optimal shared savings contracts in supply chains linear contracts and double moral hazard in many supply chains consumption of indirect materials sold by a supplier to a customer for use in her production process can be reduced by efforts exerted by either party since traditional supply contracts provide no incentive for the supplier to exert such effort shared savings contracts have been proposed as a way to improve incentives in the channel leading to more efficient effort choices by the two parties such shared savings contracts typically combine a fixed service fee with a variable component based on consumption volume we formalize this situation using the double moral hazard framework in which both parties decide how much effort to exert by trading off the cost of their effort against the benefits that they will obtain from reduced consumption we also extend the double moral hazard framework to analyze a broader class of cost of effort functions than considered so far including the linear cost of effort functions commonly found in practice we show that the supplier can still always induce the optimal second best equilibrium with a linear shared savings contract under this broader class of functions however the behavior of the optimal contract as a function of the problem parameters becomes more complex we illustrate how small changes in the problem parameters can turn profits from being a well behaved to a poorly behaved function of the contract and provide some theoretical characterization of this phenomenon the practical significance of this is that simple linear contracts are sufficient in many double moral hazard contexts even for the broader class of functions we consider but care must be taken in selecting the optimal contract parameters

optimal pricing and return policies for perishable commodities this paper considers the pricing decision faced by a producer of a commodity with a short shelf or demand life a hierarchical model is developed and the results of the single period inventory model are used to examine possible pricing and return policies the paper shows that several such policies currently in effect are suboptimal these include those where the manufacturer offers retailers full credit for all unsold goods or where no returns of unsold goods are permitted the paper also demonstrates that a policy whereby a manufacturer offers retailers full credit for a partial return of goods may achieve channel coordination but that the optimal return allowance will be a function of retailer demand therefore such a policy cannot be optimal in a multi retailer environment it is proven however that a pricing and return policy in which a manufacturer offers retailers a partial credit for all unsold goods can achieve channel coordination in a multi retailer environment this article was originally published in marketing science volume 4 issue 2 pages 166 176 in 1985

inequality aversion and the natural rate of subjective inequality abstract this paper analyzes inequality aversion across countries and identifies factors which explain the empirical heterogeneity observed across these countries we do this by hypothesizing a natural rate of subjective inequality across countries and solving for the explicit country specific value of the inequality aversion parameter that is consistent with the hypothesized natural rate we present evidence consistent with the existence of a natural rate of subjective inequality by verifying that countries with low high tolerance for inequality have low high inequality as measured by the gini coefficient as well finally we explore the socio economic factors that are consistent with observed differences in inequality aversion across these countries finding important effects of female empowerment public education expenditures per capita income economic growth and population size

sluggish price adjustments and the link between money and price the simple quantity theory of money asserts that because the velocity of money and fullemployment output are constants if the money supply doubles the price level must also double 15 this view of the quantity theory of money is also supported by the policy ineffectiveness proposition put forward by lucas 16 sargent and wallace 20 and barro 1 the policy ineffectiveness proposition asserts that real variables like output and unemployment respond only to unanticipated movements in the money supply but do not respond to anticipated money supply associated with the systematic feedback rules one of the premises essential to the validity of this proposition is the perfect flexibility of prices the corollary of the policy ineffectiveness proposition as expounded by gordon 12 in invalidating this propositin is that because output does not respond to anticipated money supply changes and remains at the natural level the price level responds contemporaneously and proportionately to the anticipated changes in the money supply this conclusion is also consistent with barro s hypothesis that perceived movements in the money stock imply equiproportionate contemporaneous movements in the price level 3 565 66 this one to one relationship between the anticipated money supply and the price level has also been shown theoretically by barro 1 and hercowitz 13 it is this conclusion that needs to be tested by accounting for the speed of adjustments of prices the purpose of this study is to explore theoretically and empirically the link between money supply and price levels by incorporating a gradual price adjustment mechanism more specifically this study examines a the one to one relationship between the log of current money stock and the log of the price level purported by barro 3 b effects of unanticipated money growth on the aggregate price and c importance of anticipated money growth in determining the price level given the current money stock and the current and lagged values of the unanticipated money growth the key element of the study is the realization that the economy is comprised of markets with differing degrees of price adjustments numerous cases of price stickiness can be identified in modern economies as enumerated in survey work by blinder 4 also for instance devadoss and choi 6 observe that the u s agricultural program s price fixing policies such as price

managing a noncooperative supply chain with limited capacity we consider a two stage serial supply chain with capacity limits where each installation is operated by managers attempting to minimize their own costs a multiple period model is necessitated by the multiple stages capacity limits stochastic demand and the explicit consideration of inventories with appropriate salvage value functions a markov equilibrium policy is found intuitive profit dominance allows for existence of a unique equilibrium solution which is shown to be a modified echelon base stock policy this equilibrium policy structure is sustained in the infinite horizon a numerical study compares the behavior of the decentralized system with the first best integrated capacitated system the performance of this decentralized system relative to the integrated system across other parameters can be very good over a broad range of values this implies that an acceptable system performance may be attained without the imposition of a contract or other coordinating mechanism which themselves may encounter difficulties in implementation in the form of negotiation execution or enforcement of these agreements we find instances where tighter capacities may actually enhance channel efficiency we also examine the effect of capacity utilization on the system suboptimality

