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

optimal time based consolidation policy with price sensitive demand abstract we consider a single item inventory system where shipments are consolidated to reduce the transportation cost using a time based consolidation policy and develop a mathematical model to obtain the optimal price replenishment quantity and dispatch cycle to maximize the total profit the long run average profit is computed and the optimality properties are obtained using the optimality properties we develop an efficient algorithm to obtain the optimal values of price replenishment quantity and dispatch cycle for the proposed policy we then extend our results to consider quantity discount of unit dispatch cost in order to compare the performances of the proposed policy with the optimal quantity based policy extensive numerical experiments are conducted and the total profit and the customer waiting time that represents quality of service are compared we also propose the quantity time based policy which is a hybrid approach and the numerical results show that additional profit can be obtained without sacrificing quality of service

optimal dynamic pricing of inventories with stochastic demand over finite horizons in many industries managers face the problem of selling a given stock of items by a deadline we investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm s objective is to maximize expected revenues examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry which markets space such as seats on airline flights cabins on vacation cruises and rooms in hotels that become worthless if not sold by a specific time we formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp price as a function of the stock level and the length of the horizon for a particular exponential family of demand functions we find the optimal pricing policy in closed form for general demand functions we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity finally we extend our results to the case where demand is compound poisson only a finite number of prices is allowed the demand rate is time varying holding costs are incurred and cash flows are discounted the initial stock is a decision variable and reordering overbooking and random cancellations are allowed

nonlinear pricing to produce information we investigate the firm s dynamic nonlinear pricing problem when facing consumers whose tastes vary according to a scalar index we relax the standard assumption that the firm knows the distribution of this index in general the firm should determine its marginal price schedule as if it were myopic and produce information by lowering the price schedule bunching consumers at positive purchase levels should be avoided as a special case we also consider a market characterized by homogeneous consumers with a static but unknown demand curve we show that when there are repeat purchases the forward looking firm should tend towards penetration pricing otherwise its strategy should tend towards skimming we extend our insights to more general settings and discuss implications for pricing product lines

dynamic pricing of perishable assets under competition we study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon customers sequentially arrive at the market make a purchase choice and then leave immediately with some likelihood of no purchase the purchase likelihood depends on the time of purchase product attributes and current prices the demand structure includes time variant linear and multinomial logit demand models as special cases assuming deterministic customer arrival rates we show that any equilibrium strategy has a simple structure involving a finite set of shadow prices measuring capacity externalities that firms exert on each other equilibrium prices can be solved from a one shot price competition game under the current time demand structure taking into account capacity externalities through the time invariant shadow prices the former reflects the transient demand side at every moment and the latter captures the aggregate supply constraints over the sales horizon this simple structure sheds light on dynamic revenue management problems under competition which helps capture the essence of the problems under demand uncertainty we show that the equilibrium solutions from the deterministic game provide precommitted and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart when demand and supply are sufficiently large this paper was accepted by yossi aviv operations management

market structure and the value of overselling under stochastic demands in the operations management literature traditional revenue management focused on pricing and capacity allocation strategies in a two period model with stochastic demand inspired by travel and lodging industries we examine a two period model in which each seller may also adopt the overselling strategy to customers whose valuations are differentiated by timing of arrivals widely seen as a popular hedge against consumers skipping reservations we extend the stylized approaches of biyalogorsky carmon fruchter and gerstner 1999 and lim 2009 to understand the value of overselling under various market structures we find that contrary to existing literature the impact of period two pricing competition from overselling spills over to period one such that overselling may not always be a weakly dominant strategy once unlimited early demand ceases to hold in a duopoly regime we provide some numerical studies on the existence of multiple equilibria at the capacity allocation level which actually lead to different selling strategies at the equilibrium despite identical market conditions and firm characteristics

the impact of customer returns on pricing and order decisions abstract in this paper we address the simultaneous determination of price and inventory replenishment when customers return product to the firm we examine cases when the quantity of returned product is a function of both the quantity sold and the price in single and multi period problems with and without uncertainty in demand we derive results for optimal prices and order quantities and discuss how the firm should change price and inventory quantities in order to mitigate the negative effects of returns from customers

price dispersion and incomplete learning in the long run abstract in each period a seller chooses a price and the customer for that period buys either one unit or nothing the relationship between price and purchase probability is one of two linear functions it is shown that the seller behaving optimally does not necessarily learn which function is the actual relationship since there can be a positive probability of sequences of prices converging to the price at which the two functions give the same purchase probability

optimal discounting and replenishment policies for perishable products abstract we consider a retailer selling a perishable product with short shelf life and uncertain demand facing these key decisions a whether to discount old er items b how much discount to offer and c what should be the replenishment policy in order to better understand the impact of consumer behavior and shelf life on these decisions we consider four models in model a the product has a shelf life of two periods and the retailer decides whether or not to offer a discount the amount of discount is exogenous and assumed to be large enough so that all the customers prefer the old product to the new one when a discount is offered based on several numerical examples we find that a threshold discounting policy in which a discount is offered if and only if the inventory of old product is below a threshold is optimal in model b the retailer also decides how much discount to offer model c extends model b and considers a new pool of customers who are willing to purchase from the retailer when a discount is offered in both models b and c the product has a shelf life of two periods while model d explores what happens with longer shelf life we analyze and compare these models to present different managerial insights

