buyer power with atomistic upstream entry can downstream consolidation increase production and welfare abstract this paper investigates the effects of buyer power on entry into an atomistic upstream market and economic welfare under reasonable market conditions we show that industries with a few buyers induce more upstream entry than industries with a larger number of firms in particular monopsony can be more conducive to entry and lead to higher social welfare than more fragmented industry structures this seeming paradox arises because a single buyer better internalizes the positive effects of entry on later periods supply conditions than a collection of firms this result is relevant in a number of market settings including markets for specialized labor and processing markets for agricultural products

channel coordination and quantity discounts this paper presents a model for analyzing the impact of joint decision policies on channel coordination in a system consisting of a supplier and a group of homogeneous buyers the joint decision policy characterized by the unit selling price and the order quantity is coordinated through quantity discounts and franchise fees both the annual demand rate and the operating cost including the purchase ordering and inventory holding costs depend on the joint decision policy employed this paper contributes by integrating work addressing quantity discounts on inventory and ordering policies and work focusing on the control mechanism provided by quantity discounts in channel coordination it is shown that the optimal all unit quantity discount policy is equivalent to the optimal incremental quantity discount policy in achieving channel coordination furthermore it is shown that quantity discounts alone are not sufficient to guarantee joint profit maximization the analyses of the general models are illustrated by specific analytical results obtained for a given demand function

strong planning and forecast horizons for a model with simultaneous price and production decisions abstract in this paper we have solved a general inventory model with simultaneous price and production decisions both linear and non linear strictly convex production cost cases are treated upper and lower bounds are imposed on state as well as control variables the problem is solved by using the lagrangian form of the maximum principle strong planning and strong forecast horizons are obtained these arise when the state variable reaches its upper or lower bound the existence of these horizons permits the decomposition of the whole problem into a set of smaller problems which can be solved separately and their solutions put together to form a complete solution to the problem finally we derive a forward branch and bound algorithm to solve the problem the algorithm is illustrated with a simple example

spatial price discrimination in agricultural product procurement markets a computational economics approach significant transport costs and spatially distributed supply and processing create oligopsony power in agricultural markets price discrimination expressed in the form of partial or complete absorption of freight charges by processors is often observed in these environments but we understand little about how these pricing decisions are made analytical approaches are often intractable as an alternative we propose a computational economics approach to analyze a general spatial competition model and study firms choices of spatial pricing policy instead of the commonly presumed free on board pricing we find that buyers choose price discrimination either through uniform delivered pricing or through partial freight absorption

transfer pricing in a dynamic marketing operations interface abstract a transfer price mechanism is proposed to coordinate the strategies of the marketing and operations functional areas operating in a dynamic interface environment in a decentralized firm marketing and operations are strategic decision makers in a differential game in which marketing has price and advertising and operations has production as control variables and advertising goodwill and production backlog are state variables a constant transfer price is entered into the objective functionals for marketing and operations and subgame perfect feedback strategies are derived for price advertising and production as functions of the state variables the feedback strategies allow a solution for the dynamic system involving goodwill and backlog and the total payoff to the firm the sum of the payoffs to marketing and operations is determined as a function of the transfer price finally for certain parameter conditions an interior maximum of the payoff function is achieved and the optimal transfer price is identified

mixed equilibria are unstable in games of strategic complements in games with strict strategic complementarities properly mixed nash equilibria equilibria that are not in pure strategies are unstable for a broad class of learning dynamics

the competitive implications of top of the market and related contract pricing clauses this article examines the competitive implications of contract pricing arrangements which link the contract price to the subsequent cash price we focus on so called top of the market pricing tomp in cattle procurement the tomp clause is shown to have anticompetitive consequences when the same buyers who purchase contract cattle with the tomp clause also compete to procure cattle in the subsequent spot market the tomp clause reduces packers incentives to compete aggressively in the spot market although tomp pricing is not in producers collective interest rational sellers may nonetheless sign these contracts with little or no financial inducement

learning behavior and mixed strategy nash equilibria abstract the paper considers whether an adaptive justification like those commonly available for non interactive optimization models can be found for the mixed strategy nash equilibrium although it is known that such a justification is frequently available for pure strategy equilibria it is shown that all members of a wide class of behaviorally plausible learning mechanisms must fail to converge in almost all games in which the equilibrium involves mixed strategies an exact formal analogy is developed which allows these learning mechanisms to be viewed as discrete ta tonnement processes in properly chosen competitive exchange economies in the analogy the instability derives from the independence of excess demand functions except at the boundaries from own prices this independence arises because of the linearity in probabilities of von neumann morgenstern risk preferences and therefore does not extend to pure strategy equilibria in general thus assuming that agents will play equilibrium strategies implicitly assumes more sophistication when the equilibrium involves mixed strategies than when it involves only pure strategies

