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

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

inventory and credit decisions for time varying deteriorating items with up stream and down stream trade credit financing by discounted cash flow analysis abstract in today s competitive markets most firms in united kingdom and united states offer their products on trade credit to stimulate sales and reduce inventory trade credit is calculated based on time value of money on the purchase cost i e discounted cash flow analysis recently many researchers use discounted cash flow analysis only on the purchase cost but not on the revenue which is significantly larger than the purchase cost and the other costs for a sound and rigorous analysis we should use discounted cash flow analysis on revenue and costs in addition expiration date for a deteriorating item e g bread milk and meat is an important factor in consumer s purchase decision however little attention has been paid to the effect of expiration date hence in this paper we establish a supplier retailer customer supply chain model in which a the retailer receives an up stream trade credit from the supplier while grants a down stream trade credit to customers b the deterioration rate is non decreasing over time and near 100 percent particularly close to its expiration date and c discounted cash flow analysis is adopted for calculating all relevant factors revenue and costs the proposed model is an extension of more than 20 previous papers we then demonstrate that the retailer s optimal credit period and cycle time not only exist but also are unique thus the search of the optimal solution reduces to a local one finally we run several numerical examples to illustrate the problem and gain managerial insights

optimal monopolist pricing under demand uncertainty in dynamic markets we examine pricing policy for a monopolist facing uncertain demand in a market characterized by dynamics on the demand side such as diffusion or saturation effects and or on the cost side experience curve effects our model explicitly incorporates the impact of demand uncertainty and thus allows us to analyze the implications of uncertainty on the optimal price path by contrasting the stochastic policy with the corresponding deterministic policy we begin with an analysis of the general model and then focus on several special cases based on well known demand specifications to gain more specific insights and to suggest directional guidelines for dynamic pricing decisions in an uncertain environment in general the interaction among uncertainty demand and or cost dynamics and firm s discount rate thus farsighted firms operating under dynamic market conditions with high demand uncertainty such as high tech companies with innovative products for consumer or industrial markets should attach partic

the benefits of advance booking discount programs model and analysis consider a retailer who sells perishable seasonal products with uncertain demand due to the short sales season and long replenishment lead times associated with such products the retailer is unable to update demand forecasts by using actual sales data generated from the early part of the season and to respond by replenishing stocks during the season to overcome this limitation we examine the case in which the retailer develops a program called the advance booking discount abd program that entices customers to commit to their orders at a discount price prior to the selling season the time between placement and fulfillment of these precommitted orders provides an opportunity for the retailer to update demand forecasts by utilizing information generated from the precommitted orders and to respond by placing a cost effective order at the beginning of the selling season in this paper we evaluate the benefits of the abd program and characterize the optimal discount price that maximizes the retailer s expected profit

integrated inventory models considering the two level trade credit policy and a price negotiation scheme abstract this paper develops the integrated inventory models with permissible delay in payment in which customers demand is sensitive to the buyer s price the models consider the two level trade credit policy in the vendor buyer and buyer customer relationships in supply chain management a simple recursive solution procedure is proposed for the integrated models to determine the buyer s optimal pricing and production order strategy although the total profit from the buyer and vendor increases together the buyer s share lessens to compensate the buyer s loss due to the cooperative relationship a negotiation system is presented in order to allocate the profit increase to the vendor and buyer to determine the pricing and production order strategy a numerical example and sensitivity analysis are provided to illustrate the proposed model the results indicate that the total profit from the buyer and vendor together can increase although a price discount is given to the buyer in the proposed models

on the utilisation controversy a theoretical and empirical discussion of the kaleckian model of growth and distribution this paper examines the utilisation controversy around the kaleckian model of growth and distribution we show that the federal reserve data on capacity utilisation which have been used by both sides of this debate are the wrong kind of data for the issue under examination instead a more appropriate measurement can be derived from the data on the average workweek of capital we argue that the long run dynamic adjustment proposed by kaleckian scholars lacks a coherent economic rationale we provide an alternative path towards the endogeneity of the desired utilisation at the micro and macro levels finally we examine the proposed adjustment mechanism econometrically our results verify the endogeneity of the normal utilisation rate

long run competition in capacity short run competition in price and the cournot model in this article we investigate the nature of equilibrium in markets in which firms choose the scale of operation before they make pricing decisions we analyze a duopoly model in which firms choose their capacities before engaging in bertrand like price competition we demonstrate that the cournot outcome is unlikely to emerge in such markets and that the equilibrium tends to be more competitive than the cournot model would predict in addition our results indicate a tendency toward asymmetric firm sizes and price dispersion that results from the mixed strategies firms use in equilibrium

