in make-to-order manufacturing environment. Due to limited availability of the production capacity, the firm can increase revenue if it allocates priority to time-sensitive customers, charging them a higher price for the same product. The remaining capacity can then be allocated amongst the price-sensitive customers with a relatively lower price. This strategy is aimed at maximizing the overall revenue for the firm. Moreover, the quoted price and delivery time have effects on the demand in the market. In literature, the demand function is considered as a linear decreasing function with respect to price and delivery time, respectively. The challenge is to coordinate the price quotation and the delivery time quotation for customers so that it results in maximizing the net revenue for a manufacturer. There are two types of capacity settings to differentiate products by price and delivery time. These are dedicated capacity and shared capacity. In the dedicated capacity, customers are categorized into several groups. Different customer groups are served in different production facilities. Customers from one customer group share a common price quotation and a common delivery time quotation. The common price and delivery time quotation problem is formulated for a single customer group. The optimality of this problem is studied and applied to develop an algorithm to find the optimal solution in polynomial time. Numerical examples show that the common price and delivery time quotation strategy is applicable when customers are more price-sensitive rather than time-sensitive. In the situation of shared capacity, all customers are served using the same production facility. The production priority is given to the customers who are more time-sensitive. Orders from the customers who are more price-sensitive are scheduled to the rear of the production sequence. Each customer will have a unique quotation of price and a unique quotation of delivery time. The problem is formulated and proven to be NP-complete even when prices are pre-determined parameters. A branch-and-bound algorithm is developed to obtain optimal solutions for the moderate-sized problem. Moreover, a heuristic algorithm is proposed to obtain the near-optimal solution in a short time. Numerical experiments are conducted to test the performance of these two methods.