assessing the importance of oligopsony power in agricultural markets oligopoly competition among few sellers is the cornerstone of industrial organization io conversely its sister concept oligopsony competition among few buyers is scarcely mentioned for example oligopsony is not discussed in the entire two volume handbook of industrial organization and monopsony is mentioned only in the context of incentives to integrate vertically two reasons apparently account for io economists lack of interest in buyer market power i they don t think it s very important and ii they don t believe it presents any unique modeling issues relative to seller market power scherer and ross illustrate this first viewpoint arguing that average concentration on the buyers side in manufacturing is undoubtedly lower than seller concentration p 519 tirole in his masterful treatise on io theory illustrates the second dispatching monopsony power in one sentence naturally the conclusions regarding monopoly power would also hold as well for monopsony power p 65 we argue that this dismissive treatment of buyer market power is not reasonable for economists interested in agriculture and agricultural markets the scherer and ross viewpoint may apply when considering generic inputs such as labor capital and energy competition for these inputs is apt to exceed competition for the outputs they produce because firms cross product market boundaries to compete for these inputs and there is essentially no branding among input buyers to diminish price competition among them moreover these inputs are typically mobile hence in elastic supply to individual buyers limiting the exercise of oligopsony power even in geographic settings where relatively few buyers prevail this view of input markets does not apply however to first handler markets for the raw agricultural commodities that are inputs into the processed or fresh packed food products we identify the following distinctive structural characteristics of these markets

optimal pricing policy in the presence of experience effects i introduction in this paper we analyze the problem of optimal intertemporal pricing for a monopolist when cur rent and past output affect future cost and or demand conditions through experience in production and or in consumption learning by doing the experience curve contagion habit formation bandwagon and snob effects are all examples of terminologies used to describe such situations we call these experience effects for convenience and explore profit maximizing pricing behavior when such effects exist in the traditional profit maximization model a firm chooses the price output combination so as to maximize short run i e current profits the familiar mc mr equality given that price is higher than average variable cost and a nonbind ing capacity constraint is a necessary condition for price takers as well as price makers this as sumes that the current pricing decision has no bearing on the future so that long run profit is maximized by a series of short run maximizing

the marketing channel as an equilibrium set of contracts nash bargaining theory and recent developments in economic contract theory are employed in the analysis of the marketing channels individual dyadic contracts involving payment schedules between members of a simple 3 level channel are investigated with particular reference to monitoring problems and intrachannel power relations the interrelations between individual contracts are examined and the equilibrium set of contracts constituting the channel derived the performance of the channel in terms of risk sharing allocative efficiency and the distribution of gains is then evaluated it is found that the risk aversion of channel members and the cost of monitoring and enforcement affect channel efficiency and that under certain types of interdependencies and externalities the nature of the power structure is crucial to channel efficiency

a supply chain under limited time promotion the effect of customer sensitivity abstract we consider a two echelon supply chain with a supplier and a retailer facing stochastic customer demands the supplier is a leader who determines a wholesale price in response the retailer orders products and sets a price which affects customer demands the goal of both players is to maximize their profits we find the stackelberg equilibrium and show that it is unique not only when the supply chain is in a steady state but also when it is in a transient state induced by a supplier s promotion there is a maximum length to the promotion however beyond which the equilibrium ceases to exist moreover if customer sensitivity increases then the wholesale equilibrium price decreases product orders increase and product prices drop this effect well observed in real life does not however necessarily imply that the promotion is always beneficial conditions for the profitability of a limited time promotion are shown and analyzed numerically we discuss both open loop and feedback policies and derive the conditions necessary for them to remain optimal under stochastic demand fluctuations

managing channel profits a channel of distribution consists of different channel members each having his own decision variables however each channel member s decisions do affect the other channel members profits and as a consequence actions a lack of coordination of these decisions can lead to undesirable consequences for example in the simple manufacturer retailer consumer channel uncoordinated and independent channel members decisions over margins result in a higher price paid by the consumer than if those decisions were coordinated in addition the ensuing suboptimal volume leads to lower profits for both the manufacturer and the retailer this paper explores the problems inherent in channel coordination we address the following questions what is the effect of channel coordination what causes a lack of coordination in the channel how difficult is it to achieve channel coordination what mechanisms exist which can achieve channel coordination what are the strengths and weaknesses of these mechanism what is the role of nonprice variables e g manufacturer advertising retailer shelf space in coordination does the lack of coordination affect normative implications from in store experimentation can quantity discounts be a coordination mechanism are some marketing practices actually disguised quantity discounts we review the literature and present a simple formulation illustrating the roots of the coordination problem we then derive the form of the quantity discount schedule that results in optimum channel profits this article was originally published in marketing science volume 2 issue 3 pages 239 272 in 1983

on the learning and stability of mixed strategy nash equilibria in games of strategic substitutes abstract this paper analyzes the learning and stability of mixed strategy nash equilibria in games of strategic substitutes gss complementing recent work done in the case of strategic complements gsc mixed strategies in gss are of particular interest because it is well known that such games need not exhibit pure strategy nash equilibria first we establish bounds on the strategy space which indicate where randomizing behavior may occur in equilibrium second we show that mixed strategy nash equilibria are generally unstable under a wide variety of learning rules multiple examples are given

