The Backroom Effect in Retail Operations

Traditional inventory models fail to take into account the dynamics between the retail sales floor and the backroom, commonly used by retailers for extra storage. When a replenishment order for a given item arrives at a retail store, it may not fit on the allocated shelf space, making backroom storage necessary. In this article, we introduce the backroom effect (BRE) as a consequence of misalignment of case pack size, shelf space, and reorder point. This misalignment results from the fragmented nature of inventory policy decision making in the retail industry and affects basic trade‐offs in inventory models. We specify conditions under which the BRE exists, quantify the expected amount of backroom inventory, derive an optimal short‐term inventory policy, and assess the impact of the BRE on the optimal inventory policy and total costs. Our results indicate that ignoring the BRE leads to artificially high reorder points and higher total costs. The paper concludes with a discussion of theoretical and managerial implications.     

Optimal Inventory Control with Retail Pre‐Packs

A pre‐pack is a collection of items used in retail distribution. By grouping multiple units of one or more stock keeping units (SKU), distribution and handling costs can be reduced; however, ordering flexibility at the retail outlet is limited. This paper studies an inventory system at a retail level where both pre‐packs and individual items (at additional handling cost) can be ordered. For a single‐SKU, single‐period problem, we show that the optimal policy is to order into a “band” with as few individual units as possible. For the multi‐period problem with modular demand, the band policy is still optimal, and the steady‐state distribution of the target inventory position possesses a semi‐uniform structure, which greatly facilitates the computation of optimal policies and approximations under general demand. For the multi‐SKU case, the optimal policy has a generalized band structure. Our numerical results show that pre‐pack use is beneficial when facing stable and complementary demands, and substantial handling savings at the distribution center. The cost premium of using simple policies, such as strict base‐stock and batch‐ordering (pre‐packs only), can be substantial for medium parameter ranges.     

Cash‐Flow Based Dynamic Inventory Management

Small‐to‐medium‐sized enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this study, we model a firm that can finance its inventory (ordered or manufactured) with loans in order to meet random demand which in general may not be time stationary. The firm earns interest on its cash on hand and pays interest on its debt. The objective is to maximize the expected value of the firm's capital at the end of a finite planning horizon. The firm's state at the beginning of each period is characterized by the inventory level and the capital level measured in units of the product, whose sum represents the “net worth” of the firm. Our study shows that the optimal ordering policy is characterized by a pair of threshold parameters as follows. (i) If the net worth is less than the lower threshold, then the firm employs a base stock order up to the lower threshold. (ii) If the net worth is between the two thresholds, then the firm orders exactly as many units as it can afford, without borrowing. (iii) If the net worth is above the upper threshold, then the firm employs a base stock order up to the upper threshold. Further, upper and lower bounds for the threshold values are developed using two simple‐to‐compute myopic ordering policies which yield lower bounds for the value function. We also derive an upper bound for the value function by considering a sell‐back policy. Subsequently, it is shown that policies of similar structure are optimal when the loan and deposit interest rates are piecewise linear functions, when there is a maximal loan limit and when unsatisfied demand is backordered. Finally, further managerial insights are provided with extensive numerical studies.     

The Role of Contract Expirations in Service Parts Management

The majority of after‐sales service providers manage their service parts inventory by focusing on the availability of service parts. This approach, combined with automatic replenishment systems, leads to reactive inventory control policies where base stock levels are adjusted only after a service contract expires. Consequently, service providers often face excess stock of critical service parts that are difficult to dispose due to their specificity. In this study, we address this problem by developing inventory control policies taking into account contract expirations. Our key idea is to reduce the base stock level of the one‐for‐one policy before obsolescence (a full or partial drop in demand rate) occurs and let demand take away excess stock. We refer to this policy as the single‐adjustment policy. We benchmark the single‐adjustment policy with the multiple‐adjustment policy (allowing multiple base stock adjustments) formulated as a dynamic program and verify that for a wide range of instances the single‐adjustment policy is an effective heuristic for the multiple‐adjustment policy. We also compare the single‐adjustment policy with the world‐dependent base stock policy offered by Song and Zipkin (1993) and identify the parameter combinations where both policies yield similar costs. We consider two special cases of the single‐adjustment policy where the base stock level is kept fixed or the base stock adjustment is postponed to the contract expiration time. We find that the initial demand rate, contract expiration time, and size of the drop in demand rate are the three key parameters driving the choice between the single‐adjustment policy and its special cases.     