price inertia money supply and price changes price stickiness is incorporated in the partial information localizedmarket framework of rational expectation models to show that the money stock has less than an equiproportionate effect on the aggregate price and that the unanticipated monetary policy component has differing impacts on prices at the market level the empirical analysis involves estimation of generated regressor models of money forecasting and price equations using the computationally intensive parametric bootstrap method developed most recently by smith and mcaleer the results are unfavourable to the hypothesis of a one to one relationship between current money stock and prices rather they lend distinct support to conclusions of a sluggish price adjustment model that money stock has less than equiproportionate effect on prices empirical results also show that the effects of unanticipated money growth on prices vary across markets

serial supply chains with economies of scale bounds and approximations we consider two models of stochastic serial inventory systems with economies of scale for which the forms of optimal policies are known in the first model each stage has a fixed order quantity while in the second model there is a fixed order cost for external supplies for each model we show that the optimal policy parameters can be bounded and approximated by a series of independent single stage optimal policy parameters we further construct closed form bounds and approximations for the single stage solutions and apply them to the serial systems these results provide simple and effective solutions that will help to facilitate implementations in practice they also allow us to see the connections between the serial and single stage systems and sharpen our intuition on optimal policy parameters and system behavior

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

on markov equilibria in dynamic inventory competition we provide a review of the types of equilibria typically found in operations management inventory papers and a discussion on when the commonly used stationary infinite horizon open loop equilibrium may be sufficient for study we focus particularly on order up to and basestock equilibria in the context of inventory duopolies we give conditions under which the stationary infinite horizon equilibrium is also a markov perfect closed loop equilibrium these conditions are then applied to three specific duopolies the first application is one with stockout based substitution where the firms face independent direct demand but some fraction of a firm s lost sales will switch to the other firm the second application is one where shelf space display stimulates primary demand and reduces demand for the other firm s product the final application is one where the state variables represent goodwill rather than inventory these specific problems have been previously studied in both the single period and or stationary infinite horizon open loop settings but not in markov perfect closed loop settings under the markov perfect setting a variety of interesting dynamics may occur including that there may be a so called commitment value to inventory

stock wars inventory competition in a two echelon supply chain with multiple retailers this paper studies the competitive and cooperative selection of inventory policies in a two echelon supply chain with one supplier andn retailers stochastic demand is monitored continuously retailers incur inventory holding and backorder penalty costs the supplier incurs holding costs for its inventory and backorder penalty costs for backorders at the retailers the latter cost reflects the supplier s desire to maintain adequate availability of its product to consumers previous research finds the supply chain cost minimizing reorder point policies the cooperative solution the competitive solution is a nash equilibrium a set of reorder points such that no firm can deviate from the equilibrium and lower its cost it is shown that nash equilibria exist and a method is presented to find all of them in some settings the cooperative solution is a nash equilibrium competition does not necessarily lead to supply chain inefficiency in other settings competition leads to costs that are substantially higher than optimal usually but not always the competitive supply chain carries too little inventory three cooperation strategies are discussed change incentives change equilibrium and change control a set of contracts is provided that changes the firms incentives so that the optimal policy is a nash equilibrium an equilibrium change can improve performance but does not guarantee optimal performance to change control the firms let the supplier choose all reorder points a key component in vendor managed inventory that change leads to optimal supply chain performance

inventory management under market size dynamics we investigate the situation where a customer experiencing an inventory stockout at a retailer potentially leaves the firm s market in classical inventory theory a unit stockout penalty cost has been used as a surrogate to mimic the economic effect of such a departure in this study we explicitly represent this aspect of consumer behavior incorporating the diminishing effect of the consumers leaving the market upon the stochastic demand distribution in a time dynamic context the initial model considers a single firm we allow for consumer forgiveness where customers may flow back to the committed purchasing market from a nonpurchasing latent market the per period decisions include a marketing mix to attract latent and new consumers to the committed market and the setting of inventory levels we establish conditions under which the firm optimally operates a base stock inventory policy the subsequent two models consider a duopoly where the potential market for a firm is now the committed market of

an approach for developing an optimal discount pricing policy this paper addresses the problem of why and how a seller should develop a discount pricing structure even if such a pricing structure does not alter ultimate demand the situation modeled is most appropriate where the seller s product does not represent a major component of the buyer s final product where the demand for the product is derived or where the price is only one of many factors considered in making a purchase decision a model of buyer reaction to any given pricing scheme is developed to show that there exists a unified pricing policy which motivates the buyer to increase its ordering quantity per order thereby reducing the joint buyer and seller ordering and holding costs as a result the seller is able to reduce its costs while leaving the buyer no worse off and often better off the model is extended to handle variable ordering and shipping costs and situations where the seller faces numerous groups of buyers each having different ordering policies finally a case study is presented explicitly showing how the proposed pricing policy can be applied to the situation of a large seller selling to a number of different buyer groups

