Optimal production lot size under backup agreement allowing substitute products

¹ Department of Industrial Management, I-Shou University, Kaohsiung City 84001, Taiwan
² Department of Business Administration, National Pingtung University, 51 Min-Sheng E. Road, Pingtung 900, Taiwan

^* Corresponding author: chwang@mail.nptu.edu.tw

Received: 5 December 2018
Accepted: 27 April 2019

Abstract

In the fashion industry, a flexible backup agreement contract allows the retailer to order a partial amount from the backup quantity to allay the risk of uncertain market demand. However, under such a contract, the manufacturer faces the risk of bearing a huge leftover if the quantity realized by the retailer in backup is small. Accordingly, the present study considers a modified backup agreement in which the manufacturer is permitted to urgently purchase substitute products to satisfy the backup order from a third-party supplier, but at a unit purchase cost greater than the original unit manufacturing cost. The corresponding expected total profit function for the manufacturer is established and shown to be concave. The profit function is used to explore various useful properties for determining the optimal production lot size. In addition, an illustrated numerical example is provided to analyze the impact of the backup contract terms on the optimal production lot size and manufacturer’s profit.