analysis of compound bullwhip effect causes abstract this research investigates compound causes of the bullwhip effect bwe by considering an inventory system with multiple price sensitive demand streams joint price and demand dynamics are captured by a vector time series process that incorporates the stochastic co movements in price and demand we study two bwe measures one for each demand stream individually and one for the aggregated demand we show that demand parameters including demand autocorrelation cross correlation and price sensitivity serve as root causes of the bwe we prove that the impact of these parameters on the bwe can be additively decomposed conditions are established under which a pair of simultaneous compound causes may attenuate or dampen the bwe when demand streams are aggregated we derive a pooling factor that quantifies the impact of demand aggregation on order stability when positive the pooling factor corresponds to a synergy effect that captures the gain in the stability of the pooled orders conditions for the existence of the synergy effect are obtained for several special cases involving a zero leadtime we also discuss how our analytical findings can be managerially applied to bullwhip mitigation strategies

pricing and the news vendor problem a review with extensions in the newsvendor problem a decision maker facing random demand for a perishable product decides how much of it to stock for a single selling period this simple problem with its intuitively appealing solution is a crucial building block of stochastic inventory theory which comprises a vast literature focusing on operational efficiency typically in this literature market parameters such as demand and selling price are exogenous however incorporating these factors into the mode l can provide an excellent vehicle for examining how operational problems interact with marketing issues to influence decision making at the firm level in this paper we examine an extension of the newsvendor problem in which stocking quantity and selling price are set simultaneously we provide a comprehensive review that synthesizes existing results for the single period problem and develop additional results to enrich the existing knowledge base we also review and develop insight into a dynamic inventory extension of this problem and motivate the applicability of such models

dynamic pricing of inventory capacity with infrequent price changes we consider a problem of dynamically pricing a single product sold by a monopolist over a short time period if demand characteristics change throughout the period it becomes attractive for the company to adjust price continuously to respond to such changes i e price discriminate intertemporally however in practice there is typically a limit on the number of times the price can be adjusted due to the high costs associated with frequent price changes if that is the case instead of a continuous pricing rule the company might want to establish a piece wise constant pricing policy in order to limit the number of price adjustments such a pricing policy which involves optimal choice of prices and timing of price changes is the focus of this paper we analyze the pricing problem with a limited number of price changes in a dynamic deterministic environment in which demand depends on the current price and time and there is a capacity inventory constraint that may be set optimally ahead of the selling season the arrival rate can evolve in time arbitrarily allowing us to model situations in which prices decrease increase or neither we consider several plausible scenarios where pricing and or timing of price changes are endogenized various notions of complementarity single crossing property supermodularity and total positivity are explored to derive structural results conditions sufficient for the uniqueness of the solution and the monotonicity of prices throughout the sales period furthermore we characterize the impact of the capacity constraint on the optimal prices and the timing of price changes and provide several other comparative statics results additional insights are obtained directly from the solutions of various special cases

a single period stocking and pricing problem involving stochastic emergency supply abstract we develop a model for determining jointly optimal price and production policy of products with short life cycles subject to partially uncertain supply capacity within the price setting newsvendor framework we consider that demand in excess of the stocking quantity can be met by an emergency order due to the randomness of emergency supply capacity it may not always be possible to satisfy the demand completely assuming that all customers are charged the same price we explore the optimal sourcing and pricing decisions in the commonly used additive and multiplicative demand scenarios the first order conditions imply that the optimal price in the problem with random emergency supply is less than the optimal price associated with the deterministic demand problem when demand uncertainty is additive and it is greater than the optimal price associated with the deterministic demand problem when demand uncertainty is multiplicative we also find that the same type of comparative static applies in the multiplicative uncertainty case when there exists a dual source emergency system consisting of a perfectly reliable supplier and a second supplier with a stochastic capacity

actively learning about demand and the dynamics of price adjustment by observing the quantity demanded at particular prices a firm may learn about the parameters of its demand curve in such an environment price changes obstruct the learning process by inducing additional noise the authors paper constructs a dynamic model where a price setting firm endogenously controls the speed of learning the model provides a possible explanation for price inertia as a stable pricing policy allows the firm to learn more rapidly which improves future expected profits furthermore even in the long run learning continues to affect the firm s optimal price copyright 1990 by royal economic society

multi period modeling of two way price commitment under price dependent demand abstract this paper examines the use of price commitment policies in dynamic contracting in multiple period finite time horizons two specific forms of price commitment are considered one on the part of the retailer through a retail fixed markup contract and one on the part of the manufacturer through a price protection contract optimal policies for each form of price commitment are analytically derived as are optimal policies for the traditional price only and centralized supply chain scenarios that we use as comparisons we prove that optimal retail price and order size solutions exist in each period under the assumption of non increasing price dependent demand we show that the existence of retailer inventory between periods causes the optimal policies to differ from a static single period model further we show that a supplier offers a price protection policy as a signal to the retailer to resolve the gaming that naturally occurs under price only this effectively decouples the multi period dynamic contracting setting into repeated single period scenarios however the resulting behavior can actually inhibit supply chain performance on the retail commitment side we find that retail fixed markup policies are quite effective in improving supply chain efficiency we show that such policies can lead to pareto improvement over price only contracts and can even coordinate the supply chain in some situations

price smoothing and inventory this paper explains the phenomenon of price rigidity or price smoothing as the outcome of the optimal inventory policy of a multi period profit maximizing firm under demand and output uncertainties price smoothing may be manifested in two forms first price changes may be moderated with respect to those implied by the demand function and second the firm may choose to restrict price fluctuations by establishing upper and or lower bounds on prices we show that the extent of the asymmetry in price smoothing depends on the relationship between the inventory holding cost and the backlog penalty cost our model accommodates a wide range

