Risk sharing in supply chains using order bands—Analytical results and managerial insights

Abstract

This work generalizes and extends a number of basic production-inventory models. We study a periodic review non-stationary Markovian production-inventory model with stochastic demand and holding and penalty costs (all state-dependent) where goods can be procured from up to two suppliers. Each supplier quotes a state-dependent minimum order quantity (MOQ), order capacity ( C), and unit price. We concentrate on a base-stock policy that is defined by a vector of numbers—one for each lead time—indexed by the states of the Markov chain. In certain cases, our policy is optimal. For the general case, we show that there is no simple optimal policy. We use infinitesimal perturbation analysis to compute inventory levels within this class for an application motivated by international trade. For this application we find that the imposition of minimum and/or maximum order quantities provides an effective mechanism for risk sharing: the customer guarantees the supplier a minimum order every period, at an increased unit price, and in exchange the supplier grants an increase in capacity. This can more effectively match supply with demand, making the entire supply chain more profitable.