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

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

working time reduction and employment experiences in europe and economic policy recommendations the paper seeks to evaluate the evidence on the employment effects of the collective working time reductions in europe over the past 20 years while theoretical analyses produce contradictory assessments most empirical studies show positive employment effects but take insufficient account of the conditions under which the reductions in working time were implemented these conditions for the success of collective working time reductions include an active training policy designed to minimise skill shortages in the labour market the modernisation of work organisation wage increases in conjunction with productivity gains and a more equal income distribution

price trends and dynamic pricing in perishable product market consisting of superior and inferior firms abstract we consider the problem of a firm that sells perishable products with a dynamic pricing scheme in the presence of a firm offering a superior product we provide a probabilistic characterization of the optimal price process under the existence of such a firm for an aggregate demand model and for a multinomial logit demand model our results demonstrate that if the seller takes the price of the other firm into account in their optimal policy then the optimal price process tends to increase over time before the inventory level falls to one after which it decreases otherwise the price process decreases and then increases this path is called a j shaped curve before the inventory level falls to one if the price of the other firm is relatively low and the customer s valuation remains unchanged over time early in the sales period we also demonstrate numerically that when the firm uses a monopolistic policy and the difference in service quality between the two firms is large the switching time between the downward and upward trends takes place in the early stage of the sales period and in particular this j shaped phenomenon is strongly observed

a dynamic marketing operations interface model of new product updates abstract two critical success factors for nearly any firm are the introduction of new products and the integration of the marketing and operations functions within the business enterprise the series of products being considered are associated with sequential non disruptive innovations in technology but disruptive in fashion the study presents a model that integrates and builds upon the popular dynamic bass model for new product diffusion in marketing and the wagner and whitin dynamic lot sizing model a seminal model in operations management the end result is a model that simultaneously determines the optimal timing for the introduction of new product generations pricing production timing and produced quantities this model is then used to examine the impact of variations in marketing and operations parameters on both optimal profit and optimal product lifecycle length the study finds that larger profit and a faster pace of new product introductions are generally associated with faster diffusion lower price elasticity larger market potential lower new product introduction cost and more costly consumer products

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

multi item quick response system with budget constraint quick response mechanisms based on effective use of up to date demand information help retailers to reduce their inventory management costs we formulate a single period inventory model for multiple products with dependent multivariate normal demand distributions and a given overall procurement budget after placing orders based on an initial demand forecast new market information is gathered and demand forecast is updated using this more accurate second forecast the retailer decides the total stocking level for the selling season the second order is based on an improved demand forecast but it also involves a higher unit supply cost to determine the optimal ordering policy we use a computational procedure that entails solving capacitated multi item newsboy problems embedded within a dynamic programming model various numerical examples illustrate the effects of demand variability and financial constraint on the optimal policy it is found that existence of a budget constraint may lead to an increase in the initial order size it is also observed that as the budget available decreases the products with more predictable demand make up a larger share of the procurement expenditure

production planning in the case of uncertain individual demand extension for an mrp ii concept abstract to gain competitive advantage firms have increased their number of variants in recent years but as a consequence it has become more and more difficult to forecast demand data at the level of individual products over the planning horizon however practical experience shows that forecasts of aggregate demand are quite accurate exact data for individual products can be determined for the current but not for the remaining periods for the remaining periods only upper and lower bounds of the demand data for individual products can be predicted with certainty in many cases this means that production planning should follow a hierarchical planning concept first production planning should be conducted at the aggregate level over the planning horizon to determine simultaneously the resource requirements regular capacity and overtime and the quantities of the product groups in order to satisfy aggregate demand second for the immediate scheduling period the detailed planning level should determine how available production resources have to be allocated to the individual products subject to some constraints imposed by the aggregate plan mrp ii manufacturing resource planning is a production planning system which is based on a hierarchical concept and has been developed for such complex production situations the paper concludes that the mrp ii concept is only partially suited to production planning in the case of uncertain demand a hierarchical model which can be incorporated into the mrp ii concept is therefore proposed for uncertain demand an alternative method for uncertainty reduction is also briefly discussed

two period dynamic versus fixed ratio pricing in a capacity constrained duopoly this paper analyzes the impact of dynamic and fixed ratio pricing policies on firm profits and equilibrium prices under competition firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times in each period customers first purchase from the low price firm and then from the high price firm up to their inventories provided the prices are lower than the maximum they are willing to pay the main conclusions of this paper are as follows although dynamic pricing is a more sophisticated policy than fixed ratio pricing it may lead to decreased equilibrium profits under both pricing policies one firm assumes the role of a low cost high output firm while the other assumes the role of a high cost low output firm and the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices

