assortment planning and inventory decisions under stockout based substitution we present an efficient dynamic programming algorithm to determine the optimal assortment and inventory levels in a single period problem with stockout based substitution in our model total customer demand is random and comprises fixed proportion of customers of different types customer preferences are modeled through the definition of these types each customer type corresponds to a specific preference ordering among products a customer purchases the highest ranked product according to his type if any that is available at the time of his visit to the store stockout based substitution we solve the optimal assortment problem using a dynamic programming formulation we establish structural properties of the value function of the dynamic program that in particular help to characterize multiple local maxima we use the properties of the optima to solve the problem in pseudopolynomial time our algorithm also gives a heuristic for the general case i e when the proportion of customers of each type is random in numerical tests this heuristic performs better and faster than previously known methods especially when the mean demand is large the degree of substitutability is high the population is homogeneous or prices and or costs vary across products

optimal flexibility configurations in newsvendor networks going beyond chaining and pairing we study the classical problem of capacity and flexible technology selection with a newsvendor network model of resource portfolio investment the resources differ by their level of flexibility where level k flexibility refers to the ability to process k different product types we present an exact set theoretic methodology to analyze newsvendor networks with multiple products and parallel resources this simple approach is sufficiently powerful to prove that i flexibility exhibits decreasing returns and ii the optimal portfolio will invest in at most two adjacent levels of flexibility in symmetric systems and to characterize iii the optimal flexibility configuration for asymmetric systems as well the optimal flexibility configuration can serve as a theoretical performance benchmark for other configurations suggested in the literature for example although chaining is not optimal in our setting the gap is small and the inclusion of scale economies quickly favors chaining over pairing we also demonstrate how this methodology can be applied to other settings such as product substitution and queuing systems with parameter uncertainty

mathematical structure of a bilevel strategic pricing model abstract this paper is concerned with the characterization of optimal strategies for a service firm acting in an oligopolistic environment the decision problem is formulated as a leader follower game played on a transportation network where the leader firm selects a revenue maximizing price schedule that takes explicitly into account the rational behavior of the customers in the context of our analysis the follower s problem is associated with a competitive network market involving non atomic customer groups the resulting bilevel model can therefore be viewed as a model of product differentiation subject to structural network constraints

spatial competition and the theory of differentiated markets an introduction spatial economics has been both in the very center of microeconomic theory and at its periphery it has been at the center to the extent that it has followed a tradition taking its roots in hotelling s classic stability in competition paper 15 and has used spatial concepts to explain by analogy the pricing of differentiated commodities it has been at the periphery to the extent that it has considered spatial pricing as observed in real life situations and tried to rationalize and evaluate observed spatial pricing techniques the former approach focuses on f o b pricing which is apparently taken for granted the latter focuses on discriminatory pricing which appears as the most frequently used technique in the industrial world the purposes of this special issue are to bring those two approaches together and to explore some of their analytical possibilities and limitations the philosophy of this introductory paper is to show the need for an integration of both avenues in an analysis of differentiated markets we begin by discussing the assumptions of what we will call the hotellinglosch approach and their implications in terms of the problems they allow us to tackle several papers in this issue contribute new insights in this respect we then undertake a similar exercise for what may be called the greenhutohta approach focusing on spatial price discrimination to discover the possibilities it may provide for an analysis of quality choice at the outset we note that its spatial approach typically implies partition of the

a new decision rule for lateral transshipments in inventory systems this paper deals with a single echelon inventory system consisting of a number of parallel local warehouses facing compound poisson demand there are standard holding and backorder costs as well as ordering costs at all warehouses normally the warehouses replenish from an outside supplier however lateral transshipments between the warehouses are also possible such transshipments take no time but incur additional costs when a demand occurs at a warehouse the question is whether the whole demand or part of it should be covered by a lateral transshipment from another warehouse given a set of alternative decisions our decision rule minimizes the expected costs under the assumption that no further transshipments will take place this rule is then used repeatedly as a heuristic a simulation study illustrates how the suggested technique performs under different conditions

reducing the mean supply delay of spare parts using lateral transshipments policies lateral transshipment has been studied lately as a promising policy for increasing the performances of multi echelon spare parts inventory system by lateral transshipment spare parts can be moved from one location with excess inventory to another location at the same echelon in shortage with the aim of reducing supply delays of spare parts this paper will examine the relative effectiveness of two lateral shipments approaches in reducing the mean supply delay msd of a non repairable item with respect to a classical policy of no lateral shipments a simulation model of a two echelon supply network has been implemented and an experiment has been performed by varying different parameters of the supply network such as the number of warehouses locations at the lower echelon the supply lead time from the central depot the spare parts demand uncertainty and the size variability of the warehouses results show appreciable reductions of msd when lateral shipments are allowed with respect to the classical policy in almost every network configuration

enhanced lateral transshipments in a multi location inventory system in managing an inventory network two approaches to the pooling of stock have been proposed reactive transshipments respond to shortages at a location by moving inventory from elsewhere within the network while proactive stock redistribution seeks to minimize the chance of future stockouts this paper is the first to propose an enhanced reactive approach in which individual transshipments are viewed as an opportunity for proactive stock redistribution we adopt a quasi myopic approach to the development of a strongly performing enhanced reactive transshipment policy in comparison to a purely reactive approach to transshipment service levels are improved while a reduction in safety stock levels is achieved the aggregate costs incurred in managing the system are significantly reduced especially so for large networks moreover an optimal policy is determined for small networks and it is shown that the enhanced reactive policy substantially closes the gap to optimality

estimation of consumer demand with stock out based substitution an application to vending machine products the occurrence of temporary stock outs at retail is common in frequently purchased product categories available empirical evidence suggests that when faced with stock outs consumers are often willing to buy substitute items an important implication of this consumer behavior is that observed sales of an item no longer provide a good measure of its core demand rate sales of items that stock out are right censored while sales of other items are inflated because of substitutions knowledge of the true demand rates and substitution rates is important for the retailer for a variety of category management decisions such as the ideal assortment to carry how much to stock of each item and how often to replenish the stock the estimated substitution rates can also be used to infer patterns of competition between items in the category in this paper we propose methods to estimate demand rates and substitution rates in such contexts we develop a model of customer arrivals and choice between goods that explicitly allows for possible product substitution and lost sales when a customer faces a stock out the model is developed in the context of retail vending an industry that accounts for a sizable part of the retail sales of many consumer products we consider the information set available from two kinds of inventory tracking systems in the best case scenario of a perpetual inventory system in which times of stock out occurrence and cumulative sales of all goods up to these times are observed we derive maximum likelihood estimates mles of the demand parameters and show that they are especially simple and intuitive however state of the art inventory systems in retail vend ing provide only periodic data i e data in which times of stock out occurrence are unobserved or missing for these data we show how the expectation maximization em algorithm can be employed to obtain the mles of the demand parameters by treating the stock out times as missing data we show an application of the model to daily sales and stocking data pooled across multiple beverage vending machines in a midwestern u s city the vending machines in the application carry identical assortments of six brands since the number of parameters to be estimated is too large given the available data we discuss possible restrictions of the consumer choice model to accomplish the estimation our results indicate that demand rates estimated naively by using observed sales rates are biased even for items that have very few occurrences of stock outs we also find significant differences among the substitution rates of the six brands the methods proposed in our paper can be modified to apply to many nonvending retail settings in which consumer choices are observed not their preferences and choices are constrained because of unavailability of items in the choice set one such context is in store grocery retailing where similar issues of information availability arise in this context an important issue that would need to be dealt with is changes in the retail environment caused by retail promotions

