There are many studies for management problems in supply chains consisting of manufacturers and retailers. As one of such studies, a negotiation procedure for concluding a contract in a supply chain consisting of a manufacturer and a retailer has been considered based on a cooperative game theoretic approach. However, the more common situation is that a wholesaler is an intermediary between a manufacturer and a retailer. From this viewpoint, the study on the negotiation procedure for concluding a contract in the tandem supply chain that three members of a manufacturer, a wholesaler and a retailer are arranged tandem should be also investigated. On one hand, the negotiation procedure in the supply chain consisting of a manufacturer and a retailer has been considered under a situation where a probability density function (p.d.f.) of demand quantity is unknown and only the mean and variance as limited information about demand quantity are forecasted. In this study, we derive a collaborative bargaining solution for a contract in a tandem supply chain through a negotiation procedure based on the cooperative game theoretic approach under a situation where only the mean and variance of demand quantity are given as limited information. For deriving the bargaining solution in the tandem supply chain, the distribution free approach based on Cauchy-Schwarz inequality is adopted to evaluate the lower bounds of the expected profits of the manufacturer, wholesaler and retailer. As a result, a unique collaborative bargaining solution of a contract in the tandem supply chain consisting of three or more members is derived under a situation where the probability density function of demand quantity is unknown and only the mean and variance of demand quantity are given.

This study considers a production seat booking system in a make-to-stock manufacturing process with fixed lot size production.

This is a scheduling system similar to that used in airplane and train booking systems where the user assigns jobs to vacant seats and makes production plans. As a preliminary step, the user increases or decreases the number of seats in advance, taking into account demand and inventory. Setting this increase/decrease in seats is as an important decision-making process to prevent inventory shortage/excess in the system.

Our previous study adopted a more quantitative evaluation method than previous studies and proposed a method for estimating the controllable parameters for setting the number of seats to reduce shortages and inventories using multiple regression analysis. However, since the production model of our previous study is similar to the make-to-order production process, this study assumes a make-to-stock production environment with fixed-lot-size production and expands it to a more realistic production model using production instructions in a replenishing point manufacturing system, which takes inventory levels into account. We also add losses due to set-up and vacant seats to the criteria.

We quantitatively evaluated how the control parameters affect the criteria in the production model, and studied a method for estimating the control parameters for setting the number of seats to reduce the related cost using "Response Surface Method (RSM) Unity Optimization" (JUSE-StatWorks®/V5).

Based on these findings, the purpose of this paper is to help set the appropriate number of seats in a production seat booking system for a fixed-lot-size production environment.