A produce‐to‐stock system with advance demand information and secondary customers

We consider a manufacturer (i.e., a capacitated supplier) that produces to stock and has two classes of customers. The primary customer places orders at regular intervals of time for a random quantity, while the secondary customers request a single item at random times. At a predetermined time the manufacturer receives advance demand information regarding the order size of the primary customer. If the manufacturer is not able to fill the primary customer's demand, there is a penalty. On the other hand, serving the secondary customers results in additional profit; however, the manufacturer can refuse to serve the secondary customers in order to reserve inventory for the primary customer. We characterize the manufacturer's optimal production and stock reservation policies that maximize the manufacturer's discounted profit and the average profit per unit time. We show that these policies are threshold‐type policies, and these thresholds are monotone with respect to the primary customer's order size. Using a numerical study we provide insights into how the value of information is affected by the relative demand size of the primary and secondary customers. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Inventory control and periodic price discounting campaigns

This paper develops an inventory model that determines replenishment strategies for buyers facing situations in which sellers offer price‐discounting campaigns at random times as a way to drive sales or clear excess inventory. Specifically, the model deals with the inventory of a single item that is maintained to meet a constant demand over time. The item can be purchased at two different prices denoted high and low. We assume that the low price goes into effect at random points in time following an exponential distribution and lasts for a random length of time following another exponential distribution. We highlight a replenishment strategy that will lead to the lowest inventory holding and ordering costs possible. This strategy is to replenish inventory only when current levels are below a certain threshold when the low price is offered and the replenishment is to a higher order‐up‐to level than the one currently in use when inventory depletes to zero and the price is high. Our analysis provides new insight into the behavior of the optimal replenishment strategy in response to changes in the ratio of purchase prices together with changes in the ratio of the duration of a low‐price period to that of a high‐price period. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

Dynamic pricing in a dual‐market environment

This article is concerned with the determination of pricing strategies for a firm that in each period of a finite horizon receives replenishment quantities of a single product which it sells in two markets, for example, a long‐distance market and an on‐site market. The key difference between the two markets is that the long‐distance market provides for a one period delay in demand fulfillment. In contrast, on‐site orders must be filled immediately as the customer is at the physical on‐site location. We model the demands in consecutive periods as independent random variables and their distributions depend on the item's price in accordance with two general stochastic demand functions: additive or multiplicative. The firm uses a single pool of inventory to fulfill demands from both markets. We investigate properties of the structure of the dynamic pricing strategy that maximizes the total expected discounted profit over the finite time horizon, under fixed or controlled replenishment conditions. Further, we provide conditions under which one market may be the preferred outlet to sale over the other. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 531–549, 2015     

On the effectiveness of top‐down strategy for forecasting autoregressive demands

We investigate the relative effectiveness of top‐down versus bottom‐up strategies for forecasting the demand of an item that belongs to a product family. The demand for each item in the family is assumed to follow a first‐order univariate autoregressive process. Under the top‐down strategy, the aggregate demand is forecasted by using the historical data of the family demand. The demand forecast for the items is then derived by proportional allocation of the aggregate forecast. Under the bottom‐up strategy, the demand forecast for each item is directly obtained by using the historical demand data of the particular item. In both strategies, the forecasting technique used is exponential smoothing. We analytically evaluate the condition under which one forecasting strategy is preferred over the other when the lag‐1 autocorrelation of the demand time series for all the items is identical. We show that when the lag‐1 autocorrelation is smaller than or equal to 1/3, the maximum difference in the performance of the two forecasting strategies is only 1%. However, if the lag‐1 autocorrelation of the demand for at least one of the items is greater than 1/3, then the bottom‐up strategy consistently outperforms the top‐down strategy, irrespective of the items' proportion in the family and the coefficient of correlation between the item demands. A simulation study reveals that the analytical findings hold even when the lag‐1 autocorrelation of the demand processes is not identical. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

Vendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

The initial provisioning decision for insurance type items

Initial provisioning decisions (inventory stocking requirements) for low demand items often have to be made without much knowledge of what future demand rates will be. When the nature of an item is such that little demand for it is expected, the problem of whether to stock initially or risk not stocking the item is most critical. This report discusses this problem and presents decision procedures which can be used to handle this aspect of initial provisioning. The procedures relate an item's provisioning desirability to its provisioning characteristics, such as expected cost, expected resupply time, current information on its likely demand rate, and to an overall operating policy or criterion. The criterion function measures the total system degredation as a function of the events of having items out of stock when demand occurs. Several different policy functions are discussed and the provisioning decision rules which apply to each are presented. Demand rate information is handled through a Bayesian type approach. The decision rules presented in this report can be utilized to either determine stocking requirements within a budgetary constraint, or determine the relative stocking desirability on an item-by-item basis.     