single period multiproduct inventory models with substitution we study a single period multiproduct inventory problem with substitution and proportional costs and revenues we consider n products and n demand classes with full downward substitution i e excess demand for class i can be satisfied using product j for i j we first discuss a two stage profit maximization formulation for the multiproduct substitution problem we show that a greedy allocation policy is optimal we use this to write the expected profits and its first partials explicitly this in turn enables us to prove additional properties of the profit function and several interesting properties of the optimal solution in a limited computational study using two products we illustrate the benefits of solving for the optimal quantities when substitution is considered at the ordering stage over similar computations without considering substitution while ordering specifically we show that the benefits are higher with high demand variability low substitution cost low profit margins or low price to cost ratio high salvage values and similarity of products in terms of prices and costs

a semi markov decision problem for proactive and reactive transshipments between multiple warehouses abstract lateral transshipments are an effective strategy to pool inventories we present a semi markov decision problem formulation for proactive and reactive transshipments in a multi location continuous review distribution inventory system with poisson demand and one for one replenishment policy for a two location model we state the monotonicity of an optimal policy in a numerical study we compare the benefits of proactive and different reactive transshipment rules the benefits of proactive transshipments are the largest for networks with intermediate opportunities of demand pooling and the difference between alternative reactive transshipment rules is negligible

conditions that cause risk pooling to increase inventory abstract we say product a is a partial substitute for product b if a fraction of the customers who prefer b are willing to accept a when b is out of stock when demand is uncertain it is intuitive and true that a larger willing to substitute fraction implies larger expected profits a higher willing to substitute fraction allows one to pool the risk of individual products it may also be intuitive that a larger willing to substitute fraction might result in lower optimal total inventory for the full substitution structure several researchers have shown that for certain distributions such as the exponential this latter intuition is not true we show that this full substitution anomaly can occur with any right skewed demand distribution we assume i i d demand distributions unless we indicate otherwise we also show that the anomaly can occur for a number of realistic situations of partial substitution with commonly used demand distributions such as normal exponential poisson and uniform we also demonstrate the anomaly for more than one period with backlogging lost sales more than two products and with setup costs

the effect of market segmentation with demand leakage between market segments on a firm s price and inventory decisions abstract in this paper we address the simultaneous determination of price and inventory replenishment in a newsvendor setting when the firm faces demand from two or more market segments in which the firm can set different prices we allow for demand leakage from higher priced segments to lower priced segments and assume that unsatisfied demand can be backlogged we examine the case where the demands occur concurrently without priority and are met from a single inventory we consider customer s buy down behavior explicitly by modeling demand leakage as a function of segment price differentiation and characterize the structure of optimal inventory and pricing policies

the effects of selling packaged goods on inventory decisions in this paper we study within a newsboy type modeling framework the common business practice of retail firms to sell products not only as independent items but also as part of multiproduct packets packaged goods our emphasis is on understanding the effects of such practices on the inventory decisions of the firm we provide insights on the resulting level of suboptimality when inventory decisions are made with demand information only on the independent items and without accounting for the demand substitution structure induced between independent items and packaged goods our stylized model studies an environment with two products that are not direct substitutes for each other sold either independently or as part of a packet that contains one unit of each we provide necessary and sufficient optimality conditions for this model and suggest an efficient numerical search for obtaining the optimal stocking levels an extensive computational study allowed us to provide insights on the nature of the optimal stocking policies the suboptimality of independent newsboy policies the effects of demand correlation among individual products and multiproduct packets and the determining role of induced substitution structure among products during stockout occasions on the profitability of the inventory system

dynamic capacity management with substitution we examine a multiperiod capacity allocation model with upgrading there are multiple product types corresponding to multiple classes of demand and the firm purchases capacity of each product before the first period within each period after demand arrives products are allocated to customers customers who arrive to find that their product has been depleted can be upgraded by at most one level we show that the optimal allocation policy is a simple two step algorithm first use any available capacity to satisfy same class demand and then upgrade customers until capacity reaches a protection limit so that in the second step the higher level capacity is rationed we show that these results hold both when all capacity is salvaged at the end of the last demand period as well as when capacity can be replenished in the latter case an order up to policy is optimal for replenishment although finding the optimal protection limits is computationally intensive we describe bounds for the optimal protection limits that take little effort to compute and can be used to effectively solve large problems using these heuristics we examine numerically the relative value of strictly optimal capacity and dynamic rationing the value of perfect demand information and the impact of demand and economic parameters on the value of optimal substitution

some models for estimating technical and scale inefficiencies in data envelopment analysis in management contexts mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best in this capacity mathematical programming serves as a planning aid to management data envelopment analysis reverses this role and employs mathematical programming to obtain ex post facto evaluations of the relative efficiency of management accomplishments however they may have been planned or executed mathematical programming is thereby extended for use as a tool for control and evaluation of past accomplishments as well as a tool to aid in planning future activities the ccr ratio form introduced by charnes cooper and rhodes as part of their data envelopment analysis approach comprehends both technical and scale inefficiencies via the optimal value of the ratio form as obtained directly from the data without requiring a priori specification of weights and or explicit delineation of assumed functional forms of relations between inputs and outputs a separation into technical and scale efficiencies is accomplished by the methods developed in this paper without altering the latter conditions for use of dea directly on observational data technical inefficiencies are identified with failures to achieve best possible output levels and or usage of excessive amounts of inputs methods for identifying and correcting the magnitudes of these inefficiencies as supplied in prior work are illustrated in the present paper a new separate variable is introduced which makes it possible to determine whether operations were conducted in regions of increasing constant or decreasing returns to scale in multiple input and multiple output situations the results are discussed and related not only to classical single output economics but also to more modern versions of economics which are identified with contestable market theories

price variability changes in demand and the rate of interest abstract it is shown that over time prices are almost inversely proportional to quantity demanded in the case of a monopolist who produces for inventory for a monopolistically competitive firm the dependence of prices on variations of demand is weak in both market structures the rate of interest introduces an element of exponential inflation