distinguishing the source of market power structural models used to measure market power though widely employed continue to be criticized we compare alternative market power tests including nonparametric and solow residual based srb tests we develop srb methods that permit nested testing for both monopolistic and monopsonistic market power by the same firm these tests and a set of nonparametric tests are implemented to examine market power exertion by u s cigarette manufacturers from 1977 to 1993 all tests indicate that cigarette manufacturers exerted monopsonistic power in the upstream tobacco market they are mixed on whether monopolistic power exertion was exerted in the downstream market

learning a mixed strategy equilibrium in the laboratory abstract this paper examines a laboratory game with no pure strategy equilibrium and one mixed strategy equilibrium a simple adaptive model describes players strategy adjustments reasonably well as long as predictable adjustments are not easily exploited by others consistent with theory these adjustments do not lead players to equilibrium when predictable adjustments are made more easily exploited players deviate from adaptive adjustments in order to avoid exploitation and exploit others these deviations cause players to converge more strongly to equilibrium these results confirm both the predictive power of adaptive models in some settings and the instability of mixed strategy equilibria

resource allocation to defensive marketing and manufacturing strategies abstract in this paper we investigate the coordinated use of marketing and manufacturing strategies to formulate a defensive business strategy for an incumbent firm upon market entry while defensive marketing strategies have been researched extensively little has been done on defensive manufacturing strategies and even less on coordinating these two we propose a formulation for the joint formation of a defensive strategy by the marketing and production functions under budget constraint considerations the incumbent firm may allocate its resourcesto advertising and distribution expenditures as well as to manufacturing investments to reduce the unit production cost the incumbent firm has also the option of simply allocating all of its resources purely to advertising and distribution we show that while there exist cases where the optimal reaction to entry involves investments in manufacturing improvements there are also cases where defense is in marketing strategies alone we identify the market conditions that promote such reactions to entry and also provide sensitivity analysis

an experiment to evaluate bayesian learning of nash equilibrium play abstract we report on an experiment designed to evaluate the empirical implications of jordan s model of bayesian learning in games of incomplete information a finite example is constructed in which the model generates unique predictions of subjects choices in nearly all periods when the true game defined by players private information was one with a unique equilibrium in pure strategies the experimental subjects play converged to the equilibrium as jordan s theory predicts even when the subjects had not attained complete information about one another but when there were two pure strategy equilibria the theory s predictions were not consistent with observed behavior journal of economic literature classification numbers d83 c72 c92

optimal production purchasing and pricing a differential game approach abstract this paper deals with a problem of determining optimal production and pricing policies of a manufacturing firm which is supplying a retailer the latter faces a price dependent demand function towards the final consumers and wishes to determine optimal purchasing and pricing policies both firms carry inventories and backlogging is permitted the problem is modelled as a two player nonzero sum differential game with the inventory levels as the state variables the controls are the rates of production and purchasing as well as the prices assuming linear production costs but convex ordering and holding costs open loop nash controls are characterized by using switching point analysis as well as phase diagrams

on credible delegation by oligopolists a discussion of distribution channel management several papers in the recent marketing literature have suggested that delegation in distribution e g the use of independent middlemen helps manufacturers to precommit strategically to profit enhancing competitive actions further the literature suggests that the profitability of such actions depends on market structure we challenge these conclusions here this is done in two steps first we perform an analysis of the entire class of models which have been used in the literature using internally consistent assumptions about market structure and contracting the only subgame perfect equilibrium is one in which all distribution channels have infinitely many levels of delegation obviously this is not what we see in the real world next we relax a key hidden assumption namely that all intra channel agreements are observable to competitors without this assumption the usual results unravel unless channel members can offer credible guarantees that unobservable agreements do not exist the strategic effects of delegation disappear since these guarantees are virtually impossible to maintain credibly we would expect to reject the hypothesis in the earlier literature relating channel structure to competition in an empirical study controlling for observability we conclude that mechanisms other than strategic ones must be responsible for the existence of delegated channels and make some suggestions about promising avenues for future theory research in channel structure

strategic decentralization in channels the purpose of this paper is to understand the effect of strategic interaction on a manufacturer s channel structure decision in the model i analyze if there were no strategic interaction then the manufacturer would prefer vertical integration to decentralization with strategic interaction however decentralization can be a nash equilibrium strategy as mcguire and staein mcguire timothy richard staelin 1983a an industry equilibrium analysis of downstream vertical integration marketing sci 2spring 161 192 showed so the question arises what is it about strategic interaction that makes decentralization a nash equilibrium strategy the answer i give is that strategic interaction makes it possible for a manufacturer s retail demand curve to rise when he decentralizes i show that this raising of the demand curve on decentralization can happen only if one of the following mutually exclusive conditions is satisfied 1 the manufacturers products are demand substitutes at the retail level and strategic complements at the manufacturer or retailer levels 2 the manufacturer s products are demand complements at the retail level and strategic substitutes at the manufacturer or retailer levels strategic complementarity at the retailer manufacturer level means that if one retailer manufacturer raises his price then the other retailer manufacturer would raise his price as well strategic substitutability is just the opposite these results show that what is important for decentralization to occur is not how demand substitutable the two manufacturers products are as one might have thought from earlier works in the literature but rather the nature of coupling between demand dependence and strategic dependence