reducing the cost of demand uncertainty through accurate response to early sales traditionally fashion products have incurred high losses due to stockouts and inventory obsolence because long lead times coupled with a concentrated selling season force all or at least most production to be committed before demand information is available under a quick response system lead times are shortened sufficiently to allow a greater portion of production to be scheduled in response to initial demand we model and analyze the decisions required under quick response and give a method for estimating the demand probability distributions needed in our model we applied these procedures with a major fashion skiwear firm and found that cost relative to the current informal response system was reduced by enough to increase profits by 60 relative to the cost that would have been incurred if no response were used optimized response reduces cost by enough to roughly quadruple profits

inventory centralization games with price dependent demand and quantity discount consider a distribution system consisting of a set of retailers facing a single period price dependent demand of a single product by taking advantage of the risk pooling effect and the quantity volume discount provided by suppliers or third party carriers the retailers may place joint orders and keep inventory at central warehouses before demand realization and allocate inventory among themselves after demand realization to reduce their operating costs under rather general assumptions we prove that there is a stable allocation of profits among the retailers in the sense that the resulting inventory centralization game has a nonempty core we also show how to compute an allocation in the core

capacity pricing and production under supply and demand uncertainties with an application in agriculture abstract we consider capacitated joint lot sizing and pricing problems when supply and a price sensitive demand are uncertain in cases where there is excess capacity the decision maker has the option to rent her capacity we model the case where price and production quantity are determined before the yield is realized joint decisions as well as the case where the price is determined after the yield is known sequential decisions in the joint decisions case we introduce the concept of expected demand fill rate elasticity and characterize the conditions in which a one sided production and pricing policy is optimal we extend the results to the case when there is a fixed production cost and show that a two sided production and pricing policy is optimal we also investigate the conditions under which it is optimal for the decision maker to rent her capacity in addition we look at the case in which the decision maker is risk averse and analyze the effect of the risk attitude on the optimal price and production quantity we extend our model to the multi period case and the case where there is a lead time to acquire new capacity we show that a one sided production pricing and capacity planning policy is optimal in this situation as well we apply our model to the agricultural sector and present numerical examples using data from the california almond industry

dynamic stochastic inventory management with reference price effects we analyze the joint inventory and pricing decisions of a firm when demand depends on not only the current selling price but also a memory based reference price and customers are loss averse the presence of reference price effect leads to a nonconcave one period expected revenue in price and reference price we introduce a transformation technique that allows us to prove under some mild assumptions the optimality of a reference price dependent base stock list price policy which is characterized by a base stock level and a target reference price in addition we show that the target reference price is increasing in the reference price but except in the loss neutral case the base stock level is not monotone in the reference price we also show that in the steady state of the model with the reference price effect the optimal price is lower while the optimal base stock level is higher than their counterparts in the model without the reference price effect

anticipated and unanticipated effects of crude oil prices and gasoline inventory changes on gasoline prices abstract this paper examines the effect of anticipated and unanticipated changes in oil prices and gasoline inventory on us gasoline prices we estimate empirical responses to anticipated and unanticipated changes in oil prices and gasoline inventory and show that gasoline price adjustments are faster and stronger for anticipated changes in oil prices and inventory levels than for unanticipated changes furthermore this difference is statistically significant we use these findings to evaluate the cost of adjustment hypothesis suggested by borenstein and shephard 2002 we also find that there is an asymmetry in the effect of gasoline inventory on gasoline and oil prices this finding complements a well known result that positive and negative changes in oil prices have asymmetric effect on gasoline prices

impact of cost uncertainty on pricing decisions under risk aversion abstract this paper studies cost uncertainty in services despite the fact that the service sector has become the largest component of gross domestic products in most developed economies cost uncertainty and its impact on pricing decisions have not received much attention in the literature in this paper we first identify the root causes of cost uncertainty in services using the distinctive characteristics of services defined in the literature we show why cost uncertainty which has been widely neglected in the manufacturing dominated literature is pervasive in services next we investigate how cost uncertainty affects a risk averse service provider s pricing decisions in a make to order setting using the expected utility theory framework we show that cost uncertainty increases the optimal price whereas demand uncertainty reduces it as a result of the countervailing impacts the optimal price under risk aversion may be larger or smaller than the optimal risk neutral price next we study the problem of optimizing cost contingency in service contract pricing we show that the optimal cost contingency decreases as the profit of the contract increases even when the utility function exhibits an increasing absolute risk aversion finally we introduce various strategies to mitigate the risk of cost uncertainty observed in practice and propose new research problems

optimal executive compensation versus managerial power a review of lucian bebchuk and jesse fried s pay without performance the unfulfilled promise of executive compensation this essay reviews lucian a bebchuk and jesse m fried s pay without performance the unfulfilled promise of executive compensation bebchuk and fried criticize the standard view of executive compensation in which executives negotiate contracts with shareholders that provide incentives that motivate them to maximize the shareholders welfare in contrast bebchuk and fried argue that executive compensation is more consistent with executives who control their own boards and who maximize their own compensation subject to an outrage constraint they provide a host of evidence consistent with this alternative viewpoint the book can be evaluated from both positive and normative perspectives from a positive perspective much of the evidence they present especially about the camouflage and risk taking aspects of executive compensation systems is fairly persuasive however from a normative perspective the book conveys the idea that policy changes can dramatically improve executive compensation systems and consequently overall corporate performance it is unclear to me how effective potential reforms designed to achieve such changes are likely to be in practice