approximate dynamic programming for lateral transshipment problems in multi location inventory systems abstract companies commonly allocate their inventories across multiple locations based on their historical sales rates however random fluctuations in customer purchases such as those caused by weather conditions and other external factors might cause significant deviations from expected demand leading to excess stock in some locations and stockouts in others to fix this mismatch companies often turn to lateral transshipments e g the movement of stock between locations of the same echelon in this paper we examine multi location inventory systems under periodic review with multiple opportunities for proactive transshipments within one order cycle if stockouts occur demand is lost with no opportunity to backorder the objective of our model is to find an optimal policy that indicates the sources and the destinations of transshipments as well as the number of units to maximise the profit of the network we create a dynamic program that can in principal be solved to optimality using bellman s equation however the size of the state and decision spaces makes it impossible to find the optimal policy for real world sized problem instances thereby we use forward approximate dynamic programming to find a near optimal transshipment policy finally we conduct an extensive numerical study to gauge the performance of our transshipment policy for small size instances we compare our policy to the optimal one for larger scale instances we consider other practically oriented heuristics our numerical experiments show that our proposed algorithm performs very well compared to state of the art methods in the literature

decomposing technical inefficiency using the principle of least action abstract in for profit organizations profit efficiency decomposition is considered important since estimates on profit drivers are of practical use to managers in their decision making profit efficiency is traditionally due to two sources technical efficiency and allocative efficiency the contribution of this paper is a novel decomposition of technical efficiency that could be more practical to use if the firm under evaluation really wants to achieve technical efficiency as soon as possible for this purpose we show how a new version of the measure of inefficiency proportions mip which seeks the minimization of the total technical effort by the assessed firm is a lower bound of the value of technical inefficiency associated with the directional distance function the targets provided by the new mip could be beneficial for firms since it specifies how firms may become technically efficient simply by decreasing one input or increasing one output suggesting that each firm should focus its effort on a specific dimension input or output this approach is operationalized in a data envelopment analysis framework and applied to a dataset of airlines

using neoclassical consumer choice theory to produce a market map from purchase data this article presents a new model for estimating the spatial representation of objects and preference vectors from actual choice behavior of individuals or households it is based on neoclassical economic theory of consumer choice the model integrates both decisions of which good s to buy and the quantity of purchase overall preference is decomposed into price effects and intrinsic preference for the good a maximum likelihood method for estimating the model parameters is described and illustrated using choice data of ketchup brands collected by the use of electronic supermarket scanners

a static approximation for dynamic demand substitution with applications in a competitive market we propose a static approximation of dynamic demand substitution behavior based on a fluid network model and a service inventory mapping this approximation greatly enhances our ability to analyze the interdependent inventory service price and product assortment decisions in noncompetitive and competitive scenarios with demand substitution we demonstrate that the approximation is well behaved and then apply it to two previously intractable applications first we study a price and service competition between single product retailers after establishing a unique pure strategy nash equilibrium we find that competition results in lower price higher demand and a higher level of inventory we also observe that the aggregate profit and inventory level increase to positive constants as the number of retailers goes to infinity second we study a duopolistic competition on price service and product assortment we establish a pure strategy nash equilibrium for the product assortment competition and identify a condition for uniqueness we find that competition on both price and product assortment results in lower price and less variety for each competitor but the total number of products and the aggregate inventory level in a duopoly market are both likely to be higher than in a monopolistic market

managing and reallocating inventory across two markets with local information abstract consider a firm that controls inventory centrally for two separate markets that are managed by regional managers having local demand information the central planner provides a dedicated inventory level to each market to ensure a minimum service level but can reallocate inventory once associated demands are filled how should such a firm solicit regional managers to share their local information so inventory levels can be set efficiently in this paper we study a forecast sharing game in such a firm where demand information lies within regions and inventory is managed by a central decision maker we show that incentives are misaligned and truthful information sharing is not an equilibrium we study two potential ways to improve the system a regional managers directly place orders rather than simply passing demand forecasts or b a pricing scheme for inventory reallocations is imposed we show that under direct ordering a unique pure strategy bayesian nash equilibrium exists and makes retailers place orders based on their true forecasts although the requested order quantities are not system optimal e g some inventory pooling benefits are lost under an endogenous transfer pricing mechanism set by the central planner we find that a first best truth telling equilibrium is possible under certain conditions we conduct a numerical study to examine the different cases and find that when the critical fractile is high direct ordering results in lower inventories while the reverse is true when the critical fractile is low expected profit comparisons show the value of local information

who benefits from transshipment exogenous vs endogenous wholesale prices this paper studies how transshipments affect manufacturers and retailers considering both exogenous and endogenous wholesale prices for a distribution system where a single manufacturer sells to multiple identical cost retailers we consider both the manufacturer being a price taker and the manufacturer being a price setter in a single period setup under multivariate normal demand distribution in the case of the manufacturer being a price taker we provide several analytical results regarding the effects of key parameters on order quantities and profits in the case of the manufacturer being a price setter we characterize the stackelberg game that arises and provide several insights into how the game dynamics are affected by transshipments specifically we find that risk pooling makes retailers order quantities less sensitive to the wholesale price set by the manufacturer hence in general the manufacturer benefits from retailers transshipments by charging a higher wholesale price while retailers are often worse off the paper captures the effect of demand correlation and the effect of the number of retailers throughout and it illustrates the findings by a numerical example we also provide an interactive web page for numerical experiments

modified critical fractile approach for a class of partial postponement problems abstract this paper studies a single period partial postponement problem which is motivated by an inventory planning problem encountered in reebok nfl replica jersey supply chain we consider a group of regular products each facing a random demand there are two stocking options one is to procure the regular products the other is to stock a common component which can be customized later to any one of the regular products after demand realization we obtain an insightful interpretation of the optimality conditions for this class of problems and use it to obtain rules of thumb that practitioners can incorporate into their inventory models to determine the stocking levels to minimize the supply chain cost instead of proposing a numerical procedure to obtain the optimal solution we propose an adaptation of the classical critical fractile approach for this class of partial postponement problem the closed form formula obtained are surprisingly effective our numerical results suggest that this simple approach to inventory planning often comes close to the performance of the optimal solution obtained from numerical method

pricing distribution and the supply of storage abstract the belgian nitrogen fertilizer cartel announces each year a price schedule which is enforced during the coming twelve months these prices are resale prices to final users and reflect changes in costs of storage a game theoretic model is set up to rationalize this behavior for the case of instantaneous final demands and a large number of distributors habit formation in final demand is then shown to lead to even more flexible prices while transferability over time is seen to favor more rigid prices it is finally suggested that vertical integration into a competitive distribution sector can be profitable because it restores the possibility of intertemporal price discrimination

stocking decisions for low usage items in a multilocation inventory system this research shows that organizations with a number of sister plants warehouses or other stocking points can profit from the concept of proactive use of transshipments as an element of their inventory control policy for certain types of parts employing transshipments can significantly reduce the total inventory needed throughout the entire collection of stocking points the study is motivated by a real life situation involving a large utility company having 29 power generating plants in five southeastern states where there are thousands of parts that are commonly used at multiple plants at present each plant operates independently and maintains enough stock to meet its own requirements transshipments take place between plants whenever there is an emergency requirement for a part but no explicit consideration is given to this effect while deciding on stocking levels at different plants in the case we examined by setting stocking levels to explicitly take account of transshipments total system cost could be reduced by about 70 over the company s decentralized policy in general this work considers a single echelon n location continuous review inventory system in which complete pooling of stock is permitted among the locations a model is developed for slow moving expensive and consumable parts that are common to two or more locations a one for one ordering policy and queueing theory allow development and solution of a system of equations for the probability distribution of net inventory at each location a heuristic procedure is also developed to determine cost effective stocking levels actual data from the utility company are used to demonstrate the applicability of the model savings achieved as a result of pooling are reported