differential game models in management science abstract this paper reviews a number of differential games applications to management science and operations research problems published with a few exceptions during the last decade the purpose of the article is to provide the reader with an up to date account of the state of the art within this field after having stated in an introduction the general differential games framework as well as some conceptual problems we proceed to review the models which have been divided into the following functional areas investment consumption and employment production inventories and maintenance marketing advertising pricing and rd bargaining natural resources and pollution the survey concludes with some remarks on applicability solvability and directions for future research

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

competition and outsourcing with scale economies scale economies are commonplace in operations yet because of analytical challenges relatively little is known about how firms should compete in their presence this paper presents a model of competition between two firms that face scale economies i e each firm s cost per unit of demand is decreasing in demand a general framework is used which incorporates competition between two service providers with price and time sensitive demand a queuing game and competition between two retailers with fixed ordering costs and pricesensitive consumers an economic order quantity game reasonably general conditions are provided under which there exists at most one equilibrium with both firms participating in the market we demonstrate in the context of the queuing game that the lower cost firm in equilibrium may have a higher market share and a higher price an enviable situation we also allow each firm to outsource their production process to a supplier even if the supplier s technology is no better than the firms technology and the supplier is required to establish dedicated capacity so the supplier s scale can be no greater than either firm s scale we show that the firms strictly prefer to outsource we conclude that scale economies provide a strong motivation for outsourcing that has not previously been identified in the literature

monopolist pricing with dynamic demand and production cost this paper deals with pricing of a new product over time by a monopolist who maximizes the discounted profit stream the interdependency of cost and demand on cumulative production makes the problem inherently dynamic cost is assumed to be declining with cumulative production learning curve effect while demand is a function of price and cumulative sales representing word of mouth and saturation effects the paper addresses this problem in a general framework that includes several previous results as special cases and provides new insights in other situations while the learning curve and word of mouth effect cause prices to be lower than the price that maximizes immediate revenues the saturation factor has the opposite effect the price path over time is affected by these factors and the interest rate we characterize the price path under several different situations and interpret the results for policy guidelines

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

price floors and technical inefficiency in india s sugar processing industry in india cane is processed into sugar by cooperatives public enterprises and private for profit firms the indian government sets a unique floor price for each processor that is increasing in the firm s effectiveness in converting cane into sugar the floor price binds for public and private firms but not for cooperatives which rebate profits to members we argue that this price floor policy creates a disincentive for private and public firms to be technically efficient in converting cane to sugar in support of this hypothesis an analysis of 593 indian sugar factories from 1992 to 2007 reveals statistically significant differences in technical efficiency with cooperatives being the most efficient and public firms least efficient we estimate welfare losses due to the technical inefficiency attributable to the price floor policy and argue that it can be eliminated by enacting policy to base price floors upon quality of the cane input received by a factory

imperfect competition in agricultural markets and the role of cooperatives a spatial analysis important characteristics of many agricultural markets are costly to transport raw products and relatively few processors one or more of which is often a cooperative this paper analyzes pricing behavior in these oligopsonistic spatial markets and focuses specifically upon the conjecture that cooperatives may have a procompetitive effect on the behavior of rival non co op processors the existence and magnitude of a procompetitive effect is shown to depend upon a number of structural and strategic factors including competitive relations among the non co op processors and a cooperative s membership and pricing policies

imperfect competition functional forms and the size and distribution of research benefits abstract the effects of functional forms for supply and demand on the size and distribution of the returns to research are examined under a range of forms of competition under perfect competition the choice of functional form is relatively unimportant for the estimation of research benefits under imperfect competition the combination of the choice of functional forms for supply and demand and the nature of the research induced supply shift can have profound implications for the results functional form plays a much more important role than in the competitive model the most important contrast is between the constant elasticity model and the linear model along with various cases of a generalized linear model these findings are illustrated using a combination of analytical results and numerical simulations

price behavior in a dynamic oligopsony washington processing potatoes punishment strategies are necessary to sustain a collusive oligopsony in a repeated game context when demand is uncertain and only market variables are observable this article proposes a test for tacit collusion among potato processors in washington state using a dynamic regime switching model estimated with a finite mixture method the results support the existence of punishment and collusive regimes and show the welfare losses due to anti competitive behavior on the part of processors to be significant processors oligopsony power is enhanced by higher domestic production imports and existing stocks but it is ameliorated by high capacity utilization rates and exports copyright 2001 oxford university press