dynamic pricing through discounts for optimizing multiple class demand fulfillment in a multiple customer class model of demand fulfillment for a single item we consider the use of dynamic price discounts to encourage backlogging of demand for customer classes denied immediate service customers are assumed to arrive over several stages in a period and customer classes are distinguished by their contractual price and sensitivity to discounts through dynamic programming we determine the optimal discounts to offer assuming a linear model for the sensitivity of customers to such inducements we show that customers are served in class order and allocation of inventory to demand is determined by considering the current number of customers backlogged as well as the current inventory position through comparison to a naive supplier allocating inventory first come first served with no discounting we show that profits are primarily influenced by the allocation of capacity and the use of price discounts primarily benefits the second class customers overall fill rate heuristics for implementation of the solution in real time settings are given

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

can industrial outwork enhance homeworkers capabilities evidence from clusters in south asia summary there has been an increasing informalization and feminization of the labor force in developing countries over the past few decades one aspect of these twin phenomena is the growth of subcontracted homework in manufacturing homework has a dual and contradictory character it can be the source of exploitation of workers but under some conditions it can foster human development and the emergence of microenterprises and promote local development this paper draws on surveys carried out in two low income south asian countries india and pakistan where homework is widespread it examines the social protection needs of these women workers and also argues for public action to promote such work as a possible new labor intensive growth strategy in developing countries

optimal pricing and inventory control policy with quantity based price differentiation a firm facing price dependent stochastic demand aims to maximize its total expected profit over a planning horizon in addition to the regular unit selling price the firm can utilize quantity discounts to increase sales we refer to this dual pricing strategy as quantity based price differentiation at the beginning of each period the firm needs to make three decisions replenish the inventory set the unit selling price if the unit sales mode is deployed and set the quantity discount price if the quantity sales mode is deployed or the combination of the two modes of sales we identify conditions under which the optimal inventory control policy and selling pricing strategy is well structured remarkably under a utility based demand framework these conditions can be unified by a simple regularity assumption that has long been used in the auction and mechanism design literature moreover sharper structural results are yielded for the optimal selling strategy we also examine the comparative advantag

benefits of leadtime information and of its combination with demand forecast information abstract this paper studies both the benefits of leadtime information and the interrelationships among demand forecast information leadtime uncertainty and leadtime information for improving inventory control performance to this end it explicitly incorporates both leadtime information and demand forecast information into an inventory model although they have conventionally been dealt with individually in the literature specifically it considers a periodic review inventory model with uncertain leadtimes in which both leadtime information and demand forecast information are available the leadtime information is modeled as the information of the arrival of outstanding orders and the demand forecast information as the martingale model of forecast evolution mmfe the paper analyzes the way to use both leadtime information and demand forecast information for inventory control operations specifically under certain conditions the optimality of the state dependent base stock policy is shown and an effective heuristic policy is developed it also derives some managerial insights for exploiting both leadtime information and demand forecast information in the case where leadtimes are uncertain for instance while leadtime information itself significantly improves inventory control performance it also enhances the benefits of demand forecast information specifically the benefits of demand forecast information may significantly decrease as leadtime uncertainty increases however the decrease of the benefits of demand forecast information may be alleviated with leadtime information

a partially observed markov decision process for dynamic pricing in this paper we develop a stylized partially observed markov decision process pomdp framework to study a dynamic pricing problem faced by sellers of fashion like goods we consider a retailer that plans to sell a given stock of items during a finite sales season the objective of the retailer is to dynamically price the product in a way that maximizes expected revenues our model brings together various types of uncertainties about the demand some of which are resolvable through sales observations we develop a rigorous upper bound for the seller s optimal dynamic decision problem and use it to propose an active learning heuristic pricing policy we conduct a numerical study to test the performance of four different heuristic dynamic pricing policies in order to gain insight into several important managerial questions that arise in the context of revenue management

joint production and pricing decisions with setup costs and capacity constraints we consider the problem of setting prices and choosing production quantities for a single product over a finite horizon for a capacity constrained manufacturer facing price sensitive demands there is a fixed cost per production run and a variable cost per unit produced both of which may vary by period we characterize properties of the optimal solution considering cases with constant and time varying capacity and with and without speculative motive for holding inventory we show that counter to intuition optimal prices may increase as the capacity increases even when capacity is constant over the horizon we also show that increases in capacity do not always exhibit diminishing marginal returns our procedure produces solutions with much higher profits than can be obtained from a sophisticated sequential procedure in which a well informed and optimum seeking marketing department makes pricing decisions and the manufacturing department seeks to satisfy the resulting demands at minimum cost our results also suggest that firms with seasonal demand and tight capacity constraints should be more aggressive in setting prices to manage their demands than what is typically done in practice finally we discuss how a decision maker can use our procedure as an aid in solving multiproduct versions of the problem