How Inventory Cost Influences Introduction Timing of Product Line Extensions

In the industry with radical technology push or rapidly changing customer preference, it is firms' common wisdom to introduce high‐end product first, and follow by low‐end product‐line extensions. A key decision in this “down‐market stretch” strategy is the introduction time. High inventory cost is pervasive in such industries, but its impact has long been ignored during the presale planning stage. This study takes a first step toward filling this gap. We propose an integrated inventory (supply) and diffusion (demand) framework and analyze how inventory cost influences the introduction timing of product‐line extensions, considering substitution effect among successive generations. We show that under low inventory cost or frequent replenishment ordering policy, the optimal introduction time indeed follows the well‐known “now or never” rule. However, sequential introduction becomes optimal as the inventory holding gets more substantial or the product life cycle gets shorter. The optimal introduction timing can increase or decrease with the inventory cost depending on the marketplace setting, requiring a careful analysis.     

Strategic Management of Distressed Inventory

It is well known that maximizing revenue from a fixed stock of perishable goods may require discounting prices rather than allowing unsold inventory to perish. This behavior is seen in industries ranging from fashion retail to tour packages and baked goods. A number of authors have addressed the markdown management problem in which a seller seeks to determine the optimal sequence of discounts to maximize the revenue from a fixed stock of perishable goods. However, merchants who consistently use markdown policies risk training customers to “wait for the sale.” We investigate models in which the decision to sell inventory at a discount will change the future expectations of customers and hence their buying behavior. We show that, in equilibrium, a single‐price policy is optimal if all consumers are strategic and demand is known to the seller. Relaxing any of these conditions can lead to a situation in which a two‐price markdown policy is optimal. We show using numerical simulation that if customers update their expectations of availability over time, then optimal sales limit policies can evolve in a complex fashion.     

Shelf Life Extending Packaging,Inventory Control and Grocery Retailing

Retailers of perishable goods are often faced with the choice between more expensive packaging that can extend shelf life of their products and less expensive packaging that cannot. Different choices will lead to different sales, costs, and waste, and different choices require different inventory control policies. In this paper, we study the coordination of inventory and packaging decisions in a retailing environment. Items in an active package have a longer lifetime than those in a regular package and cost more. Customers always pick items with a longer lifetime first. When items with a longer lifetime are out of stock, a portion of customers are willing to buy less fresh items as substitutes. Our study shows the optimality of a “separation” policy when the substitution rate is high. In the separation policy, as the initial inventory level increases, the optimal policy changes from using active packaging only, then to using regular packaging only, and finally to ordering nothing. These results are very specific to the way perishable inventories are depleted in retailing. Our numerical study shows that although it may not be optimal in terms of cost, the adoption of active packaging can consistently achieve substantial waste reduction.     