spatial competition and spatial price discrimination the analysis of spatial competition under conditions of free entry which derives its major impetus from the seminal work of losch 1954 has been conducted in general on the assumption that the competitive firm will adopt an f o b pricing scheme see for example capozza and van order 1978 and holahan 1978 greenhut 1956 does consider some of the implications of discriminatory pricing within competitive markets but his analysis adopts an essentially short run view and provides little rationale for the choice of such a pricing policy by competitive firms this is in contrast with developments in the analysis of spatial monopoly the early work of singer 1937 and hoover 1937 and subsequent developments by for example greenhut 1956 beckmann 1976 beckmann and ingene 1976 greenhut and greenhut 1977 holahan 1975 and norman 1977 indicate that the spatial monopolist should adopt a discriminatory spatial pricing policy where spatial price discrimination is taken conventionally to mean that delivered prices do not follow an f o b scheme but that all concumers equidistant from a particular supplier pay the same price it is rarely however that the results generated by the analysis of spatial monopoly are reconsidered in the analysis of spatial competition in particular although we know that spatial price discrimination will in general increase a monopolist s profit the assumption that profit maximising spatially competitive firms will adopt f o b pricing schemes has rarely been questioned and has not been questioned within the loschian competitive framework greenhut and ohta 1975a chapter 8 and chapter 8 appendix i are notable exceptions but in both cases they depart from the loschian scheme the first objective of this paper is therefore to show that when loschian competitive firms are allowed the option of discriminatory pricing i e are free of institutional constraints which require f o b pricing they will be forced to exercise that option in order to maintain normal profits secondly we shall show that if competitive conditions change the form of price discrimination will also change and that under certain competitive conditions the degree of discrimination will increase with the degree of competition leading eventually to uniform pricing thirdly we compare two competitive cases with multi plant monopoly and derive the spatial analogue of the conventional spaceless monopoly perfect competition comparison the monopolist s plants will be larger in area and total output than each competitive firm but will supply less per consumer at a higher average price welfare comparisons are less clear cut in that they are dependent upon the type of competition we assume we show however that welfare maximisation requires marginal cost pricing where marginal cost includes transport costs and so requires f o b pricing if there are economies of scale to production it follows that welfare maximisation will require production subsidy

a heuristic joint replinishment policy for the case of heterogeneity among items abstract the q s s policy is considered among the best for solving the well known stochastic joint replenishment problem however it has some shortcomings if much heterogeneity exists among the items consequently a new heuristic control policy is constructed the cornerstone is a policy iteration improvement step assuming a single possibility for making a joint order and thus to deviate from the rule that the items are governed by independent re order and order up to s s policies but this policy iteration improvement step is done repeatedly at each demand epoch it is only required the development of one dimensional value functions of state variables in order to accomplish the policy iteration improvement step knowledge about good order up to values is important furthermore a relaxation parameter is introduced such that one can make it easier or more difficult to issue a joint order when following the policy iteration improvement step finally in case a joint order is made a vector of can order points is used to include additional items the policy is denoted a c s policy numerical results shows that the new policy performs significantly better than the q s s policy for cases with heterogeneity among items furthermore from a given optimal can order policy one can construct a better c s policy

measurement of simultaneous scale and mix changes in inputs and outputs using dea facets and rts abstract we show a new use of the efficient facets in dea specifically once we have identified all facets of the dea technology we are able to estimate the potential changes in some inputs and outputs while fixing other inputs and outputs ranges of simultaneous scale and mix changes in inputs and outputs while proportionally increasing or decreasing other inputs and outputs and finally the rts the proposed algorithms are applied to corporate planning processes of chemical companies

stocking retail assortments under dynamic consumer substitution we analyze a single period stochastic inventory model newsboy like model in which a sequence of heterogeneous customers dynamically substitute among product variants within a retail assortment when inventory is depleted the customer choice decisions are based on a natural and classical utility maximization criterion faced with such substitution behavior the retailer must choose initial inventory levels for the assortment to maximize expected profits using a sample path analysis we analyze structural properties of the expected profit function we show that under very general assumptions on the demand process total sales of each product are concave in their own inventory levels and possess the so calleddecreasing differences property meaning that the marginal value of an additional unit of the given product is decreasing in the inventory levels of all other products for a continuous relaxation of the problem we then show via counterexamples that the expected profit function is in general not even quasiconcave thus global optimization may be difficult however we propose and analyze a stochastic gradient algorithm for the problem and prove that it converges to a stationary point of the expected profit function under mild conditions finally we apply the algorithm to a set of numerical examples and compare the resulting inventory decisions to those of some simpler naive heuristics the examples show that substitution effects can have a significant impact on an assortment s gross profits the examples also illustrate some systematic distortions in inventory decisions if substitution effects are ignored in particular under substitution one should stock relatively more of popular variants and relatively less of unpopular variants than a traditional newsboy analysis indicates

optimal replenishment and rework with multiple unreliable supply sources we study a production inventory system with multiple unreliable supply sources through inspection and rework the system can improve the quality of the units received from the supply sources there are two interleaved decisions the replenishment quantities from the sources and the inspection rework quantities among the units received we show the optimal solution to the replenishment decision can be efficiently derived from a greedy algorithm and inspection rework is optimally applied to a single source identified by the algorithm furthermore in the case of linear cost functions it is optimal to place orders from two supply sources i e dual sourcing the results extend to the infinite horizon case where an order up to policy is optimal the model also readily adapts to situations in which the supply imperfection takes the form of a reduced delivery quantity yield loss

the multi item newsvendor model with cross selling and the solution when demand is jointly normally distributed abstract products are often demanded in tandem because of the cross selling effect the demand for an item can increase if sales of its cross selling associated items are achieved or decrease when the associated items are out of stock resulting in lost sales therefore a joint inventory policy should be pursued in a cross selling system this paper introduces customer driven cross selling into centralized and competitive newsvendor nv models by representing an item s effective demand as a function of other items order quantities we derive first order optimality conditions for the centralized model in addition to pure strategy nash equilibrium conditions and uniqueness conditions of the equilibria for the competitive model we further develop gradient based gb and iteration based ib algorithms to solve the centralized and competitive models respectively a computational study verifies the effectiveness of the proposed algorithms the computational results show that a larger cross selling effect leads to a larger order quantity in a centralized nv model but a smaller order quantity in a competitive nv model and a larger positive correlation between items demands leads to higher profits with smaller order quantities in both models moreover nvs will order more items if the demand variance is greater however resulting in lower profits in a competitive situation one will prefer smaller order quantities than in a centralized decision situation