coalition formation problem for sourcing contract design in supply networks abstract this article studies a coalition formation problem for cooperative replenishment with a single supplier and multiple firms we consider that a vertical cooperation between the supplier and the set of firms is already set using periodic individual contracts and we investigate the profitability of a horizontal cooperation between firms when designing collaborative contracts given the significant savings that can be realized thanks to horizontal collaboration the main interest of the potential collaborating firms is to figure out how the collaborating group should be formed and how stable alliances and coalitions should be generated in this article the two questions are studied in two business situations focusing either on the collaboration opportunities in the ordering or the transportation process in each collaborative situation a decision making approach is applied to assess the expected profitability of each firm and to determine if firms should form coalitions to maximize their profits an exact solution method based on a game theoretic approach is developed called cooperative replenishment algorithm cra which generates core stable coalitions for cost savings regarding all partner standpoints an analytical study of stability conditions regarding the ordering and transportation cost structures were performed to enhance the cra resolution procedure extensive experiments based on realistic instances are provided to validate the performance of the cra proposed in terms of solution stability and convergence the computational results also confirm the potential benefit of horizontal collaboration between firms in terms of profit maximization compared to the stand alone situation

statistical learning of service dependent demand in a multiperiod newsvendor setting we study an inventory system wherein a customer may leave the seller s market after experiencing an inventory stockout traditionally researchers and practitioners assume a single penalty cost to model this customer behavior of stockout aversion recently a stream of researchers explicitly model this customer behavior and support the traditional penalty cost approach we enrich this literature by studying the statistical learning of service dependent demand we build and solve four models a baseline model where the seller can observe the demand distribution a second model where the seller cannot observe the demand distribution but statistically learns the demand distribution a third model where the seller can learn or pay to obtain the exact information of the demand distribution and a fourth model where demand in excess of available inventory is lost and unobserved interestingly we find that all four models support the traditional penalty cost approach this result confirms the use of a state independent stockout penalty cost in the presence of demand learning more strikingly the first three models imply the same stockout penalty cost which is larger than the stockout penalty cost implied by the last model

supply chain coordination with multiple shipments the optimal inventory subsidizing contracts we study a supply chain involving a supplier retailer relationship when production lead time is long and the selling season is short the retailer has to place an order ahead of the season which resembles the classical newsvendor model however we consider the situation when the supplier agrees to deliver the order in multiple shipments in the season and then the retailer needs to determine the quantity and or timing of each shipment under a centralized setting we derive the optimal quantity and or timing decisions of the retailer under a decentralized setting incentive misalignment arises from ineffective allocation of inventory costs between the parties in addition to the well known double marginalization effect hence we devise an incentive contract which involves a risk sharing mechanism at the end of the season and an inventory subsidizing scheme for the entire season in practice the inventory subsidizing scheme can be implemented in different ways such as a direct subsidizing scheme o

factor price stabilization and the competitive firm this paper investigates the effects of factor price stabilization on production decisions of the competitive firm with ex post production flexibility factor price stabilization is achieved through changes in the guaranteed minimum price and the imposed maximum price for the risk averse firm the effect of factor price stabilization through a mean preserving contraction on capital crucially depends on whether capital and the variable input are substitutes or complements as well as the observable characteristics of the variable input demand curve

the reference effects on a retailer s dynamic pricing and inventory strategies with strategic consumers we consider a retailer that sells the same or different versions of the product season after season at the beginning of each season stage 1 the retailer places an order and sells the product at the full price as the sales unfold the retailer has an opportunity to mark down the price stage 2 which creates an incentive for strategic consumers to delay their purchases for price discount however consumers do not know the markdown price exactly when they time their purchases instead they learn from the retailer s past prices and form their estimate of the markdown price called the reference price to decide if they purchase at the full price or wait for the markdown in the current selling season we characterize the properties of the optimal ordering and markdown decisions and show that markdowns if adopted appropriately do not necessarily destroy the stability of a business even in the presence of strategic consumers furthermore the consumers reference exhibits a mean reverting pattern under certain conditions that is the reference fluctuates around a mean value reflecting the practice of most stable businesses we conduct numerical studies to investigate the impact of consumer learning about the reference price and various system parameters on the retailer s optimal strategies and profitability in the presence of strategic consumers

a new index of income inequality the b measure abstract this paper presents a new measure of income inequality that allows more weight to be given to inequality in the lower end of the income graduation the measure is non parametric and based only on the underlying lorenz curve

lower bounds for multi echelon stochastic inventory systems we establish lower bounds on the minimum cost of managing certain production distribution networks with setup costs at all stages and stochastic demands these networks include serial assembly and one warehouse multi retailer systems we obtain the bounds through novel cost allocation schemes we evaluate the bounds performance for one warehouse multi retailer systems by comparing them with simple heuristic policies the bounds are quite tight for systems with a small number of retailers we also present simplified proof of known optimality results for serial and assembly systems

joint inventory and markdown management for perishable goods with strategic consumer behavior in this paper we formulate and analyze a novel model on a firm s dynamic inventory and markdown decisions for perishable goods we consider a dynamic stochastic setting where every period consists of two phases clearance phase and regular sales phase in the clearance phase the firm decides how much to order for regular sales as well as whether to markdown some or all of the leftover inventory from the previous period that will be disposed otherwise since strategic consumers may buy the product during clearance sales for future consumption markdown may cannibalize future sales at regular price hence the firm needs to make a trade off between product spoilage and intertemporal demand substitution we show that the firm should either put all of the leftover inventory on discount or dispose all of it and the choice depends on the amount of leftover inventory from the previous period in particular the firm should introduce markdown when the amount of leftover inventory is higher than a certain th