Heuristics for Base‐Stock Levels in Multi‐Echelon Distribution Networks

We study inventory optimization for locally controlled, continuous‐review distribution systems with stochastic customer demands. Each node follows a base‐stock policy and a first‐come, first‐served allocation policy. We develop two heuristics, the recursive optimization (RO) heuristic and the decomposition‐aggregation (DA) heuristic, to approximate the optimal base‐stock levels of all the locations in the system. The RO heuristic applies a bottom‐up approach that sequentially solves single‐variable, convex problems for each location. The DA heuristic decomposes the distribution system into multiple serial systems, solves for the base‐stock levels of these systems using the newsvendor heuristic of Shang and Song (2003), and then aggregates the serial systems back into the distribution system using a procedure we call “backorder matching.” A key advantage of the DA heuristic is that it does not require any evaluation of the cost function (a computationally costly operation that requires numerical convolution). We show that, for both RO and DA, changing some of the parameters, such as leadtime, unit backordering cost, and demand rate, of a location has an impact only on its own local base‐stock level and its upstream locations’ local base‐stock levels. An extensive numerical study shows that both heuristics perform well, with the RO heuristic providing more accurate results and the DA heuristic consuming less computation time. We show that both RO and DA are asymptotically optimal along multiple dimensions for two‐echelon distribution systems. Finally, we show that, with minor changes, both RO and DA are applicable to the balanced allocation policy.     

A Bayesian Inventory Model Using Real‐Time Condition Monitoring Information

Lack of coordination between machinery fault diagnosis and inventory management for spare parts can lead to increased inventory costs and disruptions in production activity. We develop a framework for incorporating real‐time condition monitoring information into inventory decisions for spare parts. We consider a manufacturer who periodically replenishes inventory for a machine part that is subject to deterioration. The deterioration is captured via condition monitoring and modeled using a Wiener process. The resulting degradation model is used to derive the life distribution of a functioning part and to estimate the demand distribution for spare parts. This estimation is periodically updated, in a Bayesian manner, as additional information on part deterioration is obtained. We develop an inventory model that incorporates this updated demand distribution and demonstrate that a dynamic base‐stock policy, in which the optimal base‐stock level is a function of some subset of the observed condition monitoring information, is optimal. We propose a myopic critical fractile policy that captures the essence of the optimal policy, but is easier to compute. Computational experiments indicate that this heuristic performs quite well relative to the optimal policy. Adaptive inventory policies such as these can help manufacturers to increase machine availability and reduce inventory costs.     

The Failure of Practical Intuition: How Forward‐Coverage Inventory Targets Cause the Landslide Effect

Seasonal demand for products is common at many companies including Kraft Foods, Case New Holland, and Elmer's Products. This study documents how these, and many other companies, experience bloated inventories as they transition from a low season to a high season and a severe drop in service levels as they transition from a high season to a low season. Kraft has termed this latter phenomenon the “landslide effect.” In this study, we present real examples of the landslide effect and attribute its root cause to a common industry practice employing forward days of coverage when setting inventory targets. While inventory textbooks and academic articles prescribe correct ways to set inventory targets, forward coverage is the dominant method employed in practice. We investigate the magnitude and drivers of the landslide effect through both an analytical model and a case study. We find that the effect increases with seasonality, lead time, and demand uncertainty and can lower service by an average of ten points at a representative company. While the logic is initially counterintuitive to many practitioners, companies can avoid the landslide effect by using demand forecasts over the preceding lead time to calculate safety stock targets.     

Inventory Management for Customers with Alternative Lead Times

It is common for suppliers operating in batch‐production mode to deal with patient and impatient customers. This paper considers inventory models in which a supplier provides alternative lead times to its customers: a short or a long lead time. Orders from patient customers can be taken by the supplier and included in the next production cycle, while orders from impatient customers have to be satisfied from the on‐hand inventory. We denote the action to commit one unit of on‐hand inventory to patient or impatient customers as the inventory‐commitment decision, and the initial inventory stocking as the inventory‐replenishment decision. We first characterize the optimal inventory‐commitment policy as a threshold type, and then prove that the optimal inventory‐replenishment policy is a base‐stock type. Then, we extend our analysis to models to consider cases of a multi‐cycle setting, a supply‐capacity constraint, and the on‐line charged inventory‐holding cost. We also evaluate and compare the performances of the optimal inventory‐commitment policy and the inventory‐rationing policy. Finally, to further investigate the benefits and pitfalls of introducing an alternative lead‐time choice, we use the customer‐choice model to study the demand gains and losses, known as demand‐induction and demand‐cannibalization effects, respectively.     

