Stocking Decisions Research Articles

Coordination of stocking decisions in an assemble-to-order environment

Abstract This paper examines an assemble-to-order environment involving a short-life-cycle product that is sold in two different configurations, each requiring a unique component that must be stocked in advance. Both configurations of the product are assembled on the same equipment which has limited capacity. The focus of the analysis is on the determination of the appropriate stocking quantities for each of the configuration specific components. Because the same assembly capacity is often reused for different instances of the component stocking problem, we treat assembly capacity as exogenous. This represents the fact that capacity decisions are often made less frequently than are procurement/production quantity decisions. We first solve for the first-best stocking policy when the components are produced internally. We then consider the case when the components are procured from external suppliers, and investigate how different forms of contract between the assembler and the component suppliers affect coordination of the supply chain as well as each party’s profit. One particularly interesting finding is that it is possible to coordinate the supply chain with a single-price contract between each supplier and the assembler while awarding all parties positive profit.

Movement of Reservoir‐Stocked Riverine Fish between Tailwaters and Rivers

AbstractThe movement of fish from onstream impoundments into connected streams and rivers has traditionally been overlooked in fish stocking decisions but is critical to the ultimate impact of stocking riverine species into reservoirs. Hybrid saugeyes (female walleye Sander vitreus × male sauger S. canadensis) stocked into Deer Creek Reservoir, Ohio, readily move from the reservoir to the tailwater below. Downstream movement of these saugeyes from the tailwater may have consequences for native prey species and parental stocks downstream. We used fixed‐station radiotelemetry to quantify the temporal movement patterns of 203 reservoir‐stocked saugeyes from the tailwater of the reservoir, the stream flowing from the tailwater, and the river into which the stream flowed. From October 1998 through July 2000, most (75%) saugeyes never left the tailwater, and those that left returned 75% of the time. Overall, saugeyes spent 90% of their time in the tailwater, 7‐8% of their time downstream in small streams, and 2‐3% of their time farther downstream in the Scioto River (45 km downstream). No radio‐tagged saugeyes moved to the Ohio River (155 km downstream). The probability of downstream movement generally increased with increasing flow and when dissolved oxygen dropped to lethal levels in summer. The probability of movement was highest in winter and spring, when it was probably related to spawning, and low in summer (except when dissolved oxygen was low) and fall. The patterns of movement seemed to reflect the relative suitability of tailwater over stream habitat. The predominant use of and return to tailwater habitat after downstream movement limited overall stream and river residence time. Although the daily movement probability for an individual was low, when we apply these rates to all of the stocked saugeyes in the Ohio River drainage, we cannot safely conclude that only small numbers move from reservoir tailwaters to downstream river systems. We recommend that managers refrain from stocking systems for which there are concerns about native species in connected drainages.

Strategic Capacity Rationing to Induce Early Purchases

Dynamic pricing offers the potential to increase revenues. At the same time, it creates an incentive for customers to strategize over the timing of their purchases. A firm should ideally account for this behavior when making its pricing and stocking decisions. In particular, we investigate whether it is optimal for a firm to create rationing risk by deliberately understocking products. Then, the resulting threat of shortages creates an incentive for customers to purchase early at higher prices. But when does such a strategy make sense? If it is profitable to create shortages, what is the optimal amount of rationing risk to create? We develop a stylized model to study this problem. In our model, customers have heterogeneous valuations for the firm's product and face declining prices over two periods. Customers are assumed to have identical risk preferences and know the price path and fill rate in each period. Via its capacity choice, the firm is able to control the fill rate and, hence, the rationing risk faced by customers. Customers behave strategically and weigh the payoff of immediate purchases against the expected payoff of delaying their purchases. We analyze the capacity choice that maximizes the firm's profits. First, we consider a monopoly market and characterize conditions under which rationing is optimal. We examine how the optimal amount of rationing is affected by the magnitude of price changes over time and the degree of risk aversion among customers. We then analyze an oligopoly version of the model and show that competition reduces the firms' ability to profit from rationing. Indeed, there exists a critical number of firms beyond which a rationing equilibrium cannot be supported.