non cooperative and cooperative game theoretic models for usage based lease contracts abstract in this paper we study game theoretic models for lease contracts by which the owner lessor rents a piece of equipment to a user lessee the lessee decides on the optimal lease period and usage rate and the lessor is responsible for developing a maintenance policy for the equipment two non cooperative game theoretic models and a cooperative model are developed to describe the relationships between the two decision makers in the non cooperative simultaneous move game the lessee and the lessor act simultaneously and independently to make their decisions in the leader follower non cooperative game the lessor is the leader who specifies the maintenance policy first and the lessee as the follower decides on the lease period and usage rate accordingly for these two games the nash and stackelberg equilibria are obtained respectively for the cooperative game we derive the solution targeting on total profit maximization and show that this solution can be implemented as an equilibrium using a nonlinear transfer payment contract besides we compare the nash equilibrium stackelberg equilibrium and the total maximum solution to each other and our results show that the lessee and lessor can gain more profit from the cooperative contract than from the non cooperative alternatives numerical examples are provided to demonstrate the different solution methodologies and the value of cooperation

coordination mechanisms of supply chain systems supply chain management scm has become an important management paradigm as supply chain members are often separate and independent economic entities a key issue in scm is to develop mechanisms that can align their objectives and coordinate their activities so as to optimize system performance in this paper we provide a review of coordination mechanisms of supply chain systems in a framework that is based on supply chain decision structure and nature of demand this framework highlights the behavioral aspects and information need in the coordination of a supply chain the identification of these issues points out several directions of future research in this area

competitive and cooperative inventory policies in a two stage supply chain we investigate a two stage serial supply chain with stationary stochastic demand and fixed transportation times inventory holding costs are charged at each stage and each stage may incur a consumer backorder penalty cost e g the upper stage the supplier may dislike backorders at the lower stage the retailer we consider two games in both the stages independently choose base stock policies to minimize their costs the games differ in how the firms track their inventory levels in one the firms are committed to tracking echelon inventory in the other they track local inventory we compare the policies chosen under this competitive regime to those selected to minimize total supply chain costs i e the optimal solution we show that the games nearly always have a unique nash equilibrium and it differs from the optimal solution hence competition reduces efficiency furthermore the two games equilibria are different so the tracking method influences strategic behavior we show that the system optimal solution can be achieved as a nash equilibrium using simple linear transfer payments the value of cooperation is context specific in some settings competition increases total cost by only a fraction of a percent whereas in other settings the cost increase is enormous we also discuss stackelberg equilibria

dynamic capacity allocation to customers who remember past service we study the problem faced by a supplier deciding how to dynamically allocate limited capacity among a portfolio of customers who remember the fill rates provided to them in the past a customer s order quantity is positively correlated with past fill rates customers differ from one another in their contribution margins their sensitivities to the past and in their demand volatilities by analyzing and comparing policies that ignore goodwill with ones that account for it we investigate when and how customer memory effects impact supplier profits we develop an approximate dynamic programming policy that dynamically rationalizes the fill rates the firm provides to each customer this policy achieves higher rewards than margin greedy and lagrangian policies and yields insights into how a supplier can effectively manage customer memories to its advantage this paper was accepted by martin lariviere operations management

promised lead time contracts under asymmetric information we study the important problem of how a supplier should optimally share the consequences of demand uncertainty i e the cost of inventory excesses and shortages with a retailer in a two level supply chain facing a finite planning horizon in particular we characterize a multiperiod contract form the promised lead time contract that reduces the supplier s risk from demand uncertainty and the retailer s risk from uncertain inventory availability under the contract terms the supplier guarantees on time delivery of complete orders of any size after the promised lead time we characterize the optimal promised lead time and the corresponding payments that the supplier should offer to minimize her expected inventory cost while ensuring the retailer s participation in such a supply chain the retailer often holds private information about his shortage cost or his service level to end customers hence to understand the impact of the promised lead time contract on the supplier s and the retailer s performance we study the system under local control with full information and local control with asymmetric information by comparing the results under these information scenarios to those under a centrally controlled system we provide insights into stock positioning and inventory risk sharing we quantify for example how much and when the supplier and the retailer overinvest in inventory as compared to the centrally controlled supply chain we show that the supplier faces more inventory risk when the retailer has private service level information we also show that a supplier located closer to the retailer is affected less by information asymmetry next we characterize when the supplier should optimally choose not to sign a promised lead time contract and consider doing business under other settings in particular we establish the optimality of a cutoff level policy finally under both full and asymmetric service level information we characterize conditions when optimal promised lead times take extreme values of the feasible set yielding the supplier to assume all or none of the inventory risk hence the name all or nothing solution we conclude with numerical examples demonstrating our results