区分仓库与货架库存需求影响效应的零售商库存决策

既往有关库存水平影响需求条件下的库存问题研究中,通常对终端库存水平是否存在货架与零售商仓库库存水平的区别未作深入探讨。本文的研究认为,现实中许多零售商拥有仓库,其现有库存水平包括仓库库存和货架库存两部分,而影响需求的仅为与货架展示能力相关的库存,因此有必要对二者的需求影响效应进行区分。在明确这一区别的前提下,本文首先建立了供应商管理库存情况下库存水平影响需求问题的一般库存模型,给出零售商的最优订货策略;并考虑货架的容量限制,给出零售商启用仓库的判断条件。由于仓库库存仅在能够影响货架展示能力的条件下才能够影响消费需求,本文还进一步讨论了在零售商拥有仓库时,区分货架与仓库的库存水平影响需求条件下的最优库存与订货决策。这对于经营不同特征商品的零售商在进行是否需要拥有仓库,以及拥有仓库条件下的库存决策具有很好的参考价值。     

Replenishment Policies for Multi‐Product Stochastic Inventory Systems with Correlated Demand and Joint‐Replenishment Costs

This study analyzes optimal replenishment policies that minimize expected discounted cost of multi‐product stochastic inventory systems. The distinguishing feature of the multi‐product inventory system that we analyze is the existence of correlated demand and joint‐replenishment costs across multiple products. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real‐world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class (s, c, d, S)‐policies, and also develop an algorithm to compute good policies in this class, for large multi‐product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective.     

Inventory Rationing in a Make‐to‐Stock System with Batch Production and Lost Sales

We address an inventory rationing problem in a lost sales make‐to‐stock (MTS) production system with batch ordering and multiple demand classes. Each production order contains a single batch of a fixed lot size and the processing time of each batch is random. Assuming that there is at most one order outstanding at any point in time, we first address the case with the general production time distribution. We show that the optimal order policy is characterized by a reorder point and the optimal rationing policy is characterized by time‐dependent rationing levels. We then approximate the production time distribution with a phase‐type distribution and show that the optimal policy can be characterized by a reorder point and state‐dependent rationing levels. Using the Erlang production time distribution, we generalize the model to a tandem MTS system in which there may be multiple outstanding orders. We introduce a state‐transformation approach to perform the structural analysis and show that both the reorder point and rationing levels are state dependent. We show the monotonicity of the optimal reorder point and rationing levels for the outstanding orders, and generate new theoretical and managerial insights from the research findings.     

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent (s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.     

Safety Stock,Excess Capacity or Diversification: Trade‐Offs under Supply and Demand Uncertainty

Firms mitigate uncertainty in demand and supply by carrying safety stock, planning for excess capacity and diversifying supply sources. In this study, we provide a framework to jointly optimize these three levers in a periodic review infinite horizon setting, and in particular we examine how one can reduce inventory and capacity investments through proper diversification strategies. Observing that a modified base‐stock inventory policy is optimal, we find that the capacity‐diversification problem is well behaved and characterize the optimal mix of safety stock, excess capacity and extra number of supply sources. We find that higher supply uncertainty results in higher safety stock, more excess capacity, and higher diversification. But safety stock and diversification are non‐monotonic in demand uncertainty. Our results can be extended to situations in which suppliers are heterogeneous, and can be used to develop effective heuristics.     

面向批量订货和多需求类的生产与库存配给

针对一个面向两个需求类的生产企业,根据客户每次订货是否可分批交货,提出了当客户订货可分割和不可分割时供应商的最优生产和库存配给策略.分析表明,供应商的最优生产控制策略可用一个取决于系统状态的基准库存水平表示,最优的库存配给策略则用一个多层的取决于状态的配给水平向量表示.随后,该结论被推广至包含任意多个需求类的生产系统.数值分析验证了文中最优策略的有效性.     