An insurance risk management framework for disaster relief and supply chain disruption inventory planning

Government agencies, not-for-profit organizations, and private corporations often assume leading roles in the delivery of supplies, equipment, and manpower to support initial response operations after a disaster strikes. These organizations are faced with challenging logistics decisions to ensure that the right supplies (including equipment and personnel) are in the right places, at the right times, and in the right quantities. Such logistics planning decisions are further complicated by the uncertainties associated with predicting whether or not a potential threat will materialize into an emergency situation. This paper introduces newsvendor variants that account for demand uncertainty as well as the uncertainty surrounding the occurrence of an extreme event. The optimal inventory level is determined and compared to the classic newsvendor solution and the difference is interpreted as the insurance premium associated with proactive disaster-relief planning. The insurance policy framework represents a practical approach for decision makers to quantify the risks and benefits associated with stocking decisions related to preparing for disaster relief efforts or supply chain disruptions.

Can distribution explain double jeopardy patterns?

PurposeThe purpose of this paper is to provide clear insights into the influence of product availability, and thus distribution on double jeopardy (DJ) patterns, for frequently‐purchased products (FPP). This paper also aims to provide important strategies in order to maximize the efficiency of retailers' stocking decisions and manufacturers' branding efforts by discussing distribution dynamics in a set of experiments developed in light of related theoretical discussions.Design/methodology/approachThis study provides an in‐depth literature review of DJ, distribution, out‐of‐stock and consumer behavioural brand loyalty in many marketing and supply chain decisions. A practical simulation is developed to test the main hypotheses in the study in light of the theoretical discussion.FindingsThe study's results indicated that distribution might explain DJ patterns. In addition, distribution might create behavioural brand loyalty when FPP are widely available (excessive availability) in the market.Research limitations/implicationsAlthough the study provides a simulation structure and varying experiments, more field data about FPP might also enhance the study's results.Practical implicationsSmall brands can break their curse as indicated by the DJ phenomenon by focusing on distribution. Also, they might create some level of behavioural brand loyalty by being available everywhere in the market.Originality/valueThe impact of distribution on DJ has seldom been discussed in general terms previously, and has never been discussed and explored theoretically with specificity using experimental analysis. Therefore, this study provides the first evidence that distribution has a strong potential to explain the reasons behind DJ patterns and might create behavioural brand loyalty.

Ordering and pricing policies in a manufacturing and distribution supply chain for fashion products

In the paper, we develop a model of manufacturing and distribution supply chains that are operating to meet price-sensitive random demand for products with short life cycles such as fashion products. Two specific scenarios are considered. The manufacturer-controlled scenario is one where the distributor shares price-sensitive random demand with the manufacturer, and the manufacturer controls the supply chain stocking decisions and bears the risk of overstocking costs. The distributor-controlled scenario works in the opposite direction. Prevailing wisdom suggests that the manufacturer should control supply chain decisions (e.g., via vendor-managed inventory). Our results indicate that such an arrangement is against the interest of a distributor selling short life-cycle products. Furthermore, we find that the total supply chain profit is generally higher when the distributor controls the supply chain stocking decisions and bears the risk of overstocking costs.

Inventory Record Inaccuracy, Double Marginalization, and RFID Adoption

Most retailers suffer from substantial discrepancies between inventory quantities recorded in the system and stocks truly available to customers. Promising full inventory transparency, radio frequency identification (RFID) technology has often been suggested as a remedy to the problem. We consider inventory record inaccuracy in a supply chain model, where a Stackelberg manufacturer sets the wholesale price and a retailer determines how much to stock for sale to customers. We first analyze the impact of inventory record inaccuracy on optimal stocking decisions and profits. By contrasting optimal decisions in a decentralized supply chain with those in an integrated supply chain, we find that inventory record inaccuracy exacerbates the inefficiencies resulting from double marginalization in decentralized supply chains. Assuming RFID technology can eliminate the problem of inventory record inaccuracy, we determine the cost thresholds at which RFID adoption becomes profitable. We show that a decentralized supply chain benefits more from RFID technology, such that RFID adoption improves supply chain coordination.

