Offsetting inventory replenishment cycles to minimize storage space

In a recent paper, [Murthy, N.N., Benton, W.C., Rubin, P.A., 2003. Offsetting inventory cycles of items sharing storage. European Journal of Operational Research 150, 304–319] discussed the problem of offsetting inventory replenishment cycles of several items in order to minimize the maximum required storage space. They analyzed the case where replenishment cycles are given integer multiples of a basic period and proposed a heuristic to solve the problem. While they provided a good analysis of the considered problem, the proposed heuristic produces less interesting results. In the following, a simpler, more efficient and easier to implement heuristic is proposed. Numerical results are provided to prove its superiority.     

带短期价格折扣和允许两次特殊补货的库存决策模型

针对供应商提供短期价格折扣且允许零售商两次特殊补货的库存系统, 建立了以零售商库存效益最大化为目标的库存决策模型, 分析了模型的性质, 根据经济订单批量补货决策下补货时间点与折扣时段的关系, 确定了零售商在不同补货策略下的库存效益增值函数. 据此给出零售商相应的最优补货策略函数表达式, 提出了该模型的一个全局优化算法, 并通过数值算例验证了模型和算法的有效性与可行性.     

Retail replenishment models with display-space elastic demand

We study a single store multi-product inventory problem in which product sales are a composite function of shelf space. Since sales tend to deplete the amount of product on display, the effective shelf space assigned to the product diminishes with time unless replenishment occurs. We consider the problem of optimal replenishment times under these conditions. We assume a linear dependence of sales rate to effective shelf space in all our analysis. We present exact and approximate solutions for the single product and multi-product cases. For the single product case, we study the effect of space elasticity, cross elasticity and empty space elasticity on the optimal replenishment period. For the multi-product case we present a computationally attractive method using matrix exponentials and develop error bounds for this method.     

Temporary price increase during replenishment lead time

Pricing and inventory management make up together revenue management, which is a significant effort to boost revenues out of available resources. Firms use various forms of dynamic pricing, including personalized pricing, markdowns, promotions, coupons, discounts, and clearance sales, to respond to market fluctuations and demand uncertainty. In this paper, we study a temporary price increase policy, a form of dynamic pricing, for a non-perishable product, a practice used by several giant retailers such as Amazon, Walmart, and Apple. We develop a continuous review inventory model that allows for joint replenishment and pricing decisions, where the lead time is not zero. A replenishment decision controls supply, while a pricing decision controls demand. A manager exercises a temporary price increase to slow demand and avoid a stock-out situation while waiting for a shipment, which may not necessarily increase revenues, but decrease stock-out costs. The problem is to solve for the optimal replenishment and the pricing policy parameters that maximize the long-run expected profit. That is, when and how much to order and when to raise the price. In this paper, the inventory level and time trigger a price increase. We solve many numerical examples and perform extensive sensitivity analyses. Our results show that compared to a model that focuses on fixed pricing, our model brings an additional increase in profit of about 13%.     

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.     

Optimal ordering policies for periodic-review systems with replenishment cycles

In this paper, we consider inventory models for periodic-review systems with replenishment cycles, which consist of a number of periods. By replenishment cycles, we mean that an order is always placed at the beginning of a cycle. We use dynamic programming to formulate both the backorder and lost-sales models, and propose to charge the holding and shortage costs based on the ending inventory of periods (rather than only on the ending inventory of cycles). Since periods can be made any time units to suit the needs of an application, this approach in fact computes the holding cost based on the average inventory of a cycle and the shortage cost in proportion to the duration of shortage (for the backorder model), and remedies the shortcomings of the heuristic or approximate treatment of such systems (Hadley and Whitin, Analysis of Inventory Systems, Prentice-Hall, Englewood Cliffs, NJ, 1963). We show that a base-stock policy is optimal for the backorder model, while the optimal order quantity is a function of the on-hand inventory for the lost-sales model. Moreover, for the backorder model, we develop a simple expression for computing the optimal base-stock level; for the lost-sales model, we derive convergence conditions for obtaining the optimal operational parameters.     

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.     

An optimal replenishment policy for deteriorating items with effective investment in preservation technology

In this paper, considering the amount invested in preservation technology and the replenishment schedule as decision variables, we formulate an inventory model with a time-varying rate of deterioration and partial backlogging. The objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time. For any given preservation technology cost, we first prove that the optimal replenishment schedule not only exists but is unique. Next, under given replenishment schedule, we show that the total profit per unit time is a concave function of preservation technology cost. We then provide a simple algorithm to figure out the optimal preservation technology cost and replenishment schedule for the proposed model. We use numerical examples to illustrate the model.