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

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

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 two item newsboy problem with substitutability previous research on the newsboy problem is based on the assumption that in case of a shortage unsatisfied demand is lost such an assumption is inappropriate for items that have a close substitute in this paper we formulate a two item newsboy problem with substitutability tinps upper and lower bounds on the optimal order quantities of the two items are derived since analytical solutions to the problem are difficult to obtain a monte carlo simulation is used to identify the optimal solution to the tinps order quantities identified by the simulation provide higher expected profit than would have been obtainable without considering substitutability

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

joint inventory and pricing decisions for an assortment we seek optimal inventory levels and prices of multiple products in a given assortment in a newsvendor model single period stochastic demand under price based substitution but not stockout based substitution we address a demand model involving multiplicative uncertainty motivated by market share models often used in marketing the pricing problem that arises is known not to be well behaved in the sense that in its deterministic version the objective function is not jointly quasi concave in prices however we find that the objective function is still reasonably well behaved in the sense that there is a unique solution to the first order conditions and this solution is optimal for our problem

the competitive newsboy we consider a competitive version of the classical newsboy problem in which a firm must choose an inventory or production level for a perishable good with random demand and the optimal solution is a fractile of the demand distribution and investigate the impact of competition upon industry inventory a splitting rule specifies how initial industry demand is allocated among competing firms and how any excess demand is allocated among firms with remaining inventory we examine the relation between equilibrium inventory levels and the splitting rule and provide conditions under which there is a unique equilibrium our most general result is that if all excess demand is reallocated i e there is perfect substitutability then competition never leads to a decrease in industry inventory

analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem abstract this paper studies the analytical and managerial implications of product substitutability on the joint pricing and procurement decisions we consider a single period model with two products an existing product and an improved new product that can substitute the demand for the existing product in case of a shortage demand for each product follows a general distribution with an expected value that is a linear function of the price of the new product while the price of the existing product is determined by the market it is necessary to determine the new product s price and the procurement quantities of both products so as to maximize the profits we analytically show that the expected profit function is unimodal and in the existence of substitution the expected total profit is higher the optimal price and the safety stock of the new product are higher and the optimal safety stock of the existing product is less using these properties an efficient algorithm is developed we also provide a numerical analysis to demonstrate that considering substitution in advance could increase the profitability by 58 and the new product price by 5 while decreasing the total procurement quantity by 15

joint pricing and procurement of fashion products in the existence of clearance markets abstract this paper focuses on the joint pricing and procurement of fashion products in the existence of clearance markets it is assumed that the expected regular season demand is a linear decreasing function of the price and the end of period excess inventory is sold at a known discounted price in a clearance market where the demand is a random variable that follows a general distribution it is shown that the expected profit function is unimodal and the optimal procurement quantity and price can be found from the first order conditions existence of a clearance market increases the profit price and the procurement quantity in order to prove this the optimal procurement and pricing policy of a price setting retailer who does not have a clearance market is provided as opposed to the literature it is shown that the expected profit function of this problem is unimodal as well a numerical study demonstrating the magnitude of the increase in profit procurement quantity and price is reported

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

international intertemporal solvency in industrialized countries evidence and implications recent large current account deficits among industrialized countries have caused concern for policy makers some believe for example that the current buildup of claims on the u s by foreigners violates her solvency condition with respect to the rest of the world recent research 22 suggests that for a country s intertemporal solvency condition to hold the change in the country s obligations to the rest of the world i e her current account deficit must be stationary stationarity tests on current accounts were performed for the u s by trehan and walsh 22 and wickens and uctum 23 for the u s and canada by otto 15 and for twenty three countries by gundlach and sinn 10 these papers present evidence that current accounts are non stationary for several major industrialized countries including the u s the u k canada germany and japan these findings do not favor international intertemporal solvency for this reason the issue merits further investigation in this paper we test for the stationarity of current account deficits of the group of seven industrialized countries preliminary results confirm many of gundlach and sinn s 10 findings however several events during the 1980s might have caused discrete breaks in current account balances events potentially linked with current account breaks include the reduction in world inflation tax reduction and reform in the u s and other industrialized countries attempts at international macroeconomic coordination i e the plaza accord and shifts in the after tax rate of return on capital in many countries as shown in recent research on gross national product 16 2 if such breaks are not accounted for stationarity tests will be biased in favor of accepting the null hypothesis of non stationarity our results suggest strong evidence of discrete breaks in the u s and japan and some evidence favoring breaks in the u k germany and canada the break in the u s current account appears to occur in 1983 while breaks in the other countries appear to occur somewhat later between late 1984 and 1987 more importantly once these breaks are incorporated the evidence is more favorable toward the stationarity of current accounts in these countries these findings thus support intertemporal solvency for these countries