newsvendor bounds and heuristic for optimal policies in serial supply chains we consider the classicn stage serial supply systems with linear costs and stationary random demands there are deterministic transportation leadtimes between stages and unsatisfied demands are backlogged the optimal inventory policy for this system is known to be an echelon base stock policy which can be computed through minimizingn nested convex functions recursively to identify the key determinants of the optimal policy we develop a simple and surprisingly good heuristic this method minimizes 2 n separate newsvendor type cost functions each of which uses the original problem data only these functions are lower and upper bounds for the echelon cost functions their minimizers form bounds for the optimal echelon base stock levels the heuristic is the simple average of the solution bounds in extensive numerical experiments the average relative error of the heuristic is 0 24 with the maximum error less than 1 5 the bounds and the heuristic which can be easily obtained by simple spreadsheet calculations enhance the accessibility and implementability of the multiechelon inventory theory more importantly the closed form expressions provide an analytical tool for us to gain insights into issues such as system bottlenecks effects of system parameters and coordination mechanisms in decentralized systems

decentralizing cross functional decisions coordination through internal markets a firm faces many problems that are inherently cross functional to solve them successfully requires the coordinated actions of many functional representatives acting in a decentralized setting functional managers however respond to their own individual incentives and may consequently fail to maximize the overall profits of the firm we examine this issue in a setting in which the output of early actions limits the range of later actions and we propose an incentive scheme that allows the system to be successfully decentralized our mechanism is based on linear transfer prices for the intermediate output that are implemented through an internal market a market maker buys the output from one function and sells it to another she is not obliged to sell at the same price at which she bought and may set prices solely to provide incentives we illustrate the flexibility of the scheme by applying it to several models in the operations management literature

gaining more by stocking less a competitive analysis of product availability the price competition between two firms can affect their decisions about product availability with occasional stockouts a firm loses from foregone sales yet it may indirectly benefit from the higher price a competitor is able to charge the more prone customers are to search elsewhere for the product upon encountering a stockout the greater is the gain from the reduced price competition between firms this paper establishes conditions whereby the strategic interaction of reduced price competition between firms outweighs the loss from foregone sales in such cases a firm can increase its expected profits by choosing to stock less these results provide a competitive rationale for the high stockout levels observed in some retail situations and have implications for the analysis of product availability in public policy settings

decentralized inventory control in a two component assembly system abstract we investigate a two component assembly system facing stationary stochastic demand with constant component replenishment lead times holding cost are charged for each component inventory which are managed by component suppliers final product demand is backordered when cannot be fulfilled in time and a penalty cost is charged we assume the long lead time component supplier takes normal base stock policy while the short lead time component supplier takes a modified base stock policy static game and stackelberg games are considered equilibria are analyzed and the cost in equilibria are compared with the system optimal solution difference shows the deterioration of system performance caused by decentralized inventory control we try to design a mechanism to coordinate the decentralized system that is to make decentralized system perform as well as system optimal solution though the decisions separated we show that a liner transfer based on the backorder between the component suppliers qualifies this task

inventory dynamics and supply chain coordination this paper extends the theory of supply chain incentive contracts from the static newsvendor framework of the existing literature to the simplest dynamic setting a manufacturer distributes a product through retailers who compete on both price and fill rates we show that inventory durability is the key factor in determining the underlying nature of incentive distortions and their contractual resolutions when the product is highly perishable retailers are biased toward excessive price competition and inadequate inventories vertical price floors or inventory buybacks subsidies for unsold inventory can coordinate incentives in both pricing and inventory decisions when the product is less perishable the distortion is reversed and vertical price ceilings or inventory penalties can coordinate incentives

competition and cooperation in a two stage supply chain with demand forecasts we consider a serial supply chain with one supplier and one retailer each obtains some demand forecast information which may be shared or not we investigate the members benefits from sharing information the forecasts follow a variant of the martingale model of forecast evolution mmfe we construct a simple transfer payment scheme to align the players incentives with that of the overall system the main finding is that unless the players incentives are aligned in this way sharing information makes little sense it might hurt one or the other player and the system as a whole

competition for procurement contracts with service guarantees we consider a market with two suppliers and a set of buyers in search of procurement contracts with one of the suppliers in particular each buyer needs to process a certain volume of work and each supplier s ability to process the customers requests is constrained by a production capacity the procurement contracts include guarantees that the products will be available when needed and the buyers select a supplier based on their service delivery offers the suppliers are modeled as make to stock queues and compete for the buyers business the main objective of this paper is to determine how the procurement contracts are established between buyers and suppliers because each buyer selects a single supplier to establish the sourcing relationship the game fails to have a pure strategy nash equilibrium instead an equilibrium is defined as the limit equilibrium of some discrete action games

the role of inventory in delivery time competition the paper operationalizes the notion of shortage cost by considering the behavior of customers and competing firms and examines the role of inventory in response time competition we start with a single firm production control model in which customers are characterized by their preferences of price quality and delivery time the optimal production inventory policy and the optimal choice between make to order and make to stock operations are determined in simple newsboy like formulas the basic model is then extended to an n firm market game in which firms compete for orders from the aspect of early delivery one could think of this setting as an oligopoly racing market the analysis shows that competition can breed a demand for produce to stock just as other economic phenomena such as economies of scale uncertainty or seasonality can induce make to stock and that delivery time competition increases the buyer s welfare while decreasing the producer s welfare