inventory management under price based and stockout based substitution abstract we examine a stochastic inventory and pricing problem for a firm that sells two vertically differentiated products the demands for the two products are determined by total random market size and the customers net utility from buying the two products which is determined by the products quality attributes the individual quality valuation unknown to the firm and the selling prices in case the preferred product is out of stock customers may be willing to buy a substitute instead if their net utility is non negative therefore we analyze an inventory and pricing model considering price based and stockout based substitution we show that the demand function is not continuous in price by decomposing the profit function into different price regimes we are able to derive closed form expressions for the stockout based substitution rates upward and downward substitution and the optimal inventory levels under exogenous pricing under endogenous pricing we find that the profit function is not necessarily unimodal however we show that a unique solution exists for the integrated price and inventory problem under price based substitution only numerical results reveal that not considering stockout based substitution i leads to lower profit margins for high quality products and ii may cause severe supply demand mismatches throughout the entire assortment finally we show the performance of two approximated pricing policies

managing inventories with one way substitution a newsvendor analysis abstract this paper presents an insightful approach to analyze two item periodic inventory systems with one way substitution the objective is to minimize the expected total cost per period which consists of expected purchasing costs expected inventory holding costs expected shortage costs and expected adjustment costs this approach helps derive the optimality conditions in both single period and infinite horizon settings and yields useful insights into the impact of substitution on the service level the optimality of a borderline case in which the order up to level of the inflexible item is reduced to zero and the pivotal role of the purchasing cost

optimal policy for a muti product multi period non stationary stochastic production and customization problem abstract this paper is concerned with a multi product multi period non stationary stochastic production and customization problem in which a firm wishes to satisfy multi period stochastic demands for m products the firm produces a generic product that can be customized into the m products the lead time to produce the generic product is one period the generic product can be customized into any of the m products immediately assume that the costs of production customization storage and shortage are linear also assume that the unsatisfied demands for the m products at the firm in each period are lost the objective of the firm is to find a production customization policy that minimizes the expected cost over a planning horizon we obtain the conditions that ensure that a myopic production customization policy is optimal

the effect of remanufacturing on procurement decisions for resellers in secondary markets the role of remanufacturing as a competitive tool for firms has been reflected in a number of studies to show that remanufacturing can reduce the unit cost of production by reusing components however the fact that remanufacturing can be used as a strategic tool for serving secondary markets as well has not been acknowledged in the literature in this paper we study the use of remanufacturing as a tool to serve secondary markets specifically we model the case of a reseller who procures used products based on an older generation of technology from an advanced market and then uses one of two options a she can either resell a small fraction of these used products in a developing market where the technology is acceptable or b she can invest in the remanufacturing of these products and then sell them in the developing market at a higher price the main result of the paper is that using remanufacturing to serve secondary markets reduces the number of units procured from the advanced market for the reseller in addition we show based on certain cost structures that the reseller is always better off if she uses remanufacturing to a certain extent

entry timing in a secondary market when to trade abstract in volatile long lead time and short selling season markets a secondary market enables buyers to update their inventory during the selling season the decision of when to update involves complicated trade offs between forecast accuracy expected lost sales and average purchasing cost we use a two stage inventory replenishment model to identify the optimal trading time across different scenarios across most scenarios the optimal trading time is around the midpoint of the season and is sensitive to the expected profit margin and demand forecast errors we discuss the impacts of the timing decision on upstream suppliers sales and channel performance in terms of sales revenue and supply demand mismatch costs specifically secondary market trading always reduces upstream suppliers sales no matter when trading occurs but trading at an optimal time can maximize a secondary market s profit gain over the no trade scenario through reducing supply demand mismatch

optimal joint inventory and transshipment control under uncertain capacity in this paper we address the optimal joint control of inventory and transshipment for a firm that produces in two locations and faces capacity uncertainty capacity uncertainty e g due to downtime quality problems yield etc is a common feature of many production systems but its effects have not been explored in the context of a firm that has multiple production facilities we first characterize the optimal production and transshipment policies and show that uncertain capacity leads the firm to ration the inventory that is available for transshipment to the other location and characterize the structure of this rationing policy then we characterize the optimal production policies at both locations which are defined by state dependent produce up to thresholds we also describe sensitivity of the optimal production and transshipment policies to problem parameters and in particular explain how uncertain capacity can lead to counterintuitive behavior such as produce up to limits decreasing for locations that face stochastically higher demand we finally explore through a numerical study when the optimal policy is most likely to yield significant benefits compared to simple policies

effects of constrained supply and price contracts on agricultural cooperatives planning strategies depend in part on the supply flow structure of a supply chain in food supply chains many firms are constrained by raw material supply e g vegetables and milk this paper first examines the economic consequences of constrained supply in agricultural cooperatives secondly it deals with the effects of adding price contracts to the current cooperative contract this model combines an inventory policy approach and a monte carlo simulation to take into account price uncertainty we illustrate our results using the case of a dairy cooperative c 2008 elsevier b v all rights reserved

product variety and demand uncertainty why markups vary with quality we demonstrate that demand uncertainty can explain equilibrium product variety in the presence of sunk costs product variety is an efficient response to uncertainty because it reduces the expected costs associated with excess capacity we find that within the firm s product line the highest quality product has the highest profit margin but the lowest percentage margin while the lowest quality product has the highest percentage margin but the lowest absolute margin both of these relationships are consistent with evidence available from marketing studies what determines the breadth of a firm s product line we show that when production costs must be sunk in anticipation of demand demand uncertainty can lead to an increase in product variety by limiting their inventory of high quality goods and selling low quality goods once their high quality goods have stocked out firms reduce the costs associated with demand uncertainty the model helps explain the extent of product differentiation and suggests a rationale for many common retailing practices such as the use of private labels and full product line forcing by manufacturers the model also yields the testable empirical prediction that higher quality products earn higher absolute margins and lower percentage margins while differences in preferences provide a convincing explanation in many cases for product variety in retail stores we argue that another

the multiperiod multilocation inventory problem this paper studies the structure of optimal policies in general multiperiod multilocation inventory problems with proportional costs it is shown that the multiperiod problem has the same generic form in each period as a one period problem hence properties of the one period problem are inherited by the multiperiod formulation in particular the form of the optimal policy can be characterized in the special case of a leontief system structure and for a somewhat more general class it is shown that base stock policies are optimal for certain initial states for the stationary problem some results are derived about the monotonicity of the sequence of base stock vectors

approximations of dynamic multilocation production and inventory problems consider a central depot or plant which supplies several locations experiencing random demands orders are placed or production is initiated periodically by the depot the order arrives after a fixed lead time and is then allocated among the several locations the depot itself does not hold inventory the allocations are finally received at the demand points after another lag unfilled demand at each location is backordered linear costs are incurred at each location for holding inventory and for backorders also costs are assessed for orders placed by the depot the object is to minimize the expected total cost of the system over a finite number of time periods this system gives rise to a dynamic program with a state space of very large dimension we show that this model can be systematically approximated by a single location inventory problem all the qualitative and quantitative results for such problems can then be applied