the implications of costs capacity and competition on product line selection we consider a situation in which a manufacturer has to select the product s to sell as well as the selling price and production quantity of each selected product there are two substitutable products in the consideration set where product 2 has a higher quality and reservation price than that of product 1 by considering the cannibalization effect that depends on the selling price of each product the manufacturer needs to evaluate the profit function associated with three different product line options sell both products or only one of the 2 products in order to examine the impact of costs capacity and competition on the optimal product line selection optimal price and optimal production quantity analytically we present a stylized model in this paper so that we can determine the conditions under which a particular option is optimal

joint pricing and procurement of substitutable products with random demands a technical note abstract single period joint pricing and procurement of substitutable products entails one time procurement and pricing decisions for substitutable products that face price dependent stochastic demands recently karakul and chan karakul m chan l 2008 analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem european journal of operational research 190 179 204 considered this problem for two one way substitutable products authors model the demands for each product in the well known additive form where the mean demands are linear functions of the price of the high grade new product plus an additive stochastic noise term by assuming that the noise term for the low grade existing product follows a general discrete distribution and the noise term for the high grade product follows a general continuous distribution authors are able to show the unimodality of the expected profit function with respect to the procurement quantities and the price of the new product in this paper we extend this result to the case where the noise term in the demand of the low grade product follows a general continuous distribution as well

category management and coordination in retail assortment planning in the presence of basket shopping consumers this paper studies the assortment planning problem with multiple merchandise categories and basket shopping consumers i e consumers who desire to purchase from multiple categories we present a duopoly model in which retailers choose prices and variety level in each category and consumers make their store choice between retail stores and a no purchase alternative based on their utilities from each category the common practice of category management cm is an example of a decentralized regime for controlling assortment because each category manager is responsible for maximizing his or her assigned category s profit alternatively a retailer can make category decisions across the store with a centralized regime we show that cm never finds the optimal solution and provides both less variety and higher prices than optimal in a numerical study we demonstrate that profit loss due to cm can be significant finally we propose a decentralized regime that uses basket profits a new metric rather than accounting profits basket profits are easily evaluated using point of sale data and the proposed method produces near optimal solutions

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

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

a classification of the literature on the planning of substitutable products abstract a company s assortment of products and corresponding inventory levels are constrained by available resources such as production capacity storage space and capital to acquire the inventory thus customers may not always be able to find a most preferred product at the time of purchase this unsatisfied demand is often substituted with an alternative in the extant literature there have been an increasing number of studies that consider product substitution when planning product assortment inventory and capacity in conjunction with pricing in this paper we classify the literature on the planning of substitutable products published in the major om and marketing journals during the past thirty years 1974 2013 and present a comprehensive taxonomy of the literature one criterion is adopted to discuss modeling objectives and three major criteria are provided to define the nature of product substitution including substitution mechanism substitution decision maker and direction of substitutability we also identify research gaps to provide guidance for related research in the future

product availability in competitive and cooperative dual channel distribution with stock out based substitution abstract this paper investigates the impact of customers stock out based substitution on the product availability and the channel efficiency of a dual channel supply chain which consists of a supplier distributing a single product to customers through both its wholly owned direct channel and an independent retailer the supplier and its retailer with the objective of optimizing their own profit simultaneously choose their own base stock level to satisfy the stochastic demand from the customers whose channel preferences are heterogeneous and may be affected by each channel s product availability the customers dynamically substitute between the two channels in the event of a stock out the result shows that the effect of the stock out based substitution may increase or decrease the efficiency of a decentralized supply chain it is found that while the integrated supplier retailer may consolidate the base stock levels to benefit from stock out based substitution the independent supplier and retailer are more inattentive to customers stock out based substitution thus the competitive base stock levels of the decentralized dual channel supply chain rarely agree with the system optimal levels various contracts are examined to shed light on channel coordination mechanisms in addition it is shown that the channel efficiency of the dual channel distribution can be improved by the emergence of stackelberg leadership from either the supplier or the retailer