nash game model for optimizing market strategies configuration of platform products in a vendor managed inventory vmi supply chain for a product family this paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies platform product configuration and inventory policies in a vmi vendor managed inventory supply chain the manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers multiple types of products are substitutable each other to end customers the manufacturer makes its decision on raw materials procurement platform product configuration product replenishment policies to retailers with vmi price discount rate and advertising investment to maximize its profit retailers in turn consider the optimal local advertising investments and retail prices to maximize their profits this problem is modeled as a dual simultaneous non cooperative game as a dual nash game model with two sub games one is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers this paper combines analytical iterative and ga genetic algorithm methods to develop a game solution algorithm to find the nash equilibrium a numerical example is conducted to test the proposed model and algorithm and gain managerial implications

supply contracts with financial hedging we study the performance of a stylized supply chain where two firms a retailer and a producer compete in a stackelberg game the retailer purchases a single product from the producer and afterward sells it in the retail market at a stochastic clearance price the retailer however is budget constrained and is therefore limited in the number of units that he may purchase from the producer we also assume that the retailer s profit depends in part on the realized path or terminal value of some observable stochastic process we interpret this process as a financial process such as a foreign exchange rate or interest rate more generally the process can be interpreted as any relevant economic index we consider a variation the flexible contract of the traditional wholesale price contract that is offered by the producer to the retailer under this flexible contract at t 0 the producer offers a menu of wholesale prices to the retailer one for each realization of the financial process up to a future time the retailer then commits to purchasing at time a variable number of units with the specific quantity depending on the realization of the process up to time because of the retailer s budget constraint the supply chain might be more profitable if the retailer was able to shift some of the budget from states where the constraint is not binding to states where it is binding we therefore consider a variation of the flexible contract where we assume that the retailer is able to trade dynamically between zero and in the financial market we refer to this variation as the flexible contract with hedging we compare the decentralized competitive solution for the two contracts with the solutions obtained by a central planner we also compare the supply chain s performance across the two contracts we find for example that the producer always prefers the flexible contract with hedging to the flexible contract without hedging depending on model parameters however the retailer might or might not prefer the flexible contract with hedging

modeling the role of retail price formats and retailer competition types on production schedule strategy abstract to study the determinants of choice between make to order mto and make to stock mts production scientists have traditionally focused on production specific factors however the choice can be also influenced by marketing specific factors such as the pricing strategy of retailers this paper therefore develops a modeling framework to link the determination of the optimal production strategy of mts mto to the retailing strategy of edlp hilo we characterize an optimal production strategy as one that maximizes total system wide profits in a centralized system we show that the optimum production strategy would depend on whether the manufacturer is delivering to an every day low pricing edlp store or to a high low pricing store hi lo additionally the production plan is demonstrated to be a function of the nature and type of competition in the market in particular we study the duopoly model of competition under both bertrand and stackelberg conjectures

asymmetric consumer learning and inventory competition we develop a model of consumer learning and choice behavior in response to uncertain service in the marketplace learning could be asymmetric that is consumers may associate different weights with positive and negative experiences under this consumer model we characterize the steady state distribution of demand for retailers given that each retailer holds a constant in stock service level we then consider a noncooperative game in steady state between two retailers competing on the basis of their service levels the demand distributions of retailers in this game are modeled using a multiplicative aggregate market share model in which the mean demands are obtained from the steady state results for individual purchases but the model is simplified in other respects for tractability our model yields a unique pure strategy nash equilibrium we show that asymmetry in consumer learning has a significant impact on the optimal service levels market shares and profits of the retailers when retailers have different costs it also determines the extent of competitive advantage enjoyed by the lower cost retailer

vertical contracts in a supply chain and the bullwhip effect this paper shows that decentralized supply chains in which upstream firms use linear wholesale prices may experience lower upstream production and downstream sales volatility than vertically inte

on manufacturing marketing incentives stereotypically marketing is mainly concerned about satisfying customers and manufacturing is mainly interested in factory efficiency using the principal agent agency paradigm which assumes that the marketing and manufacturing managers of the firm will act in their self interest we seek incentive plans that will induce those managers to act so that the owner of the firm can attain as much as possible of the residual returns one optimal incentive plan can be interpreted as follows the owner subcontracts to pay the manufacturing manager a fixed rate for all capacity he delivers each marketing manager receives all of the returns from his product in turn all managers pay a fixed fee to the owner under this plan the marketing managers will often complain about the stock level decisions even though these levels are announced in advance under a revised plan the owner can eliminate such complaints by delegating the stocking decisions to the respective marketing managers without any loss this plan is interpreted as requiring the owner to make a futures market for manufacturing capacity paying the manufacturing manager the expected marginal value for each unit of capacity delivered receiving the realized marginal value from the marketing managers and losing money on average in the process

ranking income distributions using the geometric mean and a related general measure this paper illustrates the usefulness of a generalized welfare measure for ranking income distributions that are unordered by stochastic dominance and illuminates the properties of the measure other welfare criteria such as the arithmetic mean and rawls criteria are special cases of this generalized measure this generalized welfare measure illustrates that use of these special cases involves a subjective judgment by the observer of the relative importance of equity preference to efficiency preference