dynamic pricing behavior in perishable goods markets evidence from secondary markets for major league baseball tickets sellers of perishable goods increasingly use dynamic pricing strategies as technology makes it easier to change prices and track inventory this paper tests how accurately theoretical models of dynamic pricing describe sellers behavior in secondary markets for event tickets a classic example of a perishable good it shows that the simplest dynamic pricing models describe very accurately both the pricing problem faced by sellers and how they behave explaining why sellers cut prices dramatically by 40 percent or more as an event approaches the estimates also imply that dynamic pricing is valuable raising the average seller s expected payoff by around 16 percent

optimal policies for multiechelon inventory problems with markov modulated demand this paper considers a multistage serial inventory system with markov modulated demand random demand arises at stage 1 stage 1 orders from stage 2 etc and stage n orders from an outside supplier with unlimited stock the demand distribution in each period is determined by the current state of an exogenous markov chain excess demand is backlogged linear holding costs are incurred at every stage and linear backorder costs are incurred at stage 1 the ordering costs are also linear the objective is to minimize the long run average costs in the system the paper shows that the optimal policy is an echelon base stock policy with state dependent order up to levels an efficient algorithm is also provided for determining the optimal base stock levels the results can be extended to serial systems in which there is a fixed ordering cost at stage n and to assembly systems with linear ordering costs

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

forecasting and inventory management of short life cycle products in this paper we provide an integrated framework for forecasting and inventory management of short life cycle products the literature on forecasting and inventory management does not adequately address issues relating to short life cycle products we first propose a growth model that can be used to obtain accurate monthly forecasts for the entire life cycle of the product the model avoids limiting data requirements of traditional methods instead it extracts relevant information from past product histories and utilizes the information on total life cycle sales and the peak sales timing using disguised demand data from a personal computer pc manufacturer we validate the model next we model the inventory management problem for the short life cycle environment the uncertainty in demand is modeled through the uncertainty in the realized values of the parameters of the forecasting model the high cost of terminal inventory shortages and rapidly changing procurement costs are all included in the model extensions to the basic model are also developed using optimal control theory we derive a solution that provides valuable information on procurement cutoff time and terminal service levels a detailed example explains the characteristics of the policy and its relevance in decision making many of the issues covered in the models were brought to our attention while implementing a forecasting model at a pc manufacturer the benchmark monthly forecasts and the associated inventory levels provide information that can be very helpful in planning and controlling marketing sales and production

a decision support framework for exploring supply chain tradeoffs abstract producers of retail products continually need to determine how much of a particular product to produce the difficulty of judging correctly is compounded when the product has a short production sales interval and is made primarily for sale during the big winter shopping season e g around christmas holiday in an effort to minimize production and distribution costs decision makers would like to produce as early as possible but doing so would increase the risk of producing the wrong quantity good forecasting mitigates this problem and the use of agile supply chains allows the firm to produce later in the production sales interval both however add to the cost of production if the external environment is volatile then there would be increased uncertainty as to a desirable course of action this paper presents a simulation based decision support framework for exploring the tradeoffs in producing different quantities under a variety of supply chain configurations and alternate forecasting options given uncertain demand environments we provide an illustrative example to highlight these tradeoffs

a bayesian approach to determine the value of information in the newsboy problem abstract the potential benefits of demand forecasting in a newsboy problem are to decrease the risk of overstocking or shortage but forecasting is usually not free in this paper a model to help the decision maker in a newsboy problem to assess the value of information is presented first two cases on available demand information are considered to develop an upper bound of the cost that the decision maker would spend on forecasting then a bayesian approach to forecasting is proposed and evai the expected value of additional information is computed to help the decision maker in deciding whether to use the extra information finally the relationship between the evai and model parameters is discussed

dynamic pricing in the presence of strategic consumers and oligopolistic competition we present a dynamic pricing model for oligopolistic firms selling differentiated perishable goods to multiple finite segments of strategic consumers who are aware that pricing is dynamic and may time their purchases accordingly this model encompasses strategic behavior by both firms and consumers in a unified stochastic dynamic game in which each firm s objective is to maximize its total expected revenues and each consumer responds according to a shopping intensity allocation consumer choice model we prove the existence of a unique subgame perfect equilibrium provide equilibrium optimality conditions and prove monotonicity results for special cases the model provides insights about equilibrium price dynamics under different levels of competition asymmetry between firms and multiple market segments with varying properties we demonstrate that strategic behavior by consumers can have serious impacts on revenues if firms ignore that behavior in their dynamic pricing policies moreover ideal equilibrium responses to consumer strategic behavior can recover only a portion of the lost revenues a key conclusion is that firms may benefit more from limiting the information available to consumers than from allowing full information and responding to the resulting strategic behavior in an optimal fashion