optimizing product assortment under customer driven demand substitution abstract the problem of product assortment and inventory planning under customer driven demand substitution is analyzed and a mathematical model for this problem is provided in this paper realistic issues in a retail context such as supplier selection shelf space constraints and poor quality procurement are also taken into account the performance of three modified models one that neglects customers substitution behavior another that excludes supplier selection decision and one that ignores shelf space limitations are analyzed separately with computational experiments the results of the analysis demonstrate that neglecting customer driven substitution or excluding supplier selection or ignoring shelf space limitations may lead to significantly inefficient assortments the effects of demand variability and substitution cost on optimal assortment and supplier selection decisions as well as on the optimal revenue are also investigated the main contribution of this paper is the development of a practical and flexible model to aid retailers in finding optimal assortments to maximize the expected profit

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

the economics of product variety a survey demand for variety may arise from a taste for diversity in individual consumption and or from diversity in tastes even when each consumer chooses a single variant the full degree of variety potentially demanded will not in general be supplied because scale economies even to a small degree mean that the potential welfare or revenue gain from greater variety must be balanced against the lower unit production costs with fewer variants the economics of product variety consists essentially in analysing the effect of this balance in different situations and comparing the degree of product variety for different market structures with each other and with the optimum the survey commences with the work on market structures with single product firms generalized monopolistic competition tracing modern developments in both the chamberlinian and hotelling traditions the latter has been particularly fruitful due to the expansion of the original locational ideas into virtual spaces in product characteristics the emphasis in recent work on product variety has been on multiproduct firms in both monopolistic and oligopolistic structures including strategic market preemption although most work has been in a full information context there have been advances in product variety under imperfect information either by consumers to properties of the firms products or firms as to consumers demands

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

an industry equilibrium analysis of downstream vertical integration this paper investigates the effect of product substitutability on nash equilibrium distribution structures in a duopoly where each manufacturer distributes its goods through a single exclusive retailer which may be either a franchised outlet or a factory store static linear demand and cost functions are assumed and a number of rules about players expectations of competitors behavior are examined it is found that for most specifications product substitutability does influence the equilibrium distribution structure for low degrees of substitutability each manufacturer will distribute its product through a company store for more highly competitive goods manufacturers will be more likely to use a decentralized distribution system this article was originally published in marketing science volume 2 issue 2 pages 161 191 in 1983

optimal capacity for substitutable products under operational postponement abstract we consider a monopolist producing two substitutable products with one flexible shared capacity the demand of each product is a linear function of the prices of both products and is subject to an additive shock we study the impact of two key drivers namely the degree of substitution between the products and the level of operational postponement on the optimal capacity and the resulting expected profit we show that the relationship between the optimal capacity and the degree of product substitution is not impacted by the different postponement strategies the firm can utilize or by the different settings forced clearance versus holdback considered in the previous literature on the other hand how capacity is affected by postponement critically depends on how closely substitutable the products are in particular we show that the well known result that operational postponement and capacity are strategic complements in a single product setting van mieghem and dada 1999 no longer holds in our setting because the two substitutable products are now linked through consumer driven substitution which the firm can influence through pricing in particular capacity and operational postponement in the form of quantity postponement can be either strategic substitutes or strategic complements and this depends on both the firm s cost structure and the degree of substitution between the products we also study the impact of forced clearance on the firm s expected profit and find that clearance deteriorates the firm s earnings more when the products it offers are highly differentiated

inventory competition under dynamic consumer choice we analyze a model of inventory competition among n firms that provide competing substitutable goods each firm chooses initial inventory levels for their good in a single period newsboy like inventory model customers choose dynamically based on current availability so the inventory levels at one firm affect the demand of all competingfirms this creates a strategic interaction amongthe firms inventory decisions our work extends earlier work on variations of this problem by karjalainen 1992 lippman and mccardle 1997 and parlar 1988 specifically we model demand in a more realistic way as a stochastic sequence of heterogeneous consumers who choose dynamically from amongthe available goods or choose not to purchase based on a utility maximization criterion we also use a sample path analysis so minimal assumptions are imposed on this demand process we characterize the nash equilibrium of the resulting stocking game and prove it is unique in the symmetric case we show there is a bias toward overstocking caused by competition specifically reducing the quantity stocked at any equilibrium of the game increases total system profits and at any joint optimal set of stocking levels each firm has an individual incentive to increase its own stock for the symmetric case we show that as the number of competing firms increases the overstockingbecomes so severe that total system and individual firm profits approach zero finally we propose a stochastic gradient algorithm for computing equilibria and provide several numerical examples