Nonrobustness of the normal approximation of lead‐time demand in a (Q,R) system

For computing an optimal (Q, R) or kindred inventory policy, the current literature provides mixed signals on whether or when it is safe to approximate a nonnormal lead‐time‐demand (“LTD”) distribution by a normal distribution. The first part of this paper examines this literature critically to justify why the issue warrants further investigations, while the second part presents reliable evidence showing that the system‐cost penalty for using the normal approximation can be quite serious even when the LTD‐distribution's coefficient of variation is quite low—contrary to the prevalent view of the literature. We also identify situations that will most likely lead to large system‐cost penalty. Our results indicate that, given today's technology, it is worthwhile to estimate an LTD‐distribution's shape more accurately and to compute optimal inventory policies using statistical distributions that more accurately reflect the LTD‐distributions' actual shapes. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Sensitivity analysis on responsive pricing and production under imperfect demand updating

This paper examines three types of sensitivity analysis on a firm's responsive pricing and responsive production strategies under imperfect demand updating. Demand has a multiplicative form where the market size updates according to a bivariate normal model. First, we show that both responsive production and responsive pricing resemble the classical pricing newsvendor with posterior demand uncertainty in terms of the optimal performance and first‐stage decision. Second, we show that the performance of responsive production is sensitive to the first‐stage decision, but responsive pricing is insensitive. This suggests that a “posterior rationale” (ie, using the optimal production decision from the classical pricing newsvendor with expected posterior uncertainty) allows a simple and near‐optimal first‐stage production heuristic for responsive pricing. However, responsive production obtains higher expected profits than responsive pricing under certain conditions. This implies that the firm's ability to calculate the first‐stage decision correctly can help determine which responsive strategy to use. Lastly, we find that the firm's performance is not sensitive to the parameter uncertainty coming from the market size, total uncertainty level and information quality, but is sensitive to uncertainty originating from the procurement cost and price‐elasticity.     

The stochastic joint replenishment problem: A new policy,analysis, and insights

In this study, we propose a new parsimonious policy for the stochastic joint replenishment problem in a single‐location, N‐item setting. The replenishment decisions are based on both group reorder point‐group order quantity and the time since the last decision epoch. We derive the expressions for the key operating characteristics of the inventory system for both unit and compound Poisson demands. In a comprehensive numerical study, we compare the performance of the proposed policy with that of existing ones over a standard test bed. Our numerical results indicate that the proposed policy dominates the existing ones in 100 of 139 instances with comparably significant savings for unit demands. With batch demands, the savings increase as the stochasticity of demand size gets larger. We also observe that it performs well in environments with low demand diversity across items. The inventory system herein also models a two‐echelon setting with a single item, multiple retailers, and cross docking at the upper echelon. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Multi‐item capacitated lot‐sizing problems with setup times and pricing decisions

We study a multi‐item capacitated lot‐sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot‐sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch‐and‐price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Coordinated pricing and inventory control problems with capacity constraints and fixed ordering cost

This article addresses a single‐item, finite‐horizon, periodic‐review coordinated decision model on pricing and inventory control with capacity constraints and fixed ordering cost. Demands in different periods are random and independent of each other, and their distributions depend on the price in the current period. Each period's stochastic demand function is the additive demand model. Pricing and ordering decisions are made at the beginning of each period, and all shortages are backlogged. The objective is to find an optimal policy that maximizes the total expected discounted profit. We show that the profit‐to‐go function is strongly CK‐concave, and the optimal policy has an (s,S,P) ‐like structure. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Three ways of obtaining the average cost expression in a problem related to joint replenishment inventory control

This paper does not present a new result, rather it is meant to illustrate the choice of modelling procedures available to an analyst in a typical inventory control problem. The same “average cost per unit time” expression is developed by three quite different procedures. This variety of approaches, as well as the recounting of the author's chronological efforts to solve the problem, should be of interest to the reader. The specific inventory problem studied is one where the controller of an item is faced with random opportunities for replenishment at a reduced setup cost; the problem is an integral component of the broader problem of inventory control of a group of items whose replenishments are coordinated to reduce the costs of production, procurement, and/or transportation.     