estimating demand by using sales information inaccuracies encountered abstract demand data is integral to a company s overall information requirement this is particularly true for manufacturers and retailers with regard to capacity production and inventory planning notwithstanding the implicit inaccuracies encountered companies are predisposed to employ sales data as a primary source of information for estimating future demand in this paper by adopting a two product setting we measure inventory cost inaccuracies that arise from using sales data in estimating demand by analyzing these costs we also explore the conditions under which the resulting inaccuracies are either lessened or become acute in this context the determining rule of an induced substitution structure between the two products during stockout occasions is explicitly analyzed we use a newsboy framework in a two product environment wherein one product may be taken as a direct substitute for the other we provide necessary and sufficient optimality conditions and an extensive computational study to illustrate and support our findings and to provide additional insights on the conditions characterizing optimal stocking policies

inventory decisions for substitutable products with stock dependent demand abstract we study a retailer s inventory policy for two products the products are substitutable and have inventory dependent demand so a higher inventory level of a product increases its sales we model the joint effect of demand stimulation and product substitution on inventory decisions by considering a single period stochastic demand setting we provide the first order optimality conditions for the profit maximizing order quantities and interpret them using marginal analysis we also consider two heuristic solutions that separately account for either demand stimulation or product substitution our numerical analysis reveals that the optimal policy by appropriately using sales information that quantifies substitution and demand stimulation can produce significantly higher profits the profit benefits are lessened under certain circumstances such as when the two products have similar critical fractile values suggesting that in such instances the heuristics may be used effectively

multi location transshipment problem with capacitated transportation abstract we consider coordination among stocking locations through replenishment strategies that take explicitly into consideration transshipments transfer of a product among locations at the same echelon level we incorporate transportation capacity such that transshipment quantities between stocking locations are bounded due to transportation media or the location s transshipment policy we model different cases of transshipment capacity as a capacitated network flow problem embedded in a stochastic optimization problem under the assumption of instantaneous transshipments we develop a solution procedure based on infinitesimal perturbation analysis to solve the stochastic optimization problem where the objective is to find the policy that minimizes the expected total cost of inventory shortage and transshipments such a numerical approach provides the flexibility to solve complex problems investigating two problem settings we show the impact of transshipment capacity between stocking locations on system behavior we observe that transportation capacity constraints not only increase total cost they also modify the inventory distribution throughout the network

incorporating one way substitution policy into the newsboy problem with imprecise customer demand this paper presents an approach for solving an inventory model for single period products with maximizing its expected profit in a fuzzy environment in which the retailer has the opportunity for substitution though various structures of substitution arise in real life in this study we consider the fuzzy model for two item with one way substitution policy this one way substitutability is reasonable when the products can be stored according to certain attribute levels such as quality brand or package size again to describe uncertainty usually probability density functions are being used however there are many situations in real world that utilize knowledge based information to describe the uncertainty the objective of this study is to provide an analysis of single period inventory model in a fuzzy environment that enables us to compute the expected resultant profit under substitution an efficient numerical search procedure is provided to identify the optimal order quantities in which the utilization of imprecise demand and the use of one way substitution policy increase the average expected profit the benefit of product substitution is illustrated through numerical example

product diversion to a direct competitor a manufacturer will often limit competition among downstream partners by authorizing only a select group of retailers to carry its product however it is not uncommon for authorized retailers to create an additional competitor by diverting units to an unauthorized seller this paper presents an analytical model that demonstrates how diversion from authorized retailers to an unauthorized direct competitor can occur under circumstances not considered by the prior literature in fact diversion can represent a prisoner s dilemma whereby retailers diminish their own profit by selling to the unauthorized direct seller the authorized retailer s profit loss actually increases as the per unit diversion costs incurred by the authorized retailer decrease the model also shows that the unauthorized direct seller earns greater profit by strategically procuring a unilaterally constraining quantity even though this procurement strategy results in an equivalent increase in the quantity sold by the retailers combined the results identify a new reason for diversion and its consequences for retailers and the unauthorized direct seller

coordinating the resource investment decision for a two market price setting firm abstract we study the capacity investment decision of a two product firm that is a price setter for both products the products are of varying complexities such that the resource that can be used to produce the higher level product can also be used to produce the lower level one but not vice versa although the firm needs to make its capacity investment decision under demand uncertainty it can utilize this limited downward resource flexibility in addition to pricing to more effectively match its supply with demand as an example consider a firm that owns a main plant satisfying both end product and intermediate product demand and a subsidiary satisfying the intermediate product demand only we formulate this decision problem as a two stage stochastic programming problem with recourse and analyze the impact of coordinated decision making when the resource flexibility is taken into account in the investment decision and demand correlation on the firm s optimal investment strategy our results offer managerial principles on the firm s optimal resource investment strategy

optimal production pricing and substitution policies in continuous review production inventory systems abstract we consider the optimal production pricing and substitution policies of a continuous review production inventory system with two products a high end product and a low end product each product has its associated customer stream however the demands for the low end product may be satisfied by the high end product we formulate the problem as a markov decision process and characterize the structure of the optimal control policy which specifies when to produce for each product when to use the high end product as a substitute and how to set the optimal prices we show that a base stock production policy is optimal however the optimal base stock level for each product depends on the inventory level of the other product and it features a monotonic property we also demonstrate that the optimal substitution policy is a rationing policy with the rationing level depending on the total inventory amount we find that the optimal prices can be either decreasing or increasing in the inventory levels depending on the forms of demand functions furthermore we utilize numerical experiments to investigate the impact of different system characteristics on the benefits of using substitution and dynamic pricing finally we investigate when the dynamic pricing strategy and the substitution strategy are complements or substitutes

incentive efficient production frontiers an agency perspective on dea in this paper we examine how empirical production frontiers may contribute to the incentives of production units we consider a series of data envelopment analysis dea frontiers and we show when these may be incentive efficient in the sense that they contain all the information that are relevant for optimal incentive provision the frontiers considered include the so called constant decreasing and varying return to scale models the free disposability and the free replicability models as well as the increasing and decreasing return to scale models based on a relaxed set of assumptions also we illustrate how to design optimal incentive schemes based on such frontiers contents 1 introduction 2 the incentive problem 3 production frontiers and productivity measures 4 incentive efficient production frontiers 5 extensions 6 an example 7 final remarks mathematical appendix references

dynamic capacity management with general upgrading this paper studies a capacity management problem with upgrading a firm needs to procure multiple classes of capacities and then allocate the capacities to satisfy multiple classes of customers that arrive over time a general upgrading rule is considered i e unmet demand can be satisfied using multistep upgrade no replenishment is allowed and the firm has to make the allocation decisions without observing future demand we first characterize the structure of the optimal allocation policy which consists of parallel allocation and then sequential rationing specifically the firm first uses capacity to satisfy the same class demand as much as possible then considers possible upgrading decisions in a sequential manner we also propose a heuristic based on certainty equivalence control to solve the problem numerical analysis shows that the heuristic is fast and delivers close to optimal profit for the firm finally we conduct extensive numerical studies to derive insights into the problem it is foun