process innovation activity in a mixed oligopoly the role of cooperatives this article develops a sequential game theoretic model of heterogeneous producers to examine the market and welfare effects of cooperative involvement in process innovation activity in the agricultural sector the analysis examines an open membership input supplying cooperative co op that maximizes member welfare and finances its innovation activity through retained earnings analytical results show that the presence of the co op can increase the arrival rate of innovations while reducing the price of agricultural inputs cooperative involvement in innovation activity can thus be welfare enhancing and socially desirable with its effectiveness being determined by the degree of producer heterogeneity and the size of innovation costs

marketing production decisions in an industrial channel of distribution this paper presents a model that considers the interface between marketing and production decisions in a channel of distribution of industrial goods comprised of a manufacturer and a distributor the key issue investigated is the nature of the coordination within the channel in light of an unstable pattern of seasonal demand the investigation which focuses on dynamic issues considers production activities such as product delivery and inventory policy and their link to marketing strategies such as pricing policies the focus here is on the dynamic nature of the coordinational aspects of the various policies for example the following questions are addressed what is the distributor s pricing strategy throughout the season what is the nature of the contractual price in the channel under what conditions should the distributor carry no inventory throughout the seasonal period under what conditions should the manufacturer carry no inventory what is the impact of the seasonal parameters and differing h

the effects of imperfect competition on the size and distribution of research benefits studies of agricultural research benefits usually assume perfectly competitive markets studies that have allowed for market power of agribusiness firms have generally assumed unrealistic pure monopsony or monopoly behavior this paper allows for processing firms to exhibit a range of degrees of oligopsony power in buying raw farm products and oligopoly power in selling processed farm products the results indicate that different types of research induced technical change can exacerbate or ameliorate distortions from the exercise of market power by agribusiness firms which affects the size and especially the distribution of research benefits

strategic upfront marketing channel integration as an entry barrier abstract this paper investigates an organizational design problem concerning whether duopolistic firms competing in a product market should vertically integrate or separate their marketing channels in a dynamic noncooperative game setting previous operational research models have shown that the separation of the marketing channel with the adoption of a two part tariff contract is the dominant strategy compared with integration for each firm if the two firms face retail price competition and thereby constitutes the subgame perfect nash equilibrium spne contrary to this previous insight this paper demonstrates that if exogenous parameters that characterize fixed costs product substitutability and a demand function fall into a specific region marketing channel integration dominates the separation strategy when one of the two firms is the incumbent firm while the other is a potential entrant in other words the well known result in the price setting game can be reversed when we take entry threats into consideration specifically we show that upfront vertical integration of the marketing channel enables the incumbent to deter the entry of the potential competitor and to monopolize the market in the spne this result has operational implications for a firm confronting the threat of potential rivals entering the market in that the firm can use this apparently inferior strategy as a commitment device which creates a virtual entry barrier

uncoupled dynamics do not lead to nash equilibrium it is notoriously difficult to formulate sensible adaptive dynamics that guarantee convergence to nash equilibrium in fact short of variants of exhaustive search deterministic or stochastic there are no general results of course there are many important interesting and well studied particular cases see the books of jorgen w weibull 1995 fernando vegaredondo 1996 larry samuelson 1997 drew fudenberg and david k levine 1998 josef hofbauer and karl sigmund 1998 h peyton young 1998 and the discussion in section iv below here we provide a simple answer to the question why is that so our answer is that the lack of a general result is an intrinsic consequence of the natural requirement that dynamics of play be uncoupled among the players that is the adjustment of a player s strategy does not depend on the payoff functions or utility functions of the other players it may depend on the other players strategies as well as on the payoff function of the player himself this is a basic informational condition for dynamics of the adaptive or behavioral type it is important to emphasize that unlike the existing literature see section iv we make no rationality assumptions our dynamics are not best reply dynamics or better reply or payoffimproving or monotonic and so on what we show is that the impossibility result is due only to an informational requirement that the dynamics be uncoupled

participation games market entry coordination and the beautiful blonde abstract we find the nash equilibria for monotone n player symmetric games where each player chooses whether to participate examples include market entry games coordination games and the bar room game depicted in the movie a beautiful mind the symmetric nash equilibrium involves excessive participation a common property resource problem if participants payoffs are decreasing in the number of participants and insufficient participation if payoffs are increasing with decreasing payoffs there can be many equilibria but with increasing payoffs there are only 3 some comparative static properties of changing one player s participation payoffs are counterintuitive especially with more than two players

oligopsony power asset specificity and hold up evidence from the broiler industry in this article we look for empirical evidence of hold up in broiler industry production contracts by using the cross sectional national survey of broiler growers first we focus on the problem of under investment and hypothesize that the degree of agent s grower s under investment systematically depends on the principal s integrator s market power and the level of asset specificity second we provide an indirect test of hold up by looking at the grower contract payoffs as a function of the frequency of the housing facilities upgrade requests and the principal s market power the results show moderate empirical support for the presence of hold up

