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

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

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

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

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

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

optimal investment strategies for flexible resources considering pricing and correlated demands we study the optimal resource investment decision faced by a two product price setting firm that operates in a monopolistic setting and employs a postponed pricing scheme the firm has the option to invest in dedicated resources as well as a more expensive flexible resource that can satisfy both products while the resource investment decision is made under demand uncertainty pricing and resource allocation decisions are postponed to the time when demand curves are realized our analysis provides the structure of the firm s optimal resource investment strategy as a function of demand parameters and investment costs and shows that the flexible resource investment decision follows athreshold policy we also show that it can be optimal for the firm to invest in the flexible resource even when demand patterns are perfectly positively correlated the reason for flexible capacity investment in this case is financial rather than risk pooling on the other hand we show that it can be optimal for the firm not to invest in the flexible resource even when demand patterns are perfectly negatively correlated the flexible resource investment decision in this case depends on the profitability of the two products based on our analysis we provide principles on the firm s optimal resource investment decision

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

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

optimal dynamic pricing and ordering decisions for perishable products abstract in this paper we determine the order quantity and the prices for a perishable product with a multiple period lifetime demands for products of different ages are dependent on the prices of mutually substitutable products the problem for a product with lifetime of two periods is first analyzed and the stochastic dynamic programming model is developed given the inventory level for the old product product of age 2 the expected profit is a concave function of the order quantity the price of the new product product of age 1 and the discounted price of the old product product of age 2 the computational results show that the total profit significantly increases when demand transfers between products of different ages are considered for a product with lifetime of longer than two periods a heuristic based on the optimal solution for a single period problem is proposed for a multiple period problem

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

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

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

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

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

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

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

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

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

choice and individual welfare we propose an abstract method of systematically assigning a rational ranking to non rationalizable choice data our main idea is that any method of ascribing welfare to an individual as a function of choice is subjective and depends on the economist undertaking the analysis we provide a simple example of the type of exercise we propose namely we define an individual welfare functional as a mapping from stochastic choice functions into weak orders a stochastic choice function or choice distribution gives the empirical frequency of choices for any possible opportunity set framing factors may also be incorporated into the model we require that for any two alternatives x and y if our individual welfare functional recommends x over y given two distinct choice distributions then it also recommends x over y for any mixture of the two choice distributions together with some mild technical requirements such an individual welfare functional must weight every opportunity set and assign a utility to each alternative x which is the sum across all opportunity sets of the weighted probability of x being chosen from the set it therefore requires us to have a prior view about how important or representative a choice of x at a given situation is

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

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

experimental methods for the general economist five lessons from the lab i review five primary results from experimental economics that impact the economics profession as a whole these results regard the relative un importance of subject sophistication in laboratory markets the importance of gender on economic outcomes the propensity for humans to behave in less than fully rational ways the importance of trading institutions on economic performance and the behavioral relevance of economic theory i find that economics as a profession has benefited from the use of experimental methods by fostering a dialogue between theorists and empiricists better informing policy and improving data collection techniques

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

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

risk pooling through physical probabilistic selling abstract this paper investigates the impacts of a new type of probabilistic selling p s where the retailer orders specific products and package some as a discounted physical probabilistic product ppp rather than merely a virtual choice we call this p s strategy as physical probabilistic selling p p s the price gap between the specific products and the probabilistic product results in demand reshape i e some customers who originally buy specific products will switch to buying the probabilistic product which decreases aggregate demand uncertainty however the price discount decreases the profit margin considering this trade off we develop a three product newsvendor model to address the question of how to set the price for the ppp and make inventory allocation decisions we prove that there are two effects under p p s namely the risk pooling effect due to demand reshape and the risk diversification effect due to inventory flexibility with demand uncertainty p p s can improve the retailer s profit at lower inventory levels with proper demand reshape induced by the optimal price discount p p s is more profitable with smaller product differentiation higher customer price sensitivity higher demand uncertainty and lower package cost with supply uncertainty we demonstrate through numerical studies that p p s is a viable strategy to combat asymmetrical supply risk that yields higher profits and service levels

setting the right incentives for global planning and operations we study incentive issues seen in a firm performing global planning and manufacturing and local demand management the stochastic demands in local markets are best observed by the regional business units and the firm relies on the business units forecasts for planning of global manufacturing operations we propose a class of performance evaluation schemes that induce the business units to reveal their private demand information truthfully by turning the business units demand revelation game into a potential game with truth telling being a potential maximizer an appealing refinement of nash equilibrium moreover these cooperative performance evaluation schemes satisfy several essential fairness notions after analyzing the characteristics of several performance evaluation schemes in this class we extend our analysis to include the impact of effort on demand

multi period inventory games with information update this paper addresses the multi period inventory game of two substitutable products with learning in which the demand distribution form in each period is known but one or more parameters are unknown in advance the retailers update the estimates of the unknown parameters using the historical demand information as the transaction proceeds at each period the retailers check the initial inventories and update the forecasts about their demands first then they place the orders which are delivered immediately finally the demands are realized and satisfied by the available inventories the unsatisfied demand of one retailer switches to another and is satisfied by the other s left inventory unsatisfied demand is lost and the excess inventories incur a holding cost all the information is common knowledge the objectives of the two retailers are to make proper ordering decisions to maximize their total expected discount profits respectively we model the problem as a dynamic bayesian game with multi dimension state space we give the conditions under which the state space can be reduced we prove the existence and uniqueness of nash equilibrium and show that the equilibrium ordering strategy is the base stock policy the computation of the base stock levels can be reduced to a game with one dimension state space moreover for the case with perishable product the computation of the base stock levels can be reduced to the newsboy game

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