The Value of Information for Managing Retail Inventory Remotely

An important difference between both manufacturing and wholesaling vs. retail is the information available concerning inventory. Typically, far less information characterizes retail. Here, an extreme environment of information shortfall is examined. The environment is technically termed “unattended points of sale,” but colloquially called vending machines. Once inventory is loaded into a machine, information on demand and inventory level is not observed until the scheduled reloading date. Technological advances and business process changes have drawn attention to the value of information (VOI) in retail inventory in many venues. Moreover, technology is now available that allows unattended points of sale to report inventory information. Capturing the value of this information requires changes in current business practice. We demonstrate the value of capturing information analytically in an environment with restrictive demand assumptions. Experiments in an environment with realistic demand assumptions and parameter values show that the VOI depends greatly on operating characteristics and can range from negligible effects to increasing profitability 30% or more in actual practice.     

MANAGING CYCLIC INVENTORIES

Cyclic inventory is the buffer following a machine that cycles over a set of products, each of which is subsequently consumed in a continuous manner. Scheduling such a machine is interesting when the changeover times from one product to another are non‐trivial—which is generally the case. This problem has a substantial literature, but the common practices of “lot‐splitting” and “maximization of utilization” suggest that many practitioners still do not fully understand the principles of cyclic inventory. This paper is a tutorial that demonstrates those principles. We show that cyclic inventory is directly proportional to cycle length, which in turn is directly proportional to total changeover time, and inversely proportional to machine utilization. We demonstrate the virtue of “maximum changeover policies” in minimizing cyclic inventory—and the difficulty in making the transition to an increased level of demand. In so doing, we explicate the different roles of cyclic inventory, transitional inventory, and safety stock. We demonstrate the interdependence of the products in the cycle—the lot‐size for one product cannot be set independently of the remaining products. We also give necessary conditions for consideration of improper schedules (i.e., where a product can appear more than once in the cycle), and demonstrate that both lot‐splitting and maximization of utilization are devastatingly counter‐productive when changeover time is non‐trivial.     

THE VALUE OF SKU RATIONALIZATION IN PRACTICE (THE POOLING EFFECT UNDER SUBOPTIMAL INVENTORY POLICIES AND NONNORMAL DEMAND)

Several approaches to the widely recognized challenge of managing product variety rely on the pooling effect. Pooling can be accomplished through the reduction of the number of products or stock‐keeping units (SKUs), through postponement of differentiation, or in other ways. These approaches are well known and becoming widely applied in practice. However, theoretical analyses of the pooling effect assume an optimal inventory policy before pooling and after pooling, and, in most cases, that demand is normally distributed. In this article, we address the effect of nonoptimal inventory policies and the effect of nonnormally distributed demand on the value of pooling. First, we show that there is always a range of current inventory levels within which pooling is better and beyond which optimizing inventory policy is better. We also find that the value of pooling may be negative when the inventory policy in use is suboptimal. Second, we use extensive Monte Carlo simulation to examine the value of pooling for nonnormal demand distributions. We find that the value of pooling varies relatively little across the distributions we used, but that it varies considerably with the concentration of uncertainty. We also find that the ranges within which pooling is preferred over optimizing inventory policy generally are quite wide but vary considerably across distributions. Together, this indicates that the value of pooling under an optimal inventory policy is robust across distributions, but that its sensitivity to suboptimal policies is not. Third, we use a set of real (and highly erratic) demand data to analyze the benefits of pooling under optimal and suboptimal policies and nonnormal demand with a high number of SKUs. With our specific but highly nonnormal demand data, we find that pooling is beneficial and robust to suboptimal policies. Altogether, this study provides deeper theoretical, numerical, and empirical understanding of the value of pooling.