Flexibility Analysis on a Supply Chain Contract: Deterministic and Stochastic Settings Event

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This study examines the key parameters underpinning the Quantity Flexibility (QF) contract within two-echelon supply chains, where the supplier periodically delivers goods to the retailer as agreed in the contract. Due to the uncertainty of the demand, the retailer, in concert with the supplier, aims to develop a policy at strategic level, that determines the optimal nominal order quantity (Q) and the variation rate B to ensure the actual order quantity satisfies the actual demand with a minimum total purchasing, holding and shortage costs over the contract length. The approach taken in this study is aimed at solving the problem in two different settings. One is called the deterministic setting, where the demands are considered as deterministic and the other is called stochastic setting, where the demands are stochastic and stationary. For the deterministic setting, a parametric Linear Programming (pLP) model is developed from the retailer's perspective to help analyse the optimal combination of values of B and Q. The convexity property of the objective function of the total cost with respect to both B and Q has been examined. Due to the fact that the optimal solution cannot be analytically found, we numerically evaluate the best combinations of B and Q to draw some managerial insights based on the findings. For the stochastic setting, this study analyses the long-run behaviour of the system when the signed contract is executed and calculates the mathematical expectation of per-period total purchasing, inventory holding and backlogging costs, as a function of the contracting parameters B and Q. The optimal values of these parameters are calculated through simulation of various demand patterns. For this purpose, we consider the basic case with zero lead time and a very simple order policy during the execution of the contract. These assumptions are nevertheless reasonable in the context of a car manufacturer and a supplier delivering Just-In-Time (JIT) parts using a QF contract. The evolution of the inventory position can be modelled with a Markov chain and the long-run behaviour of the system can then be analysed by considering the steady-state. Due to mathematical intractability, the steady-state is estimated through simulation.