structural analysis of manufacturer pricing in the presence of a strategic retailer consumer goods manufacturers usually sell their brands to consumers through common independent retailers theoretical research on such channel structures has analyzed the optimal behavior of channel members under alternative assumptions of manufacturer retailer interaction vertical strategic interaction research in empirical industrial organization has focused on analyzing the competitive interactions between manufacturers horizontal strategic interaction decision support systems have made various assumptions about retailer pricing rules e g constant markup category profit maximization the appropriateness of such assumptions about strategic behavior for any specific market however is an empirical question this paper therefore empirically infers 1 the vertical strategic interaction vsi between manufacturers and retailer 2 the horizontal strategic interaction hsi between manufacturers simultaneously with the vsi and 3 the pricing rule used by a retailer the approach is particularly appealing because it can be used with widely available scanner data where there is no information on wholesale prices researchers usually have no access to wholesale prices even manufacturers who have access to their own wholesale prices usually have limited information on competitors wholesale prices in the absence of wholesale prices we derive formulae for wholesale prices using game theoretic solution techniques under the specific assumptions of vertical and horizontal strategic interaction and retailer pricing rules we then embed the formulae for wholesale prices into the estimation equations while our empirical illustration is using scanner data without wholesale prices the model itself can be applied when wholesale prices are available early research on the inference of hsi among manufacturers in setting wholesale prices using scanner data e g kadiyali et al 1996 1999 made the simplifying assumption that retailers charge a constant margin this assumption enabled them to infer wholesale prices and analyze competitive interactions between manufacturers in this paper we show that this model is econometrically identical to a model that measures retail price coordination across brands hence the inferred cooperation among manufacturers could be exaggerated by the coordinated pricing category management done by the retailer we find empirical support for this argument this highlights the need to properly model and infer vsi simultaneously to accurately estimate the hsi when using data at the retail level functional forms of demand have been evaluated in terms of the fit of the model to sales data but recent theoretical research on channels lee and staelin 1997 tyagi 1999 has shown that the functional form has serious implications for strategic behavior such as retail passthrough while the logit and linear model implies equilibrium passthrough of less than 100 lee and staelin call this vertical strategic substitute vss the multiplicative model implies optimal passthrough of greater than 100 vertical strategic complement vsc because passthrough rates on promotions have been found to be below or above 100 chevalier and curhan 1976 armstrong 1991 we empirically test the appropriateness of the logit vss and the multiplicative vsc functional form for the data we perform our analysis in the yogurt and peanut butter categories for the two biggest stores in a local market we found that the vss implications of the logit fit the data better than the multiplicative model we also find that for both categories the best fitting model is one in which 1 the retailer maximizes category profits 2 the vsi is manufacturer stackelberg and 3 manufacturer pricing hsi is tacitly collusive the fact that the retailer maximizes category profits is consistent with theoretical expectations the inference that the vsi is manufacturer stackelberg reflects the institutional reality of the timing of the game retailers set their retail prices after manufacturers set their wholesale prices note that in the stores and product categories that we analyze the two manufacturers own the dominant brands with combined market shares of about 82 in the yogurt market and 65 in the peanut butter market the result is also consistent with a balance of power argument in the literature the finding that manufacturer pricing is tacitly collusive is consistent with the argument that firms involved in long term competition in concentrated markets can achieve tacit collusion managers use decision support systems for promotion planning that routinely make assumptions about vsi hsi and the functional form the results from our analysis are of substantive import in judging the appropriateness of assumptions made in such decision support systems

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

when should a manufacturer set its direct price and wholesale price in dual channel supply chains abstract applying an observable delay game framework developed in noncooperative game theory we investigate the timing problem concerning when a manufacturer managing dual channel supply chains consisting of a retail channel and a direct channel should post its wholesale price and direct price conventionally operational research models describing dual channel supply chains examine price competition where the retailer and the manufacturer simultaneously determine the retail and direct prices respectively in contrast to this conventional setting our model demonstrates that such simultaneous price competition never arises if the manufacturer and retailer can choose not only the level of the price but also the timing of pricing if the manufacturer sets the direct price after setting the wholesale price to the retailer the retailer accelerates the timing of retail pricing prior to the direct price setting by the manufacturer our findings suggest that the manufacturer should post the direct price before or upon but not after setting the wholesale price for the retailer this upfront posting of the direct price not only constitutes the subgame perfect nash equilibrium of the noncooperative game between channel members but also maximizes the profits for a manufacturer employing multichannel sales strategies

analysis of a supply control program under uncertainty and imperfect competition chinese cabbage in taiwan researchers have often attributed the farm wholesale price spread after adjusting for marketing costs as compensation for marketing firms risk bearing however price spreads in excess of marketing costs can also be due to marketing firms exercise of market power in settings where both imperfect competition and marketer risk aversion are plausible a modeling framework must be sufficiently general to accommodate both types of behavior this article develops and estimates such a model in the context of fresh produce marketing and develops the implications for analysis of supply control programs the model is applied to the production and marketing of chinese cabbage in taiwan and specifically to the analysis of supply control programs implemented in this industry by the taiwanese government the empirical results provide little support for the hypothesis that marketing firms exhibit risk averse behavior but they do show that marketing firms exercise oligopsony power in procurement of the product from farmers and that this power is positively related to the quantity supplied in each market period this provides a heretofore unexplored impetus for supply controls intended to raise producer incomes however such controls are also rendered less effective by imperfect competition because marketing firms capture part of the benefits from supply reduction

