Customer rejection to guide lead time quotation and pricing decisions

• Published in: The Journal of the Operational Research Society 2021-06, Vol.72 (6), p.1358-1372
• Main Authors: Hammami, Ramzi, Frein, Yannick, Albana, Abduh Sayid
• Format: Article
• Language: English
• Subjects: Automatic; endogenous demand; Engineering Sciences; Lead time quotation; M/M/1/K; order acceptance; pricing
• ISSN: 0160-5682; 1476-9360; 0160-5682
• DOI: 10.1080/01605682.2020.1718556

The lead time (LT) quotation and pricing models in make-to-order environments usually assume that all arriving orders are accepted. Hence, despite the loss of demand, the firm must quote a relatively long LT to tackle the situations where there are too many waiting orders. This paper investigates the policy of accepting orders based on the state of the system and, consequently, rejecting customers when the number of waiting orders is larger than a given threshold value. Indeed, if there are less than K jobs in the system (K fixed), then the new order is accepted and a pair of LT and price are quoted to the customer. Otherwise, the order is rejected. Thus, we model the firm's operations as a M/M/1/K queue instead of the commonly-used M/M/1 queue. We determine the optimal solution for K = 1 and solve the problem numerically for K ≥ 2. We show that our policy can be more profitable than the all-orders acceptance policy. We provide insights into when should a K be imposed and how such a K should be chosen. We find that the higher the sensitivity of demand to price or to LT is, the lower the optimal value of K.