Flexibility analysis on a supply chain contract using a parametric Linear Programming model

This research paper builds on existing knowledge in the field of parametric Linear Programming (pLP) and proposes a continuous mathematical model that considers a multi-period Quantity Flexibility (QF) contract between a car manufacturer (buyer) and external parts supplying company. The supplier periodically delivers parts to the car manufacturer as agreed in the contract. Due to the uncertainty of the demand for parts, the car manufacturer -in concert with the supplier-aims to develop a policy -at strategic level, that determines the optimal nominal order quantity (Q) and variation rate (β) underpinning the contract that ensures the actual order quantity satisfies the actual demand and the total cost is minimised over the contract length. The behaviour of the mathematical model has been examined in order to establish its feasibility and convexity, consequently guaranteeing an optimal solution. Simulations have been carried out to evaluate the relationship of the total cost with respect to the variation rate and the nominal quantity ordered.