revenue management under joint pricing and capacity allocation competition abstract we investigate joint pricing and capacity allocation decisions of a duopoly each of which competes in selling a fixed amount of substitutable perishable goods in both early discount and regular full fare markets with demand uncertainty upon a firm s stockout unsatisfied demand spillovers to the competitor depending on the substitutability of products offered by the two firms we first show that there exists a pure strategy nash equilibrium for identical firms there exists a unique pure strategy nash equilibrium that is symmetric then we study how firms pricing and capacity allocation decisions depend on operational and market conditions in particular we show that more cut throat competition in the full fare market never leads to a rise in the price and a fall in the protection level simultaneously in the full fare market we demonstrate a similar result of comparative statics for the competition intensity in the discount market in comparison with a monopolist s optimal decision a duopoly equilibrium never results in a situation that definitely benefits the full fare consumers in both dimensions of price and availability finally we examine how the adoption of early discount as practiced in the airline industry may benefit competing firms when one of the two firms first introduces early discount sales we find that there is a free ride effect for the other firm interestingly the free rider can benefit more than the adopter especially with stronger competition

review of inventory systems with deterioration since 2001 abstract this paper presents an up to date review of the advances made in the field of inventory control of perishable items deteriorating inventory the last extensive review on this topic dates back to 2001 goyal s k and giri b c recent trends in modeling of deteriorating inventory european journal of operational research 134 1 16 since then over two hundred articles on this subject have been published in the major journals on inventory control indicating the need for a new review we use the classification of goyal and giri based on shelf life characteristics and demand characteristics contributions are highlighted by discussing main system characteristics including price discounts backordering or lost sales single or multiple items one or two warehouses single or multi echelon average cost or discounted cash flow and payment delay

efficient supply contracts for fashion goods with forecast updating and two production modes we examine the problem of developing supply contracts that encourage proper coordination of forecast information and production decisions between a manufacturer and distributor of high fashion seasonal products operating in a two mode production environment the first production mode is relatively cheap but requires a long lead time while the second is expensive but offers quick turnaround we focus on contracts of the form w1 w2 b wherewi is the wholesale price offered for production modei andb is a return price offered for items left over at the end of the season we find that such a contract can coordinate the manufacturer and distributor to act in the best interest of the channel the pricing conditions needed to ensure an efficient solution vary depending on the degree of demand forecast improvement between periods and the manufacturer s access to forecast information we also examine whether these conditions ensure a pareto optimal solution with respect to two traditional production settings

pre season stocking and pricing decisions for fashion retailers with multiple information updating abstract motivated by the industrial practice we investigate in this paper the pre season inventory and pricing decisions for fashion retailers before the selling season a retailer can place orders for a seasonal fashion product from her supplier at two distinct stages via two different delivery modes market information from the sales of a pre seasonal product is collected and used to update the demand forecast of the seasonal product at the succeeding stages by using bayesian approach we formulate a dynamic optimization problem and obtain the optimal stocking policy after the ordered seasonal product has arrived and just before the start of the selling season the retailer can determine the optimal selling price of the product with respect to the latest demand information and the amount of product on hand we study the pricing policy under different objectives sensitivity analysis is carried out and the features of the policies are revealed managerial insights are generated

the folk theorem with imperfect public information the authors study repeated games in which players observe a public outcome that imperfectly signals the actions played they provide conditions guaranteeing that any feasible individually rational payoff vector of the stage game can arise as a perfect equilibrium of the repeated game with sufficiently little discounting the central condition requires that there exist action profiles with the property that for any two players no two deviations one by either player give rise to the same probability distribution over public outcomes the results apply to principal agent partnership oligopoly and mechanism design models and to one shot games with transferable utilities copyright 1994 by the econometric society

inventory control in a fluctuating demand environment we present an inventory model where the demand rate varies with an underlying state of the world variable this variable can represent economic fluctuations or stages in the product life cycle for example we derive some basic characteristics of optimal policies and develop algorithms for computing them in addition we show that certain monotonicity patterns in the problem data are reflected in the optimal policies

strategic investments trading and pricing under forecast updating this paper considers two independent firms that invest in resources such as capacity or inventory based on imperfect market forecasts as time progresses and new information becomes available the firms update their forecasts and have the option to trade their resources the trade contract is determined as the bargaining equilibrium or alternatively as the price equilibrium assuming a fairly general form of the profit functions we characterize the nash equilibrium investment levels which are first best under the price equilibrium trade contract but not under the bargaining equilibrium trade contract to gain additional insights we then focus on firms that face stochastic demand functions with constant price elasticity and have contingent pricing power assuming a general forecast evolution process we characterize the impact of the option to trade and the firms cooperation on equilibrium investments expected prices profits and consumer surplus finally to study the main driving forces of trading we employ a well established and empirically tested forecast updating model in which the forecast evolution process follows a two dimensional geometric brownian motion under this model we prove that the equilibrium investments expected prices profits and consumer surplus are nondecreasing in the quality and timing of forecast revisions in market variability and in foreign exchange volatility but are nonincreasing in market correlation