optimal bundle formation and pricing of two products with limited stock abstract in this study we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm one of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit product demands follow a poisson process with a price dependent rate customer reservation prices are assumed to have a joint distribution we study the impact of reservation price distributions initial inventory levels product prices demand arrival rates and cost of bundling we observe that the expected profit decreases as the correlation between the reservation prices of two products increases with negative correlation bundling cost has a significant impact on the number of bundles formed when the product prices are low the retailer sells individual products as well as the bundle mixed bundling when they are high the retailer sells only bundles pure bundling the expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases for high starting inventory levels the retailer reduces bundle price and offers more bundles the number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases impacts of substitutability and complementarity of products are also investigated the retailer forms more bundles or charges higher prices for the bundle or both as the products become more complementary and less substitutable

the impact of product substitution on retail merchandising abstract we analyze the impact of product substitution on two key aspects of retail merchandising order quantities and expected profits to perform this analysis we extend the basic news vendor model to include the possibility that a product with surplus inventory can be used as a substitute for out of stock products this extension requires a definition and an approximation for the resulting effective demand under substitution a service rate heuristic is developed to solve the extended problem the performance of this heuristic is evaluated using an upper bound generated by solving the associated lagrangian dual problem our analysis suggests that this heuristic provides a tractable and accurate method to determine order quantities and expected profits under substitution we apply this heuristic to examine how the level of demand uncertainty and correlation and the degree of substitution between products affect order quantities and expected profits under substitutable demand in addition we use the heuristic to better understand the mechanism by which substitution improves expected profits

on the relationship between inventory costs and variety benefits in retailassortments consider a category of product variants distinguished by some attribute such as color or flavor a retailer must construct an assortment for the category i e select a subset variants to stock and determine purchase quantities for each offered variant we analyze this problem using a multinomial logit model to describe the consumer choice process and a newsboy model to represent the retailer s inventory cost we show that the optimal assortment has a simple structure and provide insights on how various factors affect the optimal level of assortment variety we also develop a formal definition of the level of fashion in a category using the theory of majorization and examine its implications for category profits

coordinated decisions for substitutable products in a common retailer supply chain abstract this paper studies coordination mechanisms in a supply chain which consists of two suppliers with capacity uncertainties selling differential yet substitutable products through a common retailer who faces price sensitive random demand of these two products we develop in a noncompetitive setting three coordination models revenue sharing return policy and combination of revenue sharing and return policy and contrast them with a basic and uncoordinated model we are able to establish the ordinal relationship among the retailer s ordering and pricing decisions and analytically compare the performances between certain models when two suppliers are identical we find that the retailer s ordering and pricing decisions in the model with return policy in the case of identical suppliers are independent of demand or supply uncertainty our numerical results reveal that the performances of coordination models in the case of nonidentical suppliers resemble those in the case of identical suppliers we find that the retailer will place a larger order quantity in models where her average cost per unit sold is smaller we also find that product substitutability and uncertainties have different effects on chain performances

the cost of domestic energy prices to saudi arabia abstract the issue of subsidies on domestic energy prices has moved up the policy agenda most recently as a result of the g20 commitment in september 2009 to phase out such subsidies however what constitutes a subsidy is complex and controversial the iea in its last world energy outlook claimed that saudi arabia was second in the world in terms of its levels of subsidy on domestic energy prices however because saudi arabia is a price maker in the international oil market the methodology used by the iea is seriously flawed this paper explains the problems with the methodology for computing subsidies and explains the correct method in the case of saudi arabia it then attempts to measure the levels of subsidy in saudi arabia using this methodology however while it converts the iea s subsidy of 23 billion into a net profit of 5 7 billion it goes on to point out that the current low price regime is causing problems for saudi arabia

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

co production processes with random yields in the semiconductor industry a wide variety of manufacturing operations can be characterized as co production with substitutable demand that is there are many situations in which the availability of two or more items are related and because of randomness in either supply or demand it can be advantageous to substitute one of these items for another our research was motivated by the semiconductor industry where chips are produced in large batches because of the presence of randomness in the process individual chips in a given batch can perform differently because some customers have stricter specifications than others chips within the same batch can be classified and sold as different products according to their measurable performance we model the production and inventory problem as a stochastic dynamic program in which the objective is to minimize the costs of meeting contractual obligations after developing heuristic methods of solving the problem in practice we validate them against a lower bound on the cost of an optim

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