Dynamic routing of prioritized warranty repairs

Recent years have seen a strong trend toward outsourcing warranty repair services to outside vendors. In this article we consider the problem of dynamically routing warranty repairs to service vendors when warranties have priority levels. Each time an item under warranty fails, it is sent to one of the vendors for repair. Items covered by higher priority warranty receive higher priority in repair service. The manufacturer pays a fixed fee per repair and incurs a linear holding cost while an item is undergoing or waiting for repair. The objective is to minimize the manufacturer's long‐run average cost. Because of the complexity of the problem, it is very unlikely that there exist tractable ways to find the optimal routing strategies. Therefore, we propose five heuristic routing procedures that are applicable to real‐life problems. We evaluate the heuristics using simulation. The simulation results show that the index‐based “generalized join the shortest queue” policy, which applies a single policy improvement step to an initial state‐independent policy, performs the best among all five heuristics. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Economic ordering decisions with market choice flexibility

Standard approaches to classical inventory control problems treat satisfying a predefined demand level as a constraint. In many practical contexts, however, total demand is comprised of separate demands from different markets or customers. It is not always clear that constraining a producer to satisfy all markets is an optimal approach. Since the inventory‐related cost of an item depends on total demand volume, no clear method exists for determining a market's profitability a priori, based simply on per unit revenue and cost. Moreover, capacity constraints often limit a producer's ability to meet all demands. This paper presents models to address economic ordering decisions when a producer can choose whether to satisfy multiple markets. These models result in a set of nonlinear binary integer programming problems that, in the uncapacitated case, lend themselves to efficient solution due to their special structure. The capacitated versions can be cast as nonlinear knapsack problems, for which we propose a heuristic solution approach that is asymptotically optimal in the number of markets. The models generalize the classical EOQ and EPQ problems and lead to interesting optimization problems with intuitively appealing solution properties and interesting implications for inventory and pricing management. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Purchase and retrieval competition for seasonal produce

We study the competition problem of purchase and multiretrieval of perishable seasonal produce, where wholesalers purchase and stock their products in the first period, and then retrieve and sell them in subsequent periods. We first consider the duopoly case and assume that the prices are exogenous and fluctuate. In each period, after the price realization, the wholesalers retrieve some stock from their warehouses to satisfy their demands. One wholesaler's unsatisfied customers can switch to another and be satisfied by its left retrieved products. Any unsold retrieved stock has no salvage value and any unsatisfied demand is lost. The unretrieved stock is carried to the next period at a perishable rate. The wholesalers compete for the substitute demand by determining their own purchase and retrieval quantities. We show the existence and uniqueness of a pure-strategy Nash equilibrium, and that the Nash equilibrium strategy has the simple “sell-down-to” structure. We also consider the general N-person game and show the existence of the Nash equilibrium, and characterize the structure of the equilibrium strategy for the symmetric case. In addition, we consider the case with endogenous prices, and show that the problem reduces to a repeated newsvendor game with price and inventory competition. We derive the conditions under which a unique Nash equilibrium exists and characterize the equilibrium strategy. Finally, we conduct numerical studies to examine the impacts of the model parameters on the equilibrium outcomes and to generate managerial insights.     

Contracts and coordination: Supply chains with uncertain demand and supply

Considering a supply chain with a supplier subject to yield uncertainty selling to a retailer facing stochastic demand, we find that commonly studied classical coordination contracts fail to coordinate both the supplier's production and the retailer's procurement decisions and achieve efficient performance. First, we study the vendor managed inventory (VMI) partnership. We find that a consignment VMI partnership coupled with a production cost subsidy achieves perfect coordination and a win‐win outcome; it is simple to implement and arbitrarily allocates total channel profit. The production cost subsidy optimally chosen through Nash bargaining analysis depends on the bargaining power of the supplier and the retailer. Further, motivated by the practice that sometimes the retailer and the supplier can arrange a “late order,” we also analyze the behavior of an advance‐purchase discount (APD) contract. We find that an APD with a revenue sharing contract can efficiently coordinate the supply chain as well as achieve flexible profit allocation. Finally, we explore which coordination contract works better for the supplier vs. the retailer. It is interesting to observe that Nash bargaining solutions for the two coordination contracts are equivalent. We further provide recommendations on the applications of these contracts. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 305–319, 2016     

When is a base stock policy optimal in recovering disrupted cyclic schedules?