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

competitive strategies for two firms with asymmetric production cost structures we model joint production marketing strategies for two firms with asymmetric production cost structures in competition the first firm called the production smoother faces a convex production cost and a linear inventory holding cost the second firm called the order taker faces a linear production cost and holds no inventory each firm is assumed to vary continuously over time both its production rate and its price in view of an unstable surge pattern of demand the underlying theoretical motivation is to investigate the temporal nature of the equilibrium policies of two competing firms one operating at or near capacity the production smoother and one operating significantly below capacity the order taker we characterize and compare the equilibrium strategies of the two competing firms among our results we show that if the duopolistic production smoother finds it optimal to hold inventory then he will begin the season by building up inventory continue by drawing down inventory until i

optimal pricing and production in an inventory model abstract this paper deals with the problem of simultaneously determining the optimal price policy and production rate over a given planning horizon for nonlinear demand functions and convex inventory and shortage cost functions the optimal solution paths are derived by using optimal control theory the treatment of linear nonsmooth cost functions requires the use of a generalized maximum principle the solution method is a phase portrait analysis providing insight into the optimal pricing and production policies as well as the resulting inventory paths moreover it is shown that in the case of nonsmooth piecewise linear cost functions the equilibrium is approached within finite time although the model is nonlinear in the control variables finally it is illustrated that exogenous fluctuations in the demand rate seasonal demand pattern amount to cyclical optimal solutions

optimal pricing strategies for new products in dynamic oligopolies this paper deals with the determination of optimal pricing policies for firms in oligopolistic markets the problem is studied as a differential game and optimal pricing policies are established as nash open loop controls cost learning effects are assumed such that unit costs are decreasing with cumulative output discounting of future profits is also taken into consideration initially the problem is addressed in a general framework and we proceed to study some specific cases that are related to models presented in recent literature three basic classes of sales dynamics are analyzed competition with price effects only competition with price as well as adoption effects and competition with adoption effects only in some cases it turns out that results which hold for the monopoly case carry over to the multi firm case in the sense that the qualitative structure of optimal pricing strategies is the same in the monopoly and the oligopoly cases however due to competitive interdependencies differences certainly exist in the levels as well as the rates of change of optimal prices

vertical strategic interaction implications for channel pricing strategy this paper examines two strategic pricing decisions within channels using foresight i e price leadership and considering category implications i e product line pricing are price leadership and product line pricing always the best pricing strategies for a channel member if not when does this occur and why by investigating these questions we address some major concerns of both marketing practitioners and scholars interested in channel management issues in addition this study provides an indepth discussion on why previous analytic studies produced answers to these questions that depend upon the choice of the form of demand functions as such this study should significantly resolve the debate among analytic marketing modelers about the right demand specification at the core of our discussion lies the concept of vertical strategic interaction which is defined in terms of the direction of a channel member s reaction to the actions of its channel partner within a given demand structure specifically if a channel member s best reaction is to reduce its margin when its channel partner increases its margin the type of vertical strategic interaction is referred to as vertical strategic substitutability vss if the best reaction is to increase the margin the environment is referred to as vertical strategic complementarity vsc if the best reaction is no margin change it is referred to as vertical strategic independence vsi using a game theoretic approach we demonstrate that these three types of vertical strategic interactions represent a key driving force for optimal decisions on channel price leadership and product line pricing our investigation involves mathematical analyses of an industry model composed of two manufacturers selling competing products both carried by two competing retailers as such the model allows for retailer product line pricing as well as manufacturer and retailer level competition in addition this general model can be used to analyze three more restrictive industry settings often found in the channels literature i e a bilateral monopoly jeuland and shugan jeuland abel steven m shugan 1983 managing channel profits marketing sci 2summer 239 72 two competing manufacturers selling through competing franchised retailers mcguire and staelin mcguire timothy w richard staelin 1983 an industry equilibrium analysis of downstream vertical integration marketing sci 2spring 161 92 and two competing manufacturers selling through one common retailer using product line pricing choi choi s chan 1991 price competition in a channel structure with a common retailer marketing sci 10fall 271 96 unlike many other channel studies most of our analyses are performed without assuming particular functional forms of demand curves thus this paper provides greater assurance that the insights from this stream of research are broadly applicable not only across industry structures but also across demand conditions the paper starts out by defining three different rules for how prices are set the manufacturer uses foresight the retailer uses foresight and neither channel member uses foresight we then show a one to one mapping between the type of vertical strategic interaction and the optimality of channel price leadership specifically a channel member finds it profitable to be a price leader for vss but prefers to be a follower for vsc for vsi channel members are indifferent to the channel price leadership issue as it has no effect on channel member profits we also show that there exist conditions under which a retailer might see a reduction in profits when it changes its policy from non product line pricing to product line pricing such conditions arise when the retailer is not a price leader and the environment is characterized by vss or vsc at a more general level this study suggests not only the value but also the cost to a firm for using superior knowledge i e foresight and or product line pricing in making strategic marketing decisions in this way ignorance can be bliss we also explore the link between demand characteristics and the three types of vertical strategic interaction we show that the type of vertical strategic interaction present in a given environment is closely related with the convexity of the demand curve and the level of demand for a given price interestingly we find that linearity of demand is not a necessary condition for any of the three types of vertical strategic demand function consequently in evaluating the robustness of analytic analyses it may be more important to determine the type of vertical strategic interaction assumed instead of whether the demand is linear or nonlinear finally our results are limited to situations where the channels are not coordinated and the retailer s precommitment to particular pricing policy and decision is credible although such situations still capture a significant portion of reality we acknowledge that the insights from this study might not be applicable in all situations