yield and allocation management in a continuous make to stock system with demand upgrade substitution abstract yield management is crucial for high tech industries to reduce over production however it is very challenging for a manufacturer to make a yield decision under the circumstance of uncertain demand and stochastic product quality for example in semiconductor manufacturing industry products are produced in batches within certain production cycle time even if the same raw material is put into the production system the product qualities measured by performance usually are not identical due to random yield in the manufacturing process since products have overlapped performance specifications products of the same batch are classified into different classes according to their qualities at the allocation stage products with higher performance can substitute for demand for products with lower performance this type of production and allocation system can be specified as a make to stock system with single material multi products multi periods upward demand substitution under random yield and uncertain demands in order to maximize profit the manufacturer needs to decide on the optimal input material quantity and the optimal allocation policy the problem is formulated as a stochastic dynamic programming model because manufacturer s profit is affected by the allocation policies atp r allocation policy is proposed to help manufacturer make real time allocation decisions a numerical experiment shows that atp r allocation policy performs better than the traditional myopic allocation policy to reduce the computation burden involved in atp r allocation policy we further propose a simplified algorithm and our experimental studies provide proof of the effectiveness of the proposed simple algorithm

multi location transshipment problem with capacitated production abstract we consider coordination among stocking locations through replenishment strategies that explicitly take into account lateral transshipments i e transfer of a product among locations at the same echelon level our basic contribution is the incorporation of supply capacity into the traditional transshipment model our goal is to analyze the impact on system behavior and on stocking locations performance of the fact that the supplier may fail to fulfill all the replenishment orders we therefore formulate the capacitated supply scenario as a network flow problem embedded in a stochastic optimization problem which is solved through a sample average approximation method we find that depending on the production capacity system behavior can vary drastically moreover in a production inventory system we find evidence that either capacity flexibility i e extra production or transshipment flexibility i e pooling is required to maintain a desired level of service

single period single product newsvendor model with random supply shock abstract in order to investigate the efficiency of policies made by the industrial administration office iao for short so as to keep market order the authors propose a shocked inventory model of one product with both genuine and counterfeit qualities the checking policies made by the iao are considered to be a random shock for the inventory model by examination of the qualities of the products which will expropriate the counterfeit products the paper makes two contributions first while discussing several conditions the authors provide a basic theory which is a kind of extension of the newsvendor problem and prove some properties of the optimal policies for the shocked inventory model with a fixed random checking rate second the authors give some recommendations as to how the iao can formulate its checking policies an example demonstrates the relationship between checking policies and optimal inventory policies

from efficiency measurement to efficiency improvement the choice of a relevant benchmark abstract this article deals with efficiency improvement and how to identify appropriate benchmarks for inefficient firms to imitate we argue that the most relevant benchmark is the most similar efficient firm having interpreted similarity in terms of input endowments the problem reduces to find the closest reference firm on the efficient subset of the isoquant to such an end we introduce the concept of input specific contractions this concept allows to find the shortest path to the efficient subset this information can be used to advise inefficient firms about which efficient firm to visit in order to detect its mistakes and to learn better managerial practices

the measurement of productive efficiency a reconsideration the purpose of this paper is to generalize the farrell indexes of productive efficiency to nonhomothetic production technologies and at the same time maintain the cost interpretation of the farrell measures since the generalized indexes rely heavily on recent developments in the estimation of frontier cost and production functions several frontier models are reviewed in addition to generalized indexes of technical allocative and overall productive efficiency a variety of single factor efficiency measures are discussed the applicability of the proposed efficiency measures is illustrated with a numerical example of electric power generation

optimal policies for inventory systems with lateral transshipments using lateral transshipments can be beneficial in order to improve service levels and to reduce system costs this paper deals with a single echelon inventory system with two identical locations demands are generated by stationary and independent poisson processes in general if a demand occurs at a location and there is no stock on hand the demand is assumed to be backordered or lost however in this paper lateral transshipments serve as an emergency supply in case of stock out in this paper the rule for lateral transshipments is given while the ordering policies for normal replenishments are optimized the transshipment rule is to always transship when there is a shortage at one location and stock on hand at the other first we assume that the locations apply r q policies for normal replenishments and show that the optimal policies are not necessarily symmetric even though the locations are identical this means that one cannot in general assume that the optimal policy is symmetric under symmetric assumptions second we relax the assumption of r q policies and derive the optimal replenishment policy using stochastic dynamic programming

strategic leaders or strategic groups a longitudinal data envelopment analysis of the u s brewing industry abstract this paper builds on strategic group theory which was originally introduced to help explain the observed variation in firm profitability across an industry this paper applies data envelopment analysis dea to identify both strategic leaders the best practice players in the industry and strategic groups to examine which are the source of the most sustained heterogeneity in the performance of u s brewers contrary to the prevalent research approach in strategy and organization research which places a premium on empirical analyses that maximize explanation of average behavior daft and lewin 1990 this paper examines extremal observations as a means of studying or inducing theories about best practice such as best strategies or most effective organization design lewin and minton 1986 the paper argues that significant insights new knowledge and unexpected theories can arise from studying the best or worst of a population the paper applies dea to a longitudinal reanalysis of u s brewing data to demonstrate its usefulness for obtaining new insights from identifying and studying industry outliers the paper raises important questions about the construct of strategic groups and illustrates how competing theories can be deduced and analyzed for explaining performance heterogeneity in the u s brewing industry

how to order and transship in multi location inventory systems the simulation optimization approach abstract the efficient control of multi location inventory systems with lateral transshipments has become increasingly important however existing models are analytically solvable only under simplifying assumptions there is a variety of heuristics to find approximate solutions but interdependencies between ordering and transshipment decisions for continuous time are not addressed thus we suggest using simulation optimization in our paper we describe a widely adaptable simulation model for mapping highly complex multi location inventory systems with lateral transshipments by applying this model to a special case from the literature and to some examples we show its validity and generality

optimal and approximate policies in multiperiod multilocation inventory models with transshipments this paper examines the effects on the optimal ordering policy and its cost of allowing for interactions among retail outlets specifically transshipments are allowed as recourse actions occurring after demands are realized but before they must be satisfied the resultant savings in holding and shortage costs are balanced against the costs of transshipment a base stock ordering policy is optimal for this model if the final period base stock order up to point is nonnegative then it will be the base stock order up to point for all periods unfortunately it can be found analytically only for two special cases where either the cost parameters are equal at every outlet or there are only two outlets these two special cases are used to validate a heuristic solution technique employing monte carlo integration which is then compared to an easily calculated base policy in order to gauge the contribution of this model the additional savings from using this heuristic policy are significant particularly for problems with many retail outlets and low transshipment costs

product differences and prices abstract under assumptions following hotelling s 1929 paper stability in competition the possibility of constructing an example in which equilibrium prices exist everywhere and the two merchants display tendencies to agglomerate is ruled out