coordination mechanisms in decentralized serial inventory systems with batch ordering this paper studies a periodic review serial supply chain in which materials are ordered and shipped according to r nq policies three information scenarios are considered depending on the level of information available echelon local and quasilocal in the echelon scenario each stage can access the inventory and cost information within its echelon comprising the stage itself and all downstream stages in the local scenario each stage only accesses its own local information finally in the quasilocal scenario each stage knows its local information plus the actual customer demands we propose coordination schemes that regulate the stages to achieve the supply chain s optimal cost under each information setting all these coordination schemes fit comfortably within an emerging practice called supply chain finance which includes the organization and technology needed to implement them

supplier manufacturer coordination in capacitated two stage supply chains abstract manufacture to order is an increasingly popular strategy in commodity electronics and other similar markets where many different product configurations can be produced from common components to succeed in this environment manufacturers need to keep both cost and order fulfillment time low in this article we compare three different mechanisms that a manufacturer whose revenues depend on order delays may use to affect its component supplier s inventory decisions these mechanisms are specifying components inventory level offering a share of the earned revenues to the supplier called simple revenue sharing and offering a two part revenue sharing scheme we show that whereas the first two approaches do not lead to supply chain coordination the two part scheme does we demonstrate with numerical experiments that up to a point the component supplier benefits from having a high utilization of its production facility whereas the manufacturer benefits from having excess production capacity

side payment contracts in two person nonzero sum supply chain games review discussion and applications this paper investigates supply chain coordination with side payment contracts we first summarize specific side payment contracts and present our review on the literature that developed general side payment schemes to coordinate supply chains following our review we discuss two criteria that a proper side payment contract must satisfy and accordingly introduce a decision dependent transfer payment function and a constant transfer term we present the condition that the transfer function must satisfy and use nash arbitration scheme and shapley value to compute the constant transfer term and derive its closed form solution next we provide a five step procedure for the development of side payment contract and apply it to four supply chain games cournot and bertrand games a two retailer supply chain game with substitutable products and a one supplier one retailer supply chain more specifically for the cournot game we construct a linear transfer function and a constant side payment to coordinate two producers for the bertrand game we build a nonlinear transfer function which is equivalent to a revenue sharing contract and show that the constant term is zero and two firms in the game equally share the system wide profit for a supply chain with substitutable products we present a side payment contract to coordinate two retailers for a two echelon supply chain we develop a proper side payment scheme that can coordinate the supply chain and also help reduce the impact of forward buying on supply chain performance

newsvendor competition under asymmetric cost information abstract we study the newsboy duopoly problem under asymmetric cost information we extend the lippman and mccardle 1997 of competitive newsboy to the case where the two firms are privately informed about their unit costs the market demand is initially split between two firms and the excess demand for each firm is reallocated to the rival firm we show the existence and uniqueness of a pure strategy equilibrium and characterize its structure the equilibrium conditions have an interesting recursive structure that enables an easy computation of the equilibrium order quantities presence of strategic interactions creates incentives to increase order quantities for all firm types except the type that has the highest possible unit cost consequently competition leads to higher total inventory in the industry however contrary to intuition this is only true when the firms are non identical a firm s equilibrium order quantity increases with a stochastic increase in the total industry demand or with an increase in his initial allocation of the total industry demand we demonstrate our model and results in an application in a dual sourcing procurement setting using data that obtained from a large manufacturing company finally we provide a full characterization of the equilibrium of the game for the special case of uniform demand and linear market shares

on continuous time optimal advertising under s shaped response continuous time monopolistic models of advertising expenditure that rely on strict response concavity have been shown to prescribe eventual spending at a constant rate however analyses of discrete analogs have suggested thats shaped response convexity for low expenditure levels may allow for the periodic optima encountered in actual practice casting the dynamic between advertising and sales in a common format an autonomous first order relationship the present paper explores extensions along three dimensions an s shaped response function the value of the discount rate and the possibility of diffusion like response supplementing the treatment by mahajan and muller 1986 a flexible class of s shaped response models is formulated for which it is demonstrated that in contrast to findings in the literature on discretized advertising models continuous periodic optima cannot be supported further a set of conditions on the advertising response function are derived that contains and extends that suggested by sasieni 1971 collectively these results both suggest a set of baseline properties that reasonable models should possess and cast doubt on the ability of first order models to capture effects of known managerial relevance

