Optimal inventory policies with non-stationary supply disruptions and advance supply information

We consider the production/inventory problem of a manufacturer (or a retailer) under non-stationary and stochastic supply availability. Although supply availability is uncertain, the supplier would be able to predict her near future shortages -and hence supply disruption to (some of) her customers- based on factors such as her pipeline stock information, production schedule, seasonality, contractual obligations, and non-contractual preferences regarding other manufacturers. We consider the case where the information on the availability of supply for the near future, which we refer to as advance supply information (ASI), is provided by the supplier. The customer demand is deterministic but non-stationary over time, and the system costs consist of fixed ordering, holding and backorder costs. We consider an all-or-nothing type of supply availability structure and we show the optimality of a state-dependent (s; S) policy. For the case with no fixed ordering cost we prove various properties of the optimal order-up-to levels and provide a simple characterization of optimal order-up-to levels. For the model with fixed ordering cost, we propose a heuristic algorithm for finding a good ordering strategy. Finally, we numerically elaborate on the value of ASI and provide managerial insights

Analysis of a decentralized supply chain under partial cooperation

In this article we analyze a decentralized supply chain consisting of a supplier and two independent retailers. In each order cycle retailers place their orders at the supplier to minimize inventory related expected costs at the end of their respective response times. There are two types of lead-times involved. At the end of the supplier lead-time, retailers are given an opportunity to readjust their initial orders (without changing the total order size) so that both retailers can improve their expected costs at the end of respective retailer lead-times (the time it takes for items to be shipped from the supplier to the retailers). Because of the possibility of cooperation at the end of supplier leadtime, each retailer will consider the other's order-up-to level in making the ordering decision. Under mild conditions we prove the existence of a unique Nash equilibrium for the retailer order-up-to levels, and show that they can be obtained by solving a set of newsboy-like equations. We also present computational analysis that provides valuable managerial insight for design and operation of decentralized systems under possibility of partial cooperation

Near-optimal modified base stock policies for the capacitated inventory problem with stochastic demand and fixed cost

In this study, we investigate a single-item, periodic-review inventory problem where the production capacity is limited and unmet demand is backordered. We assume that customer demand in each period is a stationary, discrete random variable. Linear holding and backorder cost are charged per unit at the end of a period. In addition to the variable cost charged per unit ordered, a positive fixed ordering cost is incurred with each order given. The optimization criterion is the minimization of the expected cost per period over a planning horizon. We investigate the infinite horizon problem by modeling the problem as a discrete-time Markov chain. We propose a heuristic for the problem based on a particular solution of this stationary model, and conduct a computational study on a set of instances, providing insight on the performance of the heuristic. © 2014 World Scientific Publishing Co

Analysis of a decentralized supply chain under partial cooperation

In this article, we analyze a decentralized supply chain consisting of a supplier and two independent retailers. In each order cycle, retailers place their orders at the supplier to minimize inventory-related expected costs at the end of their respective response times. There are two types of lead times involved. At the end of the supplier lead time, retailers are given an opportunity to readjust their initial orders (without changing the total order size), so that both retailers can improve their expected costs at the end of respective retailer lead times (the time it takes for items to be shipped from the supplier to the retailers). Because of the possibility of cooperation at the end of supplier lead time, each retailer will consider the other's order-up-to level in making the ordering decision. Under mild conditions, we prove the existence of a unique Nash equilibrium for the retailer order-up-to levels, and show that they can be obtained by solving a set of newsboy-like equations. We also present computational analysis that provides valuable managerial insight for design and operation of decentralized systems under the possibility of partial cooperation. © 2005 INFORMS

Erratum to: 36th International Symposium on Intensive Care and Emergency Medicine

[This corrects the article DOI: 10.1186/s13054-016-1208-6.]