flexible service capacity optimal investment and the impact of demand correlation we consider a firm that provides multiple services using both specialized and flexible capacity the problem is formulated as a two stage single period stochastic program the firm invests in capacity before the actual demand is known and optimally assigns capacity to customers when demand is realized sample applications include a car rental company s use of mid sized cars to satisfy unexpectedly high demand for compact cars and an airline s use of business class seats to satisfy economy class demand we obtain an analytical solution for a particular case when services may be upgraded by one class the simple form of the solution allows us to compare the optimal capacities explicitly with a solution that does not anticipate flexibility given that demand follows a multivariate normal distribution we analytically characterize the effects of increasing demand correlation on the optimal solution for the case with two customer classes the effects of demand correlation are intuitive increasing correlation induces a shift from flexible to dedicated capacity when there are three or more classes there are also adjustments to the resources not directly affected by the correlation change as correlation rises these changes follow an alternating pattern for example if the optimal capacity of one resource rises then the optimal capacity of the adjacent resource falls these results make precise conjectures based on numerical experiments that have existed in the literature for some time

measures of technical efficiency abstract fare and lovell j econom theory 19 1978 150 162 suggest four properties that a measure of technical efficiency should satisfy the commonly employed debreu farrell measure fails three of them necessary and sufficient conditions for a measure to satisfy the four conditions are provided and recently proposed measures are analyzed in the light of this result also it is argued that the debreu farrell measure has several desirable properties when one takes account of 1 perhaps unknown market prices and the relationship between technical and economic efficiency and 2 its characterization as a measure of economic efficiency using the shadow prices implicit in the production technology

dynamic version of the economic lot size model this article originally appeared in management science october 1958 volume 5 number 1 pp 89 96 published by the institute of management sciences a forward algorithm for a solution to the following dynamic version of the economic lot size model is given allowing the possibility of demands for a single item inventory holding charges and setup costs to vary over n periods we desire a minimum total cost inventory management scheme which satisfies known demand in every period disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full n periods

an inventory model with unidirectional lateral transshipments this paper deals with a continuous review inventory system with poisson demand in which lateral transshipments are allowed in case of a shortage at a location another location acts as a supplier if it is possible a common assumption in earlier papers is that transshipments are allowed between all locations this network configuration may however not be the best choice for many reasons one such reason is that it may be difficult to establish contracts between locations regarding the design of the transshipment policy another reason is that a system with many transshipment links is much more complex than a system with few transshipment links in this paper we study a system where transshipments are allowed only in one direction this may be a reasonable policy if the locations have very different backorder lost sales costs our approach is relatively simple and fast and works well in most cases

the switching effect of environmental taxation within bertrand differentiated duopoly we investigate second best optimal taxation of the polluting variety of a product in a bertrand duopoly with differentiated varieties the analysis provides novel insight on a useful social function of environmental regulation besides internalizing the environmental externality the taxation of the polluting variety improves the matching of consumers and product varieties and so creates a socially desirable business switching between the differentiated varieties

emergency lateral transshipments in a two location inventory system with positive transshipment leadtimes abstract we consider a single echelon continuous review inventory system for spare parts with two parallel locations each location faces independent poisson demand and backorders are allowed in this paper we consider the possibility of lateral transshipments between the locations the transshipment leadtime is positive and deterministic and there is an additional cost for making a transshipment we suggest a transshipment policy which is based on the timing of all outstanding orders and develop and solve a heuristic model by using theory and concepts from doubly stochastic poisson processes and also partial differential equations a simulation study indicates that our heuristic works very well and that the relative cost increase of disregarding the transshipment leadtime may be quite high our results also indicate that it is in general worth the effort of reducing the transshipment leadtime even if it is already relatively short

cost parametric analysis of lateral transshipment policies in two echelon supply chains abstract in this paper we examine the cost effects of two lateral intra echelon transshipment approaches in a two echelon supply chain network with a single supply source at the higher echelon and multiple retail locations at the lower through a series of simulation experiments under different operating conditions an important finding is that either of the proposed lateral shipment approaches is considerably superior to a policy of no such shipments albeit at the expense of increased transportation activity further an ad hoc emergency transshipment approach appears to be significantly more effective in terms of several important criteria as compared to a more systematic transshipment technique based on stock level equalization

an index heuristic for transshipment decisions in multi location inventory systems based on a pairwise decomposition in multi location inventory systems transshipments are often used to improve customer service and reduce cost determining optimal transshipment policies for such systems involves a complex optimisation problem that is only tractable for systems with few locations consequently simple heuristic transshipment policies are often applied in practice this paper develops an approximate solution method which applies decomposition to reduce a markov decision process model of a multi location inventory system into a number of models involving only two locations the value functions from the subproblems are used to estimate the fair charge for the inventory provided in a transshipment this estimate of the fair charge is used as the decision criterion in a heuristic transshipment policy for the multi location system a numerical study shows that the proposed heuristic can deliver considerable cost savings compared to the simple heuristics often used in practice

accounting for slacks to measure and decompose revenue efficiency in the spanish designation of origin wines with dea abstract in this paper we show how data envelopment analysis dea may be used to measure and decompose revenue inefficiency taking into account all sources of technical waste in the context of an application to assess the spanish quality wine sector in particular designation of origin do wines we try to go beyond the standard approaches which use shephard distance functions or directional distance functions to provide decomposition that incorporates slacks as a source of technical inefficiency to accomplish this we will base our analysis on a recent approach introduced in cooper et al 2011a in particular we show how an output oriented version of the weighted additive model can be used to properly identify revenue technical and allocative inefficiencies in spanish dos in the application we conclude that the main source of revenue inefficiency in this sector is technical waste and that cava can be highlighted as the do that performs as a benchmark for more numbers of units

transshipment of inventories among retailers myopic vs farsighted stability the author considers a model of a decentralized distribution system consisting of n retailers selling an identical product retailers face a stochastic demand and must order their initial inventory before this demand is realized after demand realization retailers decide how much of their unsold inventory or unsatisfied demand they want to share with other retailers this is followed by a transshipment of leftover inventories and distribution of the additional profit generated through inventory sharing the author addresses the following issue suppose that the retailers distribute the profit from inventory sharing according to an allocation rule that induces retailers to share their residuals in a way that maximizes the additional profit such as the shapley value but may not belong to the core is it likely that in this framework all retailers will jointly share their residuals and not form subcoalitions previous research has looked at this problem from a myopic viewpoint and concluded that the grand coalition is not stable unlike the prior work the author looks at stability in a farsighted sense that is retailers do not consider only their immediate payoffs but are also concerned with reactions of other retailers to their actions in a symmetric setting with identical additional unit revenues from transshipments generated by all retailers farsighted retailers always maximize their allocations by not defecting from the grand coalition the author also provides conditions when the same is true for nonidentical additional unit revenues

assortment planning and inventory decisions under a locational choice model we consider a single period assortment planning and inventory management problem for a retailer using a locational choice model to represent consumer demand we first determine the optimal variety product location and inventory decisions under static substitution and show that the optimal assortment consists of products equally spaced out such that there is no substitution among them regardless of the distribution of consumer preferences the optimal solution can be such that some customers prefer not to buy any product in the assortment and such that the most popular product is not offered we then obtain bounds on profit when customers dynamically substitute using the static substitution for the lower bound and a retailer controlled substitution for the upper bound we thus define two heuristics to solve the problem under dynamic substitution and numerically evaluate their performance this analysis shows the value of modeling dynamic substitution and identifies conditions in which the static substitution solution serves as a good approximation