newsvendor problem with clearance pricing abstract the newsvendor nv problem assumes that the salvage clearance price at which the leftover inventory is disposed of is a given parameter of the problem in this paper we relax this assumption and consider the nv problem with the salvage clearance price as a decision variable we have drawn from the literatures on the nv problem and clearance markdown dynamic pricing to develop three stochastic models in this paper in the first model we assume that while the seasonal demand is exogenous and stochastic the end of season demand is endogenous and deterministic the second model extends the first model by assuming that the end of season demand is endogenous and stochastic finally the third model considers that both the seasonal and end of season demands are endogenous and stochastic we have provided solution procedures for solving the stochastic optimization problems we have also performed sensitivity analyses to assess the sensitivity of the optimal expected profit and order quantity to different problem parameters specifically we have found that the optimal expected profit is most sensitive to the variable cost per unit mean seasonal demand and market potential of end of season demand our models will be useful for retailers of products with a short selling season and a short end of season period for clearance sale of leftover inventory such that there is a single replenishment opportunity at the beginning of the season and a single opportunity for setting the salvage price for clearance sale based on the leftover inventory and end of season demand pattern the paper is concluded with possible directions for future research

conditions of reverse bullwhip effect in pricing under joint decision of replenishment and pricing abstract a reverse bullwhip effect in pricing rbp occurs when an amplification of price variability takes place moving from the upstream suppliers to the downstream customers in a supply chain in this study we investigate rbp conditions for supply chains where joint replenishment and pricing decisions are made commencing with a single stage supply chain in which a retailer faces a random and price sensitive demand we extend the results to a multi stage supply chain using a leader follower game theoretical framework we discuss rbp conditions for supply chains where newsvendor and continuous review inventory policies are employed and present numerical examples for commonly used demand functions

revenue management through dynamic cross selling in e commerce retailing we consider the problem of dynamically cross selling products e g books or services e g travel reservations in the e commerce setting in particular we look at a company that faces a stream of stochastic customer arrivals and may offer each customer a choice between the requested product and a package containing the requested product as well as another product what we call a packaging complement given consumer preferences and product inventories we analyze two issues 1 how to select packaging complements and 2 how to price product packages to maximize profits we formulate the cross selling problem as a stochastic dynamic program blended with combinatorial optimization we demonstrate the state dependent and dynamic nature of the optimal package selection problem and derive the structural properties of the dynamic pricing problem in particular we focus on two practical business settings with the emergency replenishment model and without the lost sales model the possibility of inventory replenishment in the case of a product stockout for the emergency replenishment model we establish that the problem is separable in the initial inventory of all products and hence the dimensionality of the dynamic program can be significantly reduced for both models we suggest several packaging pricing heuristics and test their effectiveness numerically

dynamic capacity management with uncertain demand and dynamic price inspired from practices of chinese real estate firms we study dynamic capacity management problems for a firm that sells homogeneous goods over a finite or infinite selling horizon provided that demand is uncertain retail price is exogenous but changes according to an auto regressive process and there is holding cost for remaining inventory in each period the capacity problems facing the firm include to determine an initial stock at the beginning of the selling season and to allocate the remaining quantity for the current and future sale in each period to maximize the firm s total expected discounted profit by using markov decision processes we show the optimality of a so called save up to level policy i e it is optimal to allocate as much as the save up to level to future periods if possible in each period and the existence of the optimal initial stock moreover we characterize monotone properties of the optimal save up to level and the optimal initial stock numerical analysis shows that compared to the policy with zero save up to level i e always allocating all the remaining inventory to the current period the advantage of the policy proposed in the present paper is significant when price rising trend is large holding cost is low initial price is high or demand variation is either high or low

combined pricing and inventory control under uncertainty this paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty more specifically we analyze the following single item periodic review model demands in consecutive periods are independent but their distributions depend on the item s price in accordance with general stochastic demand functions the price charged in any given period can be specified dynamically as a function of the state of the system a replenishment order may be placed at the beginning of some or all of the periods stockouts are fully backlogged we address both finite and infinite horizon models with the objective of maximizing total expected discounted profit or its time average value assuming that prices can either be adjusted arbitrarily upward or downward or that they can only be decreased we characterize the structure of an optimal combined pricing and inventory strategy for all of the above types of models we also develop an efficient value iteration method to compute these optimal strategies finally we report on an extensive numerical study that characterizes various qualitative properties of the optimal strategies and corresponding optimal profit values

a general equilibrium model for industries with price and service competition this paper develops a stochastic general equilibrium inventory model for an oligopoly in which all inventory constraint parameters are endogenously determined we propose several systems of demand processes whose distributions are functions of all retailers prices and all retailers service levels we proceed with the investigation of the equilibrium behavior of infinite horizon models for industries facing this type of generalized competition under demand uncertainty we systematically consider the following three competition scenarios 1 price competition only here we assume that the firms service levels are exogenously chosen but characterize how the price and inventory strategy equilibrium vary with the chosen service levels 2 simultaneous price and service level competition here each of the firms simultaneously chooses a service level and a combined price and inventory strategy 3 two stage competition the firms make their competitive choices sequentially in a first stage all firms simultaneously choose a service level in a second stage the firms simultaneously choose a combined pricing and inventory strategy with full knowledge of the service levels selected by all competitors we show that in all of the above settings a nash equilibrium of infinite horizon stationary strategies exists and that it is of a simple structure provided a nash equilibrium exists in a so called reduced game we pay particular attention to the question of whether a firm can choose its service level on the basis of its own input characteristics i e its cost parameters and demand function only we also investigate under which of the demand models a firm under simultaneous competition responds to a change in the exogenously specified characteristics of the various competitors by either i adjusting its service level and price in the same direction thereby compensating for price increases decreases by offering improved inferior service or ii adjusting them in opposite directions thereby simultaneously offering better or worse prices and service