a periodic review inventory model with demand influenced by promotion decisions in this paper we use a markov decision process mdp to model the joint inventorypromotion decision problem the state variable of the mdp represents the demand state brought about by changing environmental factors as well as promotion decisions the demand state in a period determines the distribution of the random demand in that period optimal inventory and promotion decision policies in the finite horizon problem are obtained via dynamic programming under certain conditions we show that there is a threshold inventory level p for each demand state such that if the threshold is exceeded then it is desirable to promote the product for the proportional ordering cost case the optimal inventory replenishment policy is a base stock type policy with the optimal base stock level dependent on the promotion decision

dynamic pricing competition with strategic customers under vertical product differentiation we consider dynamic pricing competition between two firms offering vertically differentiated products to strategic customers who are intertemporal utility maximizers we show that price skimming arises as the unique pure strategy markov perfect equilibrium in the game under a simple condition our results highlight the asymmetric effect of strategic customer behavior on quality differentiated firms even though the profit of either firm decreases as customers become more strategic the low quality firm suffers substantially more than the high quality firm furthermore we show that unilateral commitment to static pricing by either firm generally improves profits of both firms interestingly both firms enjoy higher profit lifts when the high quality firm commits rather than when the low quality firm commits this paper was accepted by yossi aviv operations management

an inventory model with deteriorating items under inflation when a delay in payment is permissible abstract this study develops an inventory model for initial stock dependent consumption rate when a delay in payment is permissible in the inventory model shortages are not allowed the effect of the inflation rate deterioration rate initial stock dependent consumption rate and delay in payment are discussed in the study mathematical models are also derived under two different circumstances i e case i the credit period is less than or equal to the cycle time for settling the account and case ii the credit period is greater than the cycle time for settling the account besides expressions for an inventory system s total cost are derived for these two cases moreover a computational procedure and gino lasdon et al acm transactions mathematical software 4 1978 34 50 are proposed to obtain the optimal order size and cycle time the results can help managers determine the optimal total cost finally a numerical example demonstrates the applicability of the proposed model

pollution accumulation and abatement policy in a supply chain abstract this paper seeks to determine how the double marginalization phenomenon affects the tradeoff between polluting emissions and abatement activities related to pollution accumulation in a supply chain composed of one manufacturer and one retailer the environmental consequence of this inefficiency which emerges in a non cooperative vertical setting governed by a single parameter contract is overlooked in the literature on pollution control in the setup of a two stage game we investigate the impact of double marginalization for non cooperative equilibrium to check whether there are differences between dynamic and strategic effects of double marginalization on pollution accumulation both the open loop and feedback nash equilibria are derived over a finite time horizon with the cooperative solution as a benchmark

a monopolistic and oligopolistic stochastic flow revenue management model this paper studies a one shot inventory replenishment problem with dynamic pricing the customer arrival rate is assumed to follow a geometric brownian motion homogeneous customers have an isoelastic demand function and do not behave strategically we find a closed form optimal pricing policy which utilizes current demand information under this pricing policy the inventory trajectory is deterministic and a retailer sells all inventory we show that dynamic pricing coordinated with the inventory decision achieves significantly higher profits than does static pricing furthermore under oligopolistic competition we establish a weak perfect bayesian equilibrium for the price and inventory replenishment game we find the pricing equilibrium to be cooperative even in a noncooperative environment but that inventory competition results in overstock and damages profits finally we examine the trade off between dynamic pricing and price precommitment and find that flexible pricing is still beneficial provided competition is not too intense

inventory decisions for emergency supplies based on hurricane count predictions abstract this paper addresses a stochastic inventory control problem for manufacturing and retail firms who face challenging procurement and production decisions associated with hurricane seasons specifically the paper presents a control policy in which stocking decisions are based on a hurricane forecast model that predicts the number of landfall hurricanes for an ensuing hurricane season the multi period inventory control problem is formulated as a stochastic programming model with recourse where demand during each pre hurricane season period is represented as a convolution of the current period s demand and an updated estimate of demand for the ensuing hurricane season due to the computational challenges associated with solving stochastic programming problems recent scenario reduction techniques are discussed and illustrated through an example problem the proposed model specifies cost minimizing inventory strategies for simultaneously meeting stochastic demands that occur prior to the hurricane season while proactively preparing for potential demand surge during the season

a duopoly model of pricing for inventory liquidation abstract we consider the problem of pricing to liquidate inventory in a duopoly the problem is modelled as a game with complete information the unique nash equilibrium for the game which is also sequential involves mixed strategies for the sellers the equilibrium extends in a limited fashion to multi period and many seller situations