Biophysical modelling and NDVI time series to project near‐term forage supply: spectral analysis aided by wavelet denoising and ARIMA modelling

Point‐based biophysical simulation of forage production coupled with 1‐km AVHRR NDVI data was used to determine the feasibility of projecting forage conditions 84 days into the future to support stocking decision making for livestock production using autoregressive integrated moving average (ARIMA) with Box and Jenkins methodology. The study was conducted at three highly contrasting ecosystems in South Texas over the period 1989–2000. Wavelet transform was introduced as a mathematical tool to denoise the NDVI time series. The simulated forage production, NDVI and denoised NDVI (DeNDVI) were subject to spectral decomposition for the detection of periodicities. Spectral analysis revealed bimodal vegetation growth patterns in Southwestern Texas. A yearly cycle (364 days) of peak vegetation production was detected for the three study sites, another peak forage production was revealed by spectral analysis at 182 days following the first peak in vegetation production. A similar trend was found for the NDVI imageries sensing the study sites. Wavelet denoising of NDVI signal was effective in revealing clear periodicities in one study site where maximum variability of NDVI was noted. †Dr Stuth passed away on 24 April 2006. This paper is dedicated to his memory. The Box and Jenkins ARIMA modelling approach was used as a forecasting method for near‐term forage production to assist range managers in proactive operational stocking decisions to mitigate drought risk. Using denoised NDVI provided forage projections with the lowest standard error prediction (SEP) throughout the forecast 84‐day periods. However, acceptable SEP was only achieved up to 6 weeks into a projection for the forage‐only based forecasts. The ARIMA forecasting methodology appears to offer a new approach to help managers of livestock production through the creation of near real‐time early warning systems. Using satellite‐derived NDVI data as a covariate improved the forecast quality and reduced the standard error of forecast in three highly contrasting sites. Denoising the NDVI data using wavelet methods further improved the forecast quality in all study sites. The integration of AVHRR NDVI data and biophysical simulation of forage production appears a promising approach for assisting decision makers in a positive manner by assessing forage conditions in response to emerging weather conditions and near real‐time projection of available forage for grazing animals.

Managing components for assemble‐to‐order products with lead‐time‐dependent pricing: The full‐shipment model

AbstractWe study a component inventory planning problem in an assemble‐to‐order environment faced by many contract manufacturers in which both quick delivery and efficient management of component inventory are crucial for the manufacturers to achieve profitability in a highly competitive market. Extending a recent study in a similar problem setting by the same authors, we analyze an optimization model for determining the optimal component stocking decision for a contract manufacturer facing an uncertain future demand, where product price depends on the delivery times. In contrast to our earlier work, this paper considers the situation where the contract manufacturer needs to deliver the full order quantity in one single shipment. This delivery requirement is appropriate for many industries, such as the garment and toy industries, where the economies of scale in transportation is essential. We develop efficient solution procedures for solving this optimization problem. We use our model results to illustrate how the different model parameters affect the optimal solution. We also compare the results under this full‐shipment model with those from our earlier work that allows for multiple partial shipments. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Quantity discounts in single-period supply contracts with asymmetric demand information

We investigate how a supplier can use a quantity discount schedule to influence the stocking decisions of a downstream buyer that faces a single period of stochastic demand. In contrast to much of the work that has been done on single-period supply contracts, we assume that there are no interactions between the supplier and the buyer after demand information is revealed and that the buyer has better information about the distribution of demand than does the supplier. We characterize the structure of the optimal discount schedule for both all-unit and incremental discounts and show that the supplier can earn larger profits with an all-unit discount.

Benefits of considering inventory in service parts logistics network design problems with time-based service constraints

We study the integrated logistics network design and inventory stocking problem as characterized by the interdependency of the design and stocking decisions in service parts logistics. These two sets of decisions are usually considered sequentially in practice, and the associated problems are tackled separately in the research literature. The overall problem is typically further complicated due to time-based service constraints that provide lower limits on the percentage of demand satisfied within specified time windows. We introduce an optimization model that explicitly captures the interdependency between network design (location of facilities, and allocation of demands to facilities) and inventory stocking decisions (stock levels and their corresponding stochastic fill rates), and present computational results from our extensive experiments that investigate the effects of several factors including demand levels, time-based service levels and costs. We show that the integrated approach can provide significant cost savings over the decoupled approach (solving the network design first and inventory stocking next), shifting the whole efficient frontier curve between cost and service level to superior regions. We also show that the decoupled and integrated approaches may generate totally different solutions, even in the number of located facilities and in their locations, magnifying the importance of considering inventory as part of the network design models.