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

average cost single stage inventory models an analysis using a vanishing discount approach an important problem in the theory of dynamic programming is that of characterizing sufficient conditions under which the optimal policies for markov decision processes mdps under the infinite horizon discounted cost criterion converge to an optimal policy under the average cost criterion as the discount factor approaches 1 in this paper we provide for stochastic inventory models a set of such sufficient conditions these conditions unlike many others in the dynamic programming literature hold when the action space is noncompact and the underlying transition law is weakly continuous moreover we verify that these conditions hold for almost all conceivable single stage inventory models with few assumptions on cost and demand parameters as a consequence of our analysis we partially characterize for the first time optimal policies for the following inventory systems under the infinite horizon average cost criterion which have thus far been a challenge a capacitated systems with setup costs b uncapacitated systems with convex ordering costs plus a setup cost and c systems with lost sales and lead times

pricing and operational recourse in coproduction systems coproduction systems in which multiple products are produced simultaneously in a single production run are prevalent in many industries such systems typically produce a random quantity of vertically differentiated products this product hierarchy enables the firm to fill demand for a lower quality product by converting a higher quality product in addition to the challenges presented by random yields and multiple products coproduction systems often serve multiple customer classes that differ in their product valuations furthermore the sizes of these classes are uncertain employing a utility maximizing customer model we investigate the production pricing downconversion and allocation decisions in a two class stochastic demand stochastic yield coproduction system for the single class case we establish that downconversion will not occur if prices are set optimally in contrast we show that downconversion can be optimal in the two class case even if prices are set optimally we consider the benefit of postponing certain operational decisions e g the pricing or allocation rule decisions until after uncertainties are resolved we use the term recourse to denote actions taken after uncertainties have been resolved we find that recourse pricing benefits the firm much more than either downconversion or recourse allocation do implying that recourse demand management is more valuable than recourse supply management special cases of our model include the single class and two class random yield newsvendor models

inventories and the automobile market this article studies the within model year pricing production and inventory management of new automobiles using new monthly data on u s transaction prices we document that for the typical vehicle prices fall over the model year at a 9 0 annual rate concurrently both sales and inventories are hump shaped to explain these time series we formulate an industry model for new automobiles in which inventory and pricing decisions are made simultaneously the model predicts that automakers build to stock inventory management policy substantially influences the time series of prices and sales accounting for four tenths of the price decline observed over the model year

s s optimality in joint inventory pricing control an alternate approach we study a stationary single stage inventory system under periodic review with fixed ordering costs and multiple sales levers such as pricing advertising etc we show the optimality of s s type policies in these settings under both the backordering and lost sales assumptions our analysis is constructive and is based on a condition that we identify as being key to proving the s s structure this condition is entirely based on the single period profit function and the demand model our optimality results complement the existing results in this area

periodic pricing of seasonal products in retailing this paper studies intertemporal pricing policies when selling seasonal products in retail stores we first present a continuous time model where a seller faces a stochastic arrival of customers with different valuations of the product for this model we characterize the optimal pricing policies as functions of time and inventory we use this model as a benchmark against which we compare more realistic models that consider periodic pricing reviews we show that the structure of the optimal pricing policies in this case is consistent with the procedures observed in practice retail stores successively discount the product during the season and promote a liquidation sale at the end of the planning horizon we also show that the loss experienced when implementing periodic pricing reviews instead of continuous policies is small when the appropriate number of reviews is chosen several interesting economic insights emerge from our analysis for example uncertainty in the demand for new products leads to higher prices larger discounts and more unsold inventory finally we study the effect of announced discount policies on prices and profits we show that stores that have adopted this type of strategy usually set prices such that with high probability the merchandise is sold during the first periods and the largest discounts rarely take place

inventory management with auctions and other sales channels optimality of s s policies we study periodic review inventory replenishment problems with fixed ordering costs and show the optimality of s s inventory replenishment policies inventory replenishment is instantaneous i e the lead time is zero we consider several sales mechanisms e g auction mechanisms name your own price mechanisms and multiple heterogeneous sales channels we prove this result by showing that these models satisfy a recently established sufficient condition for the optimality of s s policies thus this paper shows that the optimality of s s policies extends well beyond the traditional sales environments studied so far in the inventory literature

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

revenue management of a make to stock queue motivated by recent electronic marketplaces we consider a single product make to stock manufacturing system that uses two alternative selling channels long term contracts and a spot market of electronic orders at time 0 the risk averse manufacturer selects the long term contract price at which point buyers choose one of the two channels the resulting long term contract demand is a deterministic fluid while the spot market demand is modeled as a stochastic renewal process an exponential reflected random walk model is used to model the spot market price which is correlated with the spot market demand process the manufacturer accepts or rejects each electronic order and long term contracts and accepted electronic orders are backordered if necessary the manufacturer s control problem is to select the optimal long term contract price as well as the optimal production i e busy idle and electronic order admission policies to maximize revenue minus inventory holding and backorder costs under heavy traffic conditions the problem is approximated by a diffusion control problem and analytical approximations are used to derive a policy that is simple and reasonably accurate and robust