competitive dynamic pricing with alternating offers theory and experiment abstract we propose an equilibrium model of duopolistic dynamic pricing in which a buyer alternates between two sellers for price offers over a finite time horizon the game ends when the buyer accepts a price offer or the selling season is over whichever comes first previous research granot et al 2007 shows that there are successive markdowns in equilibrium when the buyer is commonly known to be myopic our analysis suggests that when she is known to be strategic price offers over the entire selling season are constant moreover lengthening the season increases generally decreases both sellers profits when the buyer is myopic strategic an experimental study largely supports the equilibrium predictions when the buyer is myopic but not when she is strategic in the latter case early in the season sellers overprice the good arguably in an attempt to effectively shorten the season and thereby increase their profits

introduction to repeated games with private monitoring abstract we present a brief overview of recent developments in discounted repeated games with imperfect private monitoring the literature explores the possibility of cooperation in a long term relationship where each agent receives imperfect private information about the opponents actions although this class of games admits a wide range of applications such as collusion under secret price cutting exchange of goods with uncertain quality and observation errors it has fairly complex mathematical structure due to the lack of common information shared by players this is in sharp contrast to the well explored case of repeated games under public information with the celebrated folk theorems and until recently little had been known about the private monitoring case however rapid developments in the past few years have revealed the possibility of cooperation under private monitoring for some class of games journal of economic literature classification numbers c72 c73 d43 d82 l13 l41

capital utilization economic growth and convergence abstract optimal decisions by economic agents regarding the utilization of capital lead to empirically plausible speeds of convergence in one sector models of economic growth the relationship between depreciation and capital utilization plays a crucial role in slowing down convergence to the steady state cross country differences in the extent to which the capital utilization decision is internalized along the transition path may lead to differences in convergence rates even for countries with similar initial and terminal conditions finally by assuming a constant depreciation rate and full capital utilization standard growth models may be overstating the magnitude of the steady state equilibrium

hierarchical model for production planning in the case of uncertain demand the paper deals with hierarchical production planning for a multiperiod model consisting of an aggregate planning level and a detailed planning level in the case of uncertain demand at the beginning the detailed demand for the actual planning period is known whereas for future planning periods only upper and lower bounds of detailed demand are known on the other hand the aggregate demand on the product group level is supposed to be deterministic at each planning period over the whole planning horizon for the aggregate planning level robust production plans i e aggregate production plans which can be disaggregated to a feasible detailed plan for every possible detailed demand are proposed and a consistent disaggregation is executed for the detailed planning level two sets static and dynamic of sufficient conditions for robustness of the aggregate plan as well as dynamic disaggregation conditions are derived these sufficient conditions are a generalization of the results of lasserre and merce the performance of the sufficient conditions are demonstrated by a computational study which shows the potential advantage of the approach

determining the production order of two seasonal products under capacity constraint abstract in this paper the production sequence of two seasonal products is analyzed when the parameters of demand forecasts are not certainly known in advance the accuracy of these forecasts improves as the season is approached however the expected demand remains a probability variable when production decisions are made on the production order and volume of the products at the beginning of the planning horizon the novel side of the approach applied in this paper is a capacity constraint inserted into the analyses in which the production volume depends on a probability variable namely on the expected demand

on the risk based aggregate planning for seasonal products in this paper a model is developed to analyze the effect of risk incurring at companies producing highly seasonal products according to observations the closer to the season we are the better our knowledge on demand distribution this fact is reflected by a learning effect in demand distribution applied in the model where the aim is to minimize the risk connected costs originating from the unpredictable behavior of demand the paper confirms that unpredictability is only one of the decisive factors in sequencing products and other elements play an important role too the paper presents forward and backward procedures for determining the production quantities and sequencing of the products in an aggregate planning horizon

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

optimal pricing and ordering policy under permissible delay in payments abstract many researchers have assumed that the selling price is the same as the purchase cost and developed various eoq models for a retailer when the supplier offers a permissible delay in payments in this paper we complement the shortcoming of their models by considering the difference between the selling price and the purchase cost we then develop an algorithm for a retailer to determine its optimal price and lot size simultaneously when the supplier offers a permissible delay in payments our theoretical result contradicts to their conclusion that the economic replenishment interval and order quantity generally increases marginally under the permissible delay in payments

