A private contributions game for joint replenishment

We study a non-cooperative game for joint replenishment by n firms that operate under an EOQ-like setting. Each firm decides whether to replenish independently or to participate in joint replenishment, and how much to contribute to joint ordering costs in case of participation. Joint replenishment cycle time is set by an intermediary as the lowest cycle time that can be financed with the private contributions of participating firms. We characterize the behavior and outcomes under undominated Nash equilibria. © Springer-Verlag 2011

Multi-period supplier selection under price uncertainty

We consider a problem faced by a procurement manager who needs to purchase a large volume of multiple items over a planning horizon (a quarter or a year) that consists of multiple periods (months). There are multiple suppliers that are qualified to offer all or a portion of the items in consideration. Each supplier provides a base price for each item that it offers. In addition, suppliers offer various discounts to the manufacturer. The discounts are contingent on meeting various conditions on total available market, volume or spend for a single item or a group of items and reflect economies of scale and scope that may exist in suppliers' operations. Some of these discounts may be tied to future realization of a random event that can be mutually verified. We formulate the problem as a scenario based multi-stage stochastic optimization model. The model is general in the sense that it allows us to consider random events such as a drop in price that a supplier offers to other customers (which the company in consideration may also benefit if it obtains the most favored customer status from the supplier by meeting various conditions in the earlier periods), a price change in the spot market or other events that may force a supplier to disclose a new discount offer in the middle of the planning horizon. We propose two certainty equivalent heuristics for this problem and show how one can evaluate the regret of using these heuristics instead of an optimal solution. We finally present an application of our model on three procurement bidding events that took place at a major manufacturing company in 2010. The results show that considering most favored customer terms in supplier offers may create substantial savings and under certain settings, these savings may even surpass the savings that can be obtained from regular discount offers. © 2013 Hewlett-Packard Development Company, L.P