coordinating inventory control and pricing strategies with random demand and fixed ordering cost the finite horizon case we analyze a finite horizon single product periodic review model in which pricing and production inventory decisions are made simultaneously demands in different periods are random variables that are independent of each other and their distributions depend on the product price pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered the objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon we show that when the demand model is additive the profit to go functions arek concave and hence an s s p policy is optimal in such a policy the period inventory is managed based on the classical s s policy and price is determined based on the inventory position at the beginning of each period for more general demand functions i e multiplicative plus additive functions we demonstrate that the profit to go function is not necessarilyk concave and an s s p policy is not necessarily optimal we introduce a new concept the symmetrick concave functions and apply it to provide a characterization of the optimal policy

coordinating inventory control and pricing strategies under batch ordering in this paper we investigate joint pricing and inventory control problems in a finite horizon single product periodic review setting with certain uncertain supply capacities the demands in different periods are random variables whose distributions depend on the posted price exhibiting the additive form the order quantity in each period is required to be of integral multiples of a given specific batch size denoted by q inventory replenishment incurs a linear ordering cost referred to as the cost rate function the sum of holding and backorder costs can either be convex or quasi convex the objective is to determine a joint ordering and pricing decision that can maximize the total expected profit over the planning horizon we first consider the case in which the cost rate function is convex and show that the modifiedr q list price policy is optimal for the system with certain and limited capacities a special case of which is the r q list price policy when capacities become unlimited as supply capacities become random the optimal policy follows a new structure wherein the optimal order up to level and posted price must be coordinated to make the optimal safety stock level follow the r q policy we further consider the case of a quasi convex cost rate function which may arise when a service level constraint is used as a surrogate for the shortage cost we demonstrate that the r q list price policy is optimal for the system without supply capacity constraints in addition extensions to several other models are discussed the enabling technique is based on the notion of q jump convexity and its variants

technical note a note on the structure of joint inventory pricing control with leadtimes we consider a joint inventory pricing control problem for a periodic review single stage inventory system with a positive order leadtime and a linear order cost demands in consecutive periods are independent but their distributions depend on the price in accordance with a stochastic demand function of additive form pricing and ordering decisions are made simultaneously at the beginning of each period the objective is to maximize the total expected discounted profit over a finite horizon we partially characterize the structure of the optimal joint ordering and pricing policies we also show that our structural analysis can be extended to a multistage or serial inventory system with constant or stochastic leadtimes and an assemble to order system with price sensitive demand

technical note optimal product acquisition pricing and inventory management for systems with remanufacturing acquisition of used products cores is central to the success of remanufacturing programs for companies at the same time dynamic pricing strategies have been adopted in various industries to better balance supply and customer demand in this paper we study the integration of these two aspects of operations together with inventory management for a production remanufacturing firm we develop a periodic review single product inventory system with price dependent customer demand the product return in each period is random but can be actively controlled by the firm s acquisition effort the firm aims to maximize its total discounted profit over a finite planning horizon by implementing optimal production remanufacturing product acquisition and pricing strategies we first show that with an exogenous selling price the optimal production remanufacturing disposal policy is simple and characterized by three state independent parameters the optimal acquisition effort is decreasing in the aggregate inventory level of serviceable product and cores nevertheless when pricing is an endogenous decision we find that the optimal policy becomes much more complicated and its control parameters are state dependent the optimal selling price is decreasing whereas the optimal acquisition effort is increasing in the serviceable product inventory level and both decisions decrease with the aggregate inventory level

pricing and manufacturing decisions when demand is a function of prices in multiple periods in most deterministic manufacturing decision models demand is either known or induced by pricing decisions in the period that the demand is experienced however in more realistic market scenarios consumers make purchase decisions with respect to price not only in the current period but also in past and future periods we model a joint manufacturing pricing decision problem accounting for that portion of demand realized in each period that is induced by the interaction of pricing decisions in the current period and in previous periods we formulate a mathematical programming model and develop solution techniques we identify structural properties of our models and develop closed form solutions and effective heuristics for various special cases of our models finally we conduct extensive computational experiments to quantify the effectiveness of our heuristics and to develop managerial insights

joint pricing and inventory control with a markovian demand model abstract we consider the joint pricing and inventory control problem for a single product over a finite horizon and with periodic review the demand distribution in each period is determined by an exogenous markov chain pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged the surplus costs as well as fixed and variable costs are state dependent we show the existence of an optimal s s p type feedback policy for the additive demand model we extend the model to the case of emergency orders we compute the optimal policy for a class of markovian demand and illustrate the benefits of dynamic pricing over fixed pricing through numerical examples the results indicate that it is more beneficial to implement dynamic pricing in a markovian demand environment with a high fixed ordering cost or with high demand variability

a multiproduct dynamic pricing problem and its applications to network yield management a firm has inventories of a set of components that are used to produce a set of products there is a finite horizon over which the firm can sell its products demand for each product is a stochastic point process with an intensity that is a function of the vector of prices for the products and the time at which these prices are offered the problem is to price the finished products so as to maximize total expected revenue over the finite sales horizon an upper bound on the optimal expected revenue is established by analyzing a deterministic version of the problem the solution to the deterministic problem suggests two heuristics for the stochastic problem that are shown to be asymptotically optimal as the expected sales volume tends to infinity several applications of the model to network yield management are given numerical examples illustrate both the range of problems that can be modeled under this framework and the effectiveness of the proposed heuristics the results provide several fundamental insights into the performance of yield management systems