The extended economic lot scheduling problem (EELSP) is concerned with scheduling the production of a set of items in a single facility to minimize the long-run average holding, backlogging, and setup costs. Given an efficient cyclic production schedule for the EELSP, called the target schedule, we consider the problem of how to schedule production after a single schedule disruption. We propose a base stock policy, characterized by a base stock vector, that prescribes producing an item until its inventory level reaches the peak inventory of the target schedule corresponding to the item's position in the production sequence. We show that the base stock policy is always successful in recovering the target schedule. Moreover, the base stock policy recovers the target schedule at minimal excess over average cost whenever the backorder costs are proportional to the processing times. This condition holds, for example, when the value of the items is proportional to their processing times, and a common inventory carrying cost and a common service level is used for all the items. Alternatively, the proportionality condition holds if the inventory manager is willing to select the service levels from a certain set that is large enough to guarantee any minimal level of service, and then uses the imputed values for the backorder costs. When the proportionality condition holds we provide a closed-form expression for the total relevant excess over average cost of recovering the target schedule. We assess the performance of the base stock policy when the proportionality condition does not hold through a numerical study, and suggest some heuristic uses of the base stock policy. © 1994 John Wiley & Sons, Inc.     

Optimal retail assortments for substitutable items purchased in sets

We consider the problem of optimizing assortments in a multi‐item retail inventory system. In addition to the usual holding and stockout costs, there is a fixed cost for including any item in the assortment. Customers' preferences for items include both probabilistic substitution patterns and the desire to purchase sets of complementary items. We develop a demand model to capture this behavior, and derive tractable approximations that allow us to formulate the optimization problem as a 0–1 mixed integer linear program. Numerical examples are solved to illustrate key insights into how both complementary and substitute items affect the optimal assortment and the expected profit. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 793–822, 2003.     

Customer waiting-time distributions under base-stock policies in single-facility multi-item production systems

We derive efficient and highly accurate approximations for the customer waiting-time distributions experienced in stochastic economic lot scheduling systems (SELSPs) that are governed by general base-stock policies under a cyclic or more general periodic item sequence. SELSPs involve settings where several items need to be produced in a common facility with limited capacity, under significant uncertainty regarding demands, unit production times, setup times, or combinations thereof. Under a base-stock policy one continues production of a given item until a specific target level is reached; the different items are produced in a given periodic sequence, possibly with idle times inserted between the completion of an item's production batch and the setup of the next item. We also demonstrate how base-stock levels can be specified efficiently to guarantee any prescribed fill rate within a specific service window or distribution of service windows. © 1996 John Wiley & Sons, Inc.     

Dynamic capacity reservation and due date quoting in a make‐to‐order system

We consider a make‐to‐order manufacturer facing random demand from two classes of customers. We develop an integrated model for reserving capacity in anticipation of future order arrivals from high priority customers and setting due dates for incoming orders. Our research exhibits two distinct features: (1) we explicitly model the manufacturer's uncertainty about the customers' due date preferences for future orders; and (2) we utilize a service level measure for reserving capacity rather than estimating short and long term implications of due date quoting with a penalty cost function. We identify an interesting effect (“t‐pooling”) that arises when the (partial) knowledge of customer due date preferences is utilized in making capacity reservation and order allocation decisions. We characterize the relationship between the customer due date preferences and the required reservation quantities and show that not considering the t‐pooling effect (as done in traditional capacity and inventory rationing literature) leads to excessive capacity reservations. Numerical analyses are conducted to investigate the behavior and performance of our capacity reservation and due date quoting approach in a dynamic setting with multiple planning horizons and roll‐overs. One interesting and seemingly counterintuitive finding of our analyses is that under certain conditions reserving capacity for high priority customers not only improves high priority fulfillment, but also increases the overall system fill rate. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008