Optimal parameter selection problem with application to the synchronization of delivery cycles in a supply chain with Wiener process

Abstract

SummaryIn this paper, we use optimal parameter selection technique to develop two models involving single‐vendor–multiple‐buyer supply chain, which are called the dynamic independent optimization (DIO) model and the dynamic synchronized cycles (DSC) model, respectively. These models are, respectively, similar to the traditional static independent policy model and the traditional static synchronized cycle model, except that the deterministic demands of the buyers in the above two static models are now being replaced by the stochastic demands satisfying a Wiener process, which have more real‐life applications. Similar to the above static synchronized cycles model, the synchronization of the supply chain in our DSC model is also achieved by scheduling the delivery days of the buyers and coordinating them with the vendor's production cycle. Finding the optimal expected system costs of the DIO model and the DSC model involves solving optimal parameter selection problems governed by ordinary differential equations, whose final times are continuous decision variables and discrete decision variables, respectively. Computational methods have been developed for solving these problems. Numerical results show that the coordinated policy is better than the independent optimization policy, in terms of minimizing the expected system cost of the entire supply chain. Sensitivity analysis is performed to test the effect of changing the cost coefficients and the value on the performances of these models, where is the ratio of the total mean demand rate of all the buyers over the vendor's production rate.