Econometric models of Finnish non-industrial private forest owners' timber supply and timber stock

This dissertation examines the shortand long-run impacts of timber prices and other factors affecting NIPF owners' timber harvesting and timber stocking decisions. The utilitybased Faustmann model provides testable hypotheses of the exogenous variables retained in the timber supply analysis. The timber stock function, derived from a two-period biomass harvesting model, is estimated using a two-step GMM estimator based on balanced panel data from 1983 to 1991. Timber supply functions are estimated using a Tobit model adjusted for heteroscedasticity and nonnormality of errors based on panel data from 1994 to 1998. Results show that if specification analysis of the Tobit model is ignored, inconsistency and biasedness can have a marked effect on parameter estimates. The empirical results show that owner's age is the single most important factor determining timber stock; timber price is the single most important factor in harvesting decision. The results of the timber supply estimations can be interpreted using utility-based Faustmann model of a forest owner who values a growing timber in situ.

Tailored Supply Chain Decision Making Under Price-Sensitive Stochastic Demand and Delivery Uncertainty

In this paper, we study a serial two-echelon supply chain selling a procure-to-stock product in a price-sensitive market. Our analytical modelling framework incorporates optimal pricing and stocking decisions for both echelons in the presence of stochastic demand and random delivery times. We focus on understanding how these decisions for the chain are affected by its management paradigm (centralized or decentralized), and its business characteristics—price sensitivity, demand uncertainty, and delivery time variability. A novel combination of transformations enables us to analyze the framework and determine the unique optimal choices for centralized and wholesale price-based decentralized supply chains. More detailed investigation reveals that, in general, the business characteristics influence both the behavior and the optimal values of the decision variables, while the management paradigm primarily governs the optimal values. We illustrate the significance of these results in terms of how managers should tailor their decisions to align with their business requirements. Subsequently, comparison of the optimal profits between the channel partners and the management paradigms provides implications for decentralization strategy. A decentralized chain is most inefficient for moderately price-sensitive customers and uncertain environments, but is relatively more effective when dealing with mature products. We propose a contracting scheme that can improve the decentralized chain profit in reliable delivery time settings. The salient modelling insight of this paper is that ignoring the randomness of delivery time trivializes the interaction between pricing and stocking decisions. On the other hand, from a managerial viewpoint, we establish that optimal pricing policies provide the means to increase revenue and also act as strategic tools for tackling uncertainty.

Dinâmica da estratégia logística em empresas brasileiras

O objetivo do artigo é analisar a estratégia logística das empresas brasileiras a partir da mensuração do impacto de diferentes características do negócio sobre as principais decisões de produção e distribuição física de produtos acabados. Foi conduzida uma pesquisa de campo em empresas listadas no Ranking Exame para confrontar as quatro políticas propostas por Pagh e Cooper (1998), derivadas das combinações entre centralizar/descentralizar os estoques e produzir para estoque/produzir contra-pedido, com diversas características do produto, da operação e da demanda. Técnicas de análise multivariada, como as análises de regressão logística simples e multinomial, foram empregadas, permitindo o desenvolvimento de diversos modelos quantitativos. Seus resultados apontam para avanços acadêmicos e gerenciais, como a quantificação e hierarquização de relações empíricas descritas na literatura e o direcionamento da atenção gerencial para as variáveis relevantes à decisão. Os modelos também permitem avaliar a adequação dessas políticas para diferentes valores do tempo de entrega, da variabilidade das vendas e do grau de obsolescência dos produtos.

Quantity Discounts in Single Period Supply Contracts with Asymmetric Demand Information

We investigate how supplier can use a quantity discount schedule to influence the stocking decisions of a downstream buyer that faces a single period of stochastic demand. In contrast to much of the work that has been done on single-period supply contracts, we assume that there are no interactions between the supplier and the buyer after demand information is revealed and that the buyer has better information about the distribution of demand than does the supplier. We characterize the structure of the optimal discount schedule for both all-unit and incremental discounts and show that the supplier can earn larger profits with an all-unit discount.

Integrating the Promotional and Service Roles of Retail Inventories

In some retail contexts, higher inventories not only improve service levels, but also stimulate demand by serving as a promotional tool (e.g., by increasing product visibility). Motivated by a building-products retailer's practice of stocking large quantities of products to stimulate demand, we study inventory management and pricing policies when demand is uncertain but increases with stocking quantity. We first characterize the profit-maximization policy for a stochastic inventory model with a general inventory-dependent demand distribution and given price, and show that demand stimulation (by inventories) has the effect of increasing the target service level beyond the classical newsvendor model's critical fractile ratio. To underscore the importance of considering both demand stochasticity and inventory influence, we consider two functionally oriented benchmark policies—a demand-driven policy and a critical fractile policy—that might, respectively, represent marketing and inventory managers' viewpoints. Our numerical analysis reveals that the optimal policy can generate considerably higher profits than the two complementary functional perspectives. Moreover, we prove that the optimal stocking quantity always exceeds the critical fractile solution and can even exceed the demand-driven stocking quantity. We also address the problem of jointly optimizing both stocking quantity and price for demand-stimulating products using a multiplicative model to represent the influence of price and stocking quantity on the demand distribution. For this model, we show that the pricing and stocking decisions can be determined sequentially, with the optimal policy setting higher prices and stock levels than both the functional policies.