joint pricing and inventory policies for make to stock products with deterministic price sensitive demand abstract in this paper we focus on a firm selling a single make to stock product to price sensitive end customers we develop an integrated operations marketing model that can help determine the relevant profit maximizing decision variable values for two pricing policies that the firm might follow price as a decision variable which is advocated by academicians and mark up pricing used by most practitioners we first consider an eoq based model with price and order quantity as independent decision variables we then develop an analogous model where price is a mark up over operating costs per unit and order quantity becomes the sole decision variable we are able to ascertain the optimal decision variable values for each model for log linear and linear demand functions we prove that for such profit maximizing models the optimal batch size is not necessarily monotone increasing in set up cost interestingly our numerical analytical evidence suggests that from a profit perspective it is better for managers to be aggressive on price rather than reducing price too much especially for highly price sensitive and non linear demand moreover we establish that in general the profit penalty for not including inventory costs in determining the optimal batch size or ignoring the batch size optimization issue in a mark up price model is not significant only when the set up cost is quite high and or the firm faces non linear demand from highly price sensitive end consumers does it become crucial for managers to determine the exact optimal batch size and base the mark up price on the entire unit operating cost not only the unit variable production cost

fund flow versus flow flow in production theory reflections on georgescu roegen s contribution abstract the paper discusses nicholas georgescu roegen s contribution to production theory comparing it with the contributions of john von neumann and piero sraffa and emphasizing the problem of the choice of technique it is shown that georgescu roegen s fund flow approach in which fixed capital is taken to be an immutable agent can be misleading and cannot address issues that are easily handled by the alternative flow flow approach that reduces fixed capital to circulating within a joint products framework and allows adequate treatment of the wear and tear of machines as well as the problem of capital utilization

production planning of style goods with high setup costs and forecast revisions in this paper we study a problem common to a wide variety of manufacturing companies of determining the production schedule of style goods such as clothing and consumer durables under capacity constraints demand for items is stochastic and occurs in the last season of the planning horizon demand estimates are revised in each period we exploit the problem s two level hierarchical structure which is characterized by families and items production changeover costs from one family to another are high compared to other costs however changeover costs between items in the same family are negligible we first formulate this problem as a difficult to solve stochastic mixed integer programming problem then exploiting the problem s hierarchical structure we formulate a deterministic mixed integer programming problem and solve it by means of an algorithm that provides an approximate solution a lower bound is obtained by applying generalized linear programming to the approximate problem we illustrate the procedure using the disguised data of a consumer electronics company the computational results demonstrate the effectiveness of the proposed approach in a practical setting

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

optimal ordering and pricing in a quick response system quick response systems enable retailers to estimate customer demand more accurately and improve stocking decisions for perishable products with uncertain demand retailers place separate orders for a product at two different times before the selling season following the initial order additional market information is obtained and the second order amount is decided based on an improved demand forecast in some cases purchase cost associated with the second order is uncertain and demand for the product during the season depends on the selling price we present a solution procedure for finding the optimal order quantity and selling price in this setting we also study the case where any desired portion of the initial order can be cancelled after updating the demand forecast in the numerical study the optimal price is observed to be relatively insensitive to changes in demand variability

a simulation framework for forecasting uncertain lumpy demand abstract managing uncertainty when the demand is irregular and sporadic i e lumpy is a complex issue as well as an unexplored one this study analyses the behaviour of forecasting techniques when dealing with lumpy demand at the master production scheduling level in particular three forecasting techniques exponentially weighted moving average early sales and order overplanning are considered it is argued that demand lumpiness is a multidimensional phenomenon generated by different market characteristics namely numerousness of customers heterogeneity of customers frequency of order placing variety of each customer s request and correlation between customers behaviour hence the performances of the three forecasting methods are compared through simulation experiments with different values of the sources of lumpiness a framework is then proposed that indicates the domain of applicability of each forecasting technique according to the prevailing source of lumpiness in the market

a stochastic sequencing problem for style goods with forecast revisions and hierarchical structure this paper addresses the problem of simultaneously determining a production sequence and production volumes of style goods style goods have one selling season per year during the rest of the year manufacturers of style goods build up the inventory while continuously reestimating the demand in the final selling season in this problem products have a two stage hierarchy items and families the production of a family is assumed to be nonpreemptive exploiting the hierarchical structure we formulate the problem as a two stage stochastic sequencing problem the stochastic aggregate sequencing problem and the stochastic disaggregation problem to solve the stochastic aggregate sequencing problem a simple heuristic solution procedure is developed that accounts for the forecast revisions and provides a lower bound on the optimal value the heuristic is tested using the disguised data obtained from a consumer electronics company the computational results demonstrate the applicability of the proposed procedure

dynamic pricing in the presence of inventory considerations research overview current practices and future directions the benefits of dynamic pricing methods have long been known in industries such as airlines hotels and electric utilities where the capacity is fixed in the short term and perishable in recent years there has been an increasing adoption of dynamic pricing policies in retail and other industries where the sellers have the ability to store inventory three factors contributed to this phenomenon 1 the increased availability of demand data 2 the ease of changing prices due to new technologies and 3 the availability of decision support tools for analyzing demand data and for dynamic pricing this paper constitutes a review of the literature and current practices in dynamic pricing given its applicability in most markets and its increasing adoption in practice our focus is on dynamic intertemporal pricing in the presence of inventory considerations