price versus production postponement capacity and competition this article presents a comparative analysis of possible postponement strategies in a two stage decision model where firms make three decisions capacity investment production inventory quantity and price typically investments are made while the demand curve is uncertain the strategies differ in the timing of the operational decisions relative to the realization of uncertainty we show how competition uncertainty and the timing of operational decisions influence the strategic investment decision of the firm and its value in contrast to production postponement price postponement makes the investment and production inventory decisions relatively insensitive to uncertainty this suggests that managers can make optimal capacity decisions by deterministic reasoning if they have some price flexibility under price postponement additional postponement of production has relatively small incremental value therefore it may be worthwhile to consider flexible ex post pricing before production postponement reengineering while more postponement increases firm value it is counterintuitive that this also makes the optimal capacity decision more sensitive to uncertainty we highlight the different impact of more timely information which leads to higher investment and inventories and of reduced demand uncertainty which decreases investment and inventories our analysis suggests appropriateness conditions for simple make to stock and make to order strategies we also present technical sufficiency and uniqueness conditions under price postponement these results extend to oligopolistic and perfect competition for which pure equilibria are derived interestingly the relative value of operational postponement techniques seems to increase as the industry becomes more competitive

coordinating inventory control and pricing strategies for perishable products we analyze a joint pricing and inventory control problem for a perishable product with a fixed lifetime over a finite horizon in each period demand depends on the price of the current period plus an additive random term inventories can be intentionally disposed of and those that reach their lifetime have to be disposed of the objective is to find a joint pricing ordering and disposal policy to maximize the total expected discounted profit over the planning horizon taking into account linear ordering cost inventory holding and backlogging or lost sales penalty cost and disposal cost employing the concept of l concavity we show some monotonicity properties of the optimal policies our results shed new light on perishable inventory management and our approach provides a significantly simpler proof of a classical structural result in the literature moreover we identify bounds on the optimal order up to levels and develop an effective heuristic policy numerical results show that our heuristic policy performs well in both stationary and nonstationary settings finally we show that our approach also applies to models with random lifetimes and inventory rationing models with multiple demand classes

dynamic replenishment production and pricing decisions in the face of supply disruption and random price sensitive demand abstract we study a joint decision problem for replenishment production pricing strategies in the face of both supply and demand uncertainties the supply of the raw material suffers from a potential supply disruption while the demand for the finished goods is price sensitive and random we assume that the raw material is storable and unfilled demands are fully backordered we characterize the optimal policies for raw material replenishment finished goods production and pricing we find that the optimal replenishment policy is an order up to type for a given finished goods stock level while it is a threshold type for a given raw material stock level for either a given finished goods stock level or a given raw material stock level the optimal production policy is a threshold type and the optimal pricing policy is a modified list price type respectively

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

joint pricing procurement control under fluctuating raw material costs abstract we consider a firm that periodically procures raw material units stores them and processes them into finished products upon order arrivals the raw material cost evolves in a markovian fashion whereas the demand process is influenced by both the raw material cost and sales prices charged by the firm the firm controls both the raw material procurement activity and sales price in each period we show the optimality of base stock list price type of policies with the additional raw cost dependence under conditions that are verifiable when the firm engages in price competition with other firms tapping into the same raw material market and when the raw material cost process has time continuity and mean reversion tendencies we identify two monotone patterns in which policy parameters should follow as the raw material cost fluctuates cost increases are also shown to translate into price increases at low inventory levels in other circumstances however there does not appear to be a clear pattern as to how the firm should pass cost increases on to end customers our numerical evidence unequivocally supports the adaptation of procurement and pricing controls to changing raw material costs

integrating dynamic pricing and replenishment decisions under supply capacity uncertainty this paper examines an integrated decision making process regarding pricing for uncertain demand and sourcing from uncertain supply which are often studied separately in the literature our analysis of the integrated system suggests that the base stock list price policy fails to achieve optimality even under deterministic demand instead the optimal policy is characterized by two critical values a reorder point and a target safety stock under this policy a positive order is issued if and only if the inventory level is below the reorder point when this happens the optimal order and price are coordinated to achieve a constant target safety stock which aims at hedging the demand uncertainty we further investigate the profit improvement obtained from deploying dynamic pricing as opposed to static pricing our results indicate that either supply limit or supply uncertainty may induce a significant benefit from dynamic pricing and the compound effect of supply limit and uncertainty can be much more pronounced than the individual effects whether or not the supply capacity is limited has a major implication on the value of dynamic pricing under unlimited supply dynamic pricing is more valuable when procurement cost is high or when demand is more sensitive to price with limited supply however the capacity restriction tends to be relaxed reducing the value of dynamic pricing

optimal order quantity and pricing decisions in single period inventory systems abstract in this paper we consider simultaneous pricing and procurement decisions associated with a one period pure inventory model under deterministic or probabilistic demand we investigate the necessary and sufficient conditions for an type policy to be optimal for the determination of the procurement quantity we also show how the corresponding optimal price can be obtained

dynamic pricing and ordering decisions by a monopolist this paper considers the relationship between pricing and ordering decisions for a monopolistic retailer facing a known demand function where over the inventory cycle the product may exhibit i physical decay or deterioration of inventory called wastage and ii decrease in market value called value drop associated with each unit of inventory on hand the retailer is allowed to continuously vary the selling price of the product over the cycle we introduce a notion of instantaneous margin and use it to derive profit maximizing conditions for the retailer the model explains the markdown of retail goods subject to decay it also provides guidance in determining when price changes during the cycle are worthwhile due to product aging how often such changes should be made and how such changes affect ordering intervals and quantities