Positive vs. Negative Externalities in Inventory Management: Implications for Supply Chain Design

In this paper we analyze the impact of supply-side externalities existing among downstream retailers on supply chain performance. Namely, multiple retail firms face stochastic demand, purchase the product from the upstream wholesaler, and make stocking decisions that affect all other retailers in the same echelon. Two sources of inefficiencies exist in such a supply chain: One is double marginalization and the other is externalities among retailers. Whereas double marginalization always leads to inventory understocking at the retail echelon, we find that the implications of externalities are more complex, because different externalities can improve or deteriorate supply chain performance, relative to the situation without externalities. We show that the effect of externalities depends critically on whether the stocking decisions of retailers exhibit positive (complementarity) or negative (substitutability) externalities, and whether retailers are managed centrally or competitively. Under complementarity, competing retailers tend to understock the product (compared with the centralized inventory management at the retail level), thus aggravating the double-marginalization effect. This is the opposite of what happens under substitutability, where competing retailers tend to overstock the product, thus compensating for the double-marginalization effect. Hence, we conclude that supply chain coordination between retailers and the wholesaler is most important when there is downstream competition that exhibits complementarity. From the wholesaler's point of view, competition among retailers is preferable over centralization of retailers when externalities are negative, and vice versa when externalities are positive. Moreover, with competition on complements, both retailers and the wholesaler have incentives to coordinate the supply chain.

Measuring Item Fill-Rate Performance in a Finite Horizon

The standard treatment of fill rate relies on stationary and serially independent demand over an infinite horizon. Even if demand is stationary, managers are held accountable for performance over a finite horizon. In a finite horizon, the fill rate is a random variable. Studying the distribution is relevant because a vendor may be subject to financial penalty if she fails to achieve her target fill rate over a specified finite period. It is known that for a zero lead time, base-stock model, the expected value of a finite-horizon fill rate exceeds the long-run fill rate. In this paper, I investigate the behavior of the distribution of the finite-horizon fill rate when a stationary base-stock policy is used to control inventory. For a vendor facing a finite-horizon, fill-rate-level contract and using a stationary stocking policy, I examine how the the length of the review horizon (i.e., monthly or quarterly), the demand distribution, and the cost of failing to meet the target affect the stocking decision.

“Stack Them High, Let ’em Fly”: Lot-Sizing Policies When Inventories Stimulate Demand

In some retail contexts, stocking large quantities of inventory may not only improve service levels, but can also stimulate demand. For products having demand rates that increase with inventory levels, we analyze the effect of stocking decisions on firm profitability to develop managerial insights regarding the structure of the optimal inventory policy, and to understand how this policy differs from traditional approaches. When inventories stimulate demand, iteratively applying the standard economic order quantity (EOQ) model–by setting the demand rate parameter equal to the observed average demand rate in prior cycles–yields an equilibrium order quantity that is robust to demand parameter misestimation, but is suboptimal. The profit-maximizing policy orders larger quantities, and can replenish inventory even before on-hand stock fully depletes. Using an extension of a standard inventory-dependent demand model from the literature, we first provide a convenient characterization of products that require early replenishment. We demonstrate that the optimal cycle time is largely governed by the conventional trade-off between ordering and holding costs, whereas the reorder point relates to a promotions-oriented cost-benefit perspective. We show that the optimal policy yields significantly higher profits than cost-based inventory policies, underscoring the importance of profit-driven inventory management.

Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand

Abstract In this paper, we propose a simultaneous approach to incorporate inventory control decisions––such as economic order quantity and safety stock decisions––into typical facility location models, which are used to solve the distribution network design problem. A simultaneous model is developed considering a stochastic demand, modeling also the risk pooling phenomenon. We present a non-linear-mixed-integer model and a heuristic solution approach, based on Lagrangian relaxation and the sub-gradient method. In a numerical application, we found that the potential cost reduction, compared to the traditional approach, increases when the holding costs and/or the variability of demand are higher.