capital utilization and factor specificity in this study a model of firm behavior that allows the level of capital utilization to be optimally chosen by cost minimizing firms is embedded into the standard specific factors model employed in the international trade literature the resulting generalization of the specific factors model provides several new insights for instance allowing for variable utilization in either or both sectors gives rise to a greater variety of possible trade patterns than forcing utilization to remain constant similarly international differences in the willingness to work during abnormal hours generate a wider variety of trade patterns than are possible in the standard specific factors model finally this model allows a reconciliation of the dual scarcity explanation of the nineteenth century anglo american pattern of trade with the historical evidence on levels of utilization

multi level approaches to demand management in complex environments an analytical model abstract recent studies have shown that as demand becomes irregular and complex i e lumpy a possible approach for managing such uncertainty is to collect information directly from customers this implies that the sales units have to move closer to customers analyse their likely requirements and collect quantitative and structured data as well as qualitative and subjective insights however as integration with individual customers increases and data collection capabilities improve the organisational configuration of most companies becomes ever more complex and the aggregation of forecasts more difficult this paper discusses two approaches to managing demand uncertainty in complex environments in the first termed decentralised order overplanning sales units are responsible for forecasting the demand of each customer and defining requirements in the second termed centralised order overplanning forecasts provided by sales units are aggregated and further elaborated by manufacturing to define item requirements by means of an analytical model which describes the forecasting and planning process as a bayesian markovian process we show that the centralised method out performs the decentralised approach by virtue of the ability to exploit the additional information provided by commonalities between customers requests however this advantage has to be balanced against organisational costs since the centralised method splits responsibilities for forecasting and slack control between sales and manufacturing units major conflicts are likely to arise the focus and commitment on forecasting accuracy may be compromised and information may be lost when individual forecasts are sent to the manufacturing unit

a continuous time dynamic pricing model knowing the competitor s pricing strategy abstract in this paper we consider a dynamic pricing model for a firm knowing that a competitor adopts a static pricing strategy we establish a continuous time model to analyze the effect of dynamic pricing on the improvement in expected revenue in the duopoly we assume that customers arrive to purchase tickets in accordance with a geometric brownian motion we derive an explicit closed form expression for an optimal pricing policy to maximize the expected revenue it is shown that when the competitor adopts a static pricing policy dynamic pricing is not always effective in terms of maximizing expected revenue compared to a fixed pricing strategy moreover we show that the size of the reduction in the expected revenue depends on the competitor s pricing strategy numerical results are presented to illustrate the dynamic pricing policy

an economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity abstract to attract more sales suppliers frequently offer a permissible delay in payments if the retailer orders more than or equal to a predetermined quantity w in this paper we generalize goyal s k 1985 eoq under conditions of permissible delay in payments journal of the operational research society 36 335 338 economic order quantity eoq model with permissible delay in payment to reflect the following real world situations 1 the retailer s selling price per unit is significantly higher than unit purchase price 2 the interest rate charged by a bank is not necessarily higher than the retailer s investment return rate 3 many items such as fruits and vegetables deteriorate continuously and 4 the supplier may offer a partial permissible delay in payments even if the order quantity is less than w we then establish the proper mathematical model and derive several theoretical results to determine the optimal solution under various situations and use two approaches to solve this complex inventory problem finally a numerical example is given to illustrate the theoretical results

on the utilisation controversy a rejoinder and some comments the critique by gahn and gonzalez 2019 of the conclusions in nikiforos 2016 regarding what data should be used to evaluate whether capacity utilization is endogenous to demand is weak for the following reasons i the federal reserve board frb measure of utilization is not appropriate for measuring long run variations of utilization because of the method and purpose of its construction even if its difference from the measures of the average workweek of capital aww were trivial this would still be the case if anything it would show that the aww is also an inappropriate measure ii gahn and gonzalez choose to ignore the longest available estimate of the aww produced by foss which has a clear long run trend iii their econometric results are not robust to more suitable specifications of the unit root tests under these specifications the tests overwhelmingly fail to reject the unit root hypothesis iv other estimates of the aww which were not included in nikiforos 2016 confirm these conclusions v for the comparison between the aww series and the frb series they construct variables that are not meaningful because they subtract series in different units when the comparison is done correctly the results confirm that the difference between the aww series and the frb series has a unit root vi a stationary utilization rate is not consistent with any theory of the determination of capacity utilization even if demand did not play a role there is no reason to expect that all the other factors that determine utilization would change in a fashion that would keep utilization constant