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

backorder penalty cost coefficient b what could it be abstract the classical economic order quantity eoq model with planned penalized backorders pb relies on postulating a value for the backorder penalty cost coefficient b which is supposed to reflect the intangible adverse effect of the future loss of customer goodwill following a stockout recognizing that the effect of the future loss of customer goodwill should be not a direct penalty cost but a change in future demand schwartz 1966 a new approach to stockout penalties management science 12 12 b538 b544 modified the classical eoq pb model by eliminating the backorder penalty cost term from the objective function and assuming that the long run demand rate is a decreasing strictly convex function of the customer s disappointment factor defined as the complement of the demand fill rate following a stockout which in turn is an increasing strictly convex function of the demand fill rate he called the new model a perturbed demand pd model schwartz provided convincing justification for his pd model and presented several variations of it in a follow up paper but he did not solve any of these models in this paper we solve schwartz s original pd model and its variations and we discuss the implications of their solutions thus filling a gap in the literature left by schwartz moreover having been convinced that schwartz s approach is more valid than the classical approach for representing the effect of the loss of customer goodwill following a stockout but also recognizing that the classical approach is far more popular than the pd approach because of its simplicity and because of tradition we use the solution of the pd model to infer the value of b in the classical model thus providing one possible answer to the question what could b be a noteworthy implication of the solution of schwartz s original pd model is that the optimal fill rate is always 0 or 1 rendering the inferred value of b in the classical model 0 or respectively suspecting that the property of the pd function which is most likely responsible for producing this bang bang type of result is strict convexity we show that for the case where the pd function is proportional to an integer power say n of the fill rate the optimal fill rate is always 0 or 1 if and only if n 1 in which case the pd function is strictly convex in the fill rate

supply chain choice on the internet internet companies extensively use the practice of drop shipping where the wholesaler stocks and owns the inventory and ships products directly to customers at retailers request under the drop shipping arrangement the supply chain benefits from risk pooling because the inventory for multiple retailers is stocked at the same location the wholesalers another more traditional channel alternative on the internet is one in which retailers stock and own the inventory these two supply chain structures which predominate on the internet result in different inventory risk allocation stocking decisions and profits for channel members moreover the two channel alternatives can be combined into a dual strategy whereby the retailer uses local inventory as a primary source and relies on drop shipping as a backup we model the dual strategy as a noncooperative game among the retailers and the wholesaler analyze it and obtain insights into the structural properties of the equilibrium solution to facilitate development of recommendations for practicing managers finally we characterize situations in which each of three channels is preferable by specifying appropriate ranges of critical parameters including demand variability the number of retailers in the channel wholesale prices and transportation costs

effects of sourcing structure on performance in a multiple product assemble to order supply chain abstract this paper addresses the strategic pricing decisions of a decentralized assemble to order system and the effects of sourcing structure on system performance we consider an assemble to order system consisting of two substitute products and three components manufactured by different suppliers demand for the products is price sensitive the selling prices for the products are jointly determined by firms in the system we study the system under both centralized and decentralized decision making situations for the centralized system we demonstrate that there exists a unique optimal pricing solution for the decentralized system we show that there exists a unique nash equilibrium in the players pricing game we further analyze the effects of different sourcing structures on the system performance and the assembler s performance we find that reduction of suppliers in the system does not guarantee improvement of system performance different sourcing structures have different impacts on performance when the two dedicated components are sourced from a single supplier and the common component is sourced from another independent supplier the system and the assembler s performance become worse we show that the decentralized system can be effectively coordinated and the system performance can be improved with a simple profit sharing contract finally we provide comprehensive numerical examples to demonstrate some important managerial insights

inventory sharing and rationing in decentralized dealer networks an increasing number of manufacturers have started to pursue a strategy that promotes inventory sharing among the dealers in their distribution network in this paper we analyze a decentralized dealer network in which each independent dealer is given the flexibility to share his inventory we model inventory sharing as a multiple demand classes problem in which each dealer faces his own customer demand with high priority and inventory sharing requests from other dealers with low priority assuming that each dealer uses a base stock and threshold rationing policy for his inventory stocking and inventory sharing decisions we explicitly model the interactions between the dealers through inventory sharing and obtain aclosed form cost function for each dealer based on the steady state distribution of the inventory levels at the two dealers we then provide a detailed supermodularity analysis of the inventory sharing and inventory rationing game in which each dealer has a two dimensional strategy set stocking level and rationing level we show that the full sharing game in which dealers precommit to sharing all of their on hand inventory and the fixed sharing level game in which dealers precommit to sharing a portion of their on hand inventory are supermodular and thus a pure strategy nash equilibrium is guaranteed to exist for the rationing game in which dealers precommit to their stocking levels we show that there exists a dominant strategy equilibrium on the dealers sharing rationing levels finally a comprehensive computational study is conducted to highlight the impact of the manufacturer s incentives subsidies and or transshipment fees on the dealers sharing behavior

the quantity flexibility contract and supplier customer incentives consider a supply chain consisting of two independent agents a supplier e g a manufacturer and its customer e g a retailer the latter in turn serving an uncertain market demand to reconcile manufacturing procurement time lags with a need for timely response to the market such supply chains often must commit resources to production quantities based on forecasted rather than realized demand the customer typically provides a planning forecast of its intended purchase which does not entail commitment benefiting from overproduction while not bearing the immediate costs the customer has incentive to initially overforecast before eventually purchasing a lesser quantity the supplier must in turn anticipate such behavior in its production quantity decision this individually rational behavior results in an inefficient supply chain this paper models the incentives of the two parties identifying causes of inefficiency and suggesting remedies particular attention is given to the quantity flexibility qf contract which couples the customer s commitment to purchase no less than a certain percentage below the forecast with the supplier s guarantee to deliver up to a certain percentage above under certain conditions this method can allocate the costs of market demand uncertainty so as to lead the individually motivated supplier and customer to the systemwide optimal outcome we characterize the implications of qf contracts for the behavior and performance of both parties and the supply chain as a whole