Alper Şen

The newsboy problem with multiple demand classes

We consider the single item newsboy problem, where the item can be sold to different demand classes at different prices. The demands are realized sequentially over time. That is, the newsboy purchases newspapers at the beginning of the day and sells them in the morning and in the afternoon with different prices. We analyze two cases where the prices are either decreasing or increasing; the former case applies, for example, to fashion goods retailing, while the latter to airlines and hotels. In the decreasing price case, we find the optimal order quantity to maximize the expected profit with independent multiple demands. We show numerically that aggregating the multiple demands with a single average price or applying the single demand newsboy model separately to multiple demand classes may lead to large sub-optimality. In the increasing price case, we analyze a two demand class model in which a fraction of the unsatisfied lower fare demand diverts to the high fare class, thus causing dependent sales. We follow a policy of protecting the sales in the higher fare class by limiting the sales in the lower fare class. We derive both the fare allocation limit and the initial capacity, and discuss managerial implications. For both models, we give bounds on the optimal order quantity.

Lot streaming in open shops

We study lot streaming in shops in which the order the jobs are to be processed is immaterial. For a single job case, the properties of the optimal routing is determined. For the multi job case, two machine shops are analyzed. It is shown that lot streaming will improve makespan only if there is a job with large processing times. We show that there can be at most one such job and derive the optimal sublot sizes and their sequence.

Spare parts inventory management with demand lead times and rationing

We study an inventory system that consists of two demand classes. The orders in the first class need to be satisfied immediately, whereas the orders in the second class are to be filled in a given demand lead time. The two classes are also of different criticality. For this system, we propose a policy that rations the non-critical orders. Under a one-for-one replenishment policy with backordering and for Poisson demand arrivals for both classes, we first derive expressions for the service levels of both classes. The service level for the critical class is an approximation, whereas the service level for the non-critical class is exact. We then conduct a computational study to show that our approximation works reasonably, the benefits of rationing can be substantial, and the incorporation of demand lead time provides more value when the demand class with demand lead time is the critical class. The research is motivated by the spare parts service system of a major capital equipment manufacturer that faces two types of demand. For this company, the critical down orders need to be satisfied immediately, while the less critical maintenance orders can be satisfied after a fixed demand lead time. We conduct a case study with 64 representative parts and show that significant savings (as much as 14% on inventory on hand) are possible through incorporation of demand lead times and rationing.

A joint replenishment policy with individual control and constant size orders

We consider inventory systems with multiple items under stochastic demand and jointly incurred order setup costs. The problem is to determine the replenishment policy that minimises the total expected ordering, inventory holding, and backordering costs–the so-called stochastic joint replenishment problem. In particular, we study the settings in which order setup costs reflect the transportation costs and have a step-wise cost structure, each step corresponding to an additional transportation vehicle. For this setting, we propose a new policy that we call the (s, 𝒬) policy, under which a replenishment order of constant size 𝒬 is triggered whenever the inventory position of one of the items drops to its reorder point s. The replenishment order is allocated to multiple items so that the inventory positions are equalised as much as possible. The policy is designed for settings in which backorder and setup costs are high, as it allows the items to independently trigger replenishment orders and fully exploits the economies of scale by consistently ordering the same quantity. A numerical study is conducted to show that the proposed (s, 𝒬) policy outperforms the well-known (𝒬, S) policy when backorder costs are high and lead times are small.

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 multiple periods from multiple suppliers that provide base prices and discounts. Discounts are contingent on meeting various conditions on total volume or spend, and some are tied to future realizations of random events that can be mutually verified. We formulate a scenario-based multi-stage stochastic optimization model that allows us to consider random events such as a drop in price because of the most favoured customer clauses, a price change in the spot market or a new discount offer. We propose certainty-equivalent heuristics and evaluate the regret of using them. We use our model for three bidding events of a large manufacturing company. The results show that considering most favored customer clauses in supplier offers may create substantial savings that may surpass the savings from regular discount offers.

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.

Demand uncertainty and inventory turnover performance

Purpose – The purpose of this paper is to investigate the impact of demand uncertainty on inventory turnover performance through empirical modeling. In particular the authors use the inaccuracy of quarterly sales forecasts as a proxy for demand uncertainty and study its impact on firm-level inventory turnover ratios. Design/methodology/approach – The authors use regression analysis to study the effect of various measures on inventory performance. The authors use a sample financial data for 304 publicly listed US retail firms for the 25-year period from 1985 to 2009. Findings – Controlling for the effects of retail segments and year, it is found that inventory turnover is negatively correlated with mean absolute percentage error of quarterly sales forecasts and gross margin and positively correlated with capital intensity and sales surprise. These four variables explain 73.7 percent of the variation across firms and over time and 93.4 percent of the within-firm variation in the data. Practical implications...

Non-Cooperative Joint Replenishment Under Asymmetric Information

We consider jointly replenishing n ex-ante identical firms that operate under an EOQ like setting using a non-cooperative game under asymmetric information. In this game, each firm, upon being privately informed about its demand rate (or inventory cost rate), submits a private contribution to an intermediary that specifies how much it is willing to pay for its replenishment per unit of time and the intermediary determines the maximum feasible frequency for the joint orders that would finance the fixed replenishment cost. We show that a Bayesian Nash equilibrium exists and characterize the equilibrium in this game. We also show that the contributions are monotone increasing in each firm’s type. We finally conduct a numerical study to compare the equilibrium to solutions obtained under independent and cooperative ordering, and under full information. The results show that while information asymmetry eliminates free-riding in the contributions game, the resulting aggregate contributions are not as high as under full information, leading to higher aggregate costs.

Applied Materials Uses Operations Research to Design Its Service and Parts Network

Applied Materials Inc. is the global leader in nanomanufacturing technology solutions. It has a broad portfolio of innovative equipment, service, and software products and supports its customers worldwide with an extensive service and parts network with more than 100 locations. At the end of 2006, Applied Materials decided to evaluate and rationalize the design of its North American network. It set up a detailed optimization model (including 50,000 parts) to develop a network and distribution strategy. To our knowledge, this is the first large-scale multiechelon network-design model that incorporates safety stock inventory costs while considering the effects of lead time and risk pooling. The company used the models recommendations to reduce costs while maintaining or improving its service to customers. The recommendations included simplifying the distribution network by consolidating depot locations for specific customers and skipping an echelon for others, thus leading to a projected inventory reduction of

Design and analysis of mechanisms for decentralized joint replenishment

10 million. The company is currently implementing these recommendations and has already eliminated five depots. Applied Materials estimates that during the first year of implementation, inventory reductions of