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

endogenous rationality and distributions of competence abstract when decision making is costly distributions of competence endogenous rationality may arise across buyers and sellers in a market an adaptive game is used to make the point

dynamic pricing and inventory control uncertainty and competition in this paper we study a make to stock manufacturing system where two firms compete through dynamic pricing and inventory control our goal is to address competition in particular a duopoly setting together with the presence of demand uncertainty we consider a dynamic setting where multiple products share production capacity we introduce a demand based fluid model where the demand is a linear function of the price of the supplier and of her competitor the inventory and production costs are quadratic and all coefficients are time dependent a key part of the model is that no backorders are allowed and the strategy of a supplier depends on her competitor s strategy first we reformulate the robust problem as a fluid model of similar form to the deterministic one and show existence of a nash equilibrium in continuous time we then discuss issues of uniqueness and address how to compute a particular nash equilibrium i e the normalized nash equilibrium

spatial competition uniform pricing and transportation efficiency in the california processing tomato industry this study examines the role of spatial pricing in the allocation of processing tomatoes from farms to the thirty two processing facilities located in northern and central california a simple theoretical model illustrates that the industry s uniform pricing policy encourages market overlap and excessive transportation costs relative to fob pricing a nonlinear mathematical programming model is developed to determine the optimal allocation of processing tomatoes this allocation is then compared to the estimated actual allocation the analysis reveals foregone profits of only 1 9 from inefficient product allocation simulation results reveal significant competition among processors despite their separation in many cases by long distances

price and lead time decisions in dual channel supply chains abstract manufacturers today are increasingly adopting a dual channel to sell their products i e the traditional retail channel and an online direct channel empirical studies have shown that service quality we focus on the delivery lead time of the direct channel even goes beyond product price as one of the major factors influencing consumer acceptance of the direct channel delivery lead time has significant effects on demand profit and pricing strategy however there is scant literature addressing the decision on the promised delivery lead time of a direct channel and its impact on the manufacturer s and retailer s pricing decisions to fill this gap we examine the optimal decisions of delivery lead time and prices in a centralized and a decentralized dual channel supply chain using the two stage optimization technique and stackelberg game and analyze the impacts of delivery lead time and customer acceptance of a direct channel on the manufacturer s and retailer s pricing behaviours we analytically show that delivery lead time strongly influences the manufacturer s and the retailer s pricing strategies and profits our numerical studies reveal that the difference between the demand transfer ratios in the two channels with respect to delivery lead time and direct sale price customer acceptance of the direct channel and product type have great effects on the lead time and pricing decisions

a note on competitive supply chains with generalised supply costs abstract this note generalises models from two influential papers in the theory of supply chain outsourcing under competition mcguire and staelin 1983 cachon and harker 2002 the first paper studies the impact of competitive intensity on the outsourcing decision from the supplier s point of view for linear supply cost the second paper examines the impact of supply economies of scale from the retailer s point of view when selling perfectly substitutable products by considering competitive intensity and supply economies of scale simultaneously we find that equilibrium channel structures are primarily determined by the competitive intensity which is true even under supply diseconomies of scale the key message in the second paper of scale economies driving retailer s outsourcing supply decision is highly dependent on the assumption of perfect substitutes our finding has no qualitative difference when either the suppliers or the retailers are modeled as the channel leader and make the outsourcing decisions

information production decisions and intra firm bargaining a firm s factor suppliers often receive private signals which are useful in managerial decision making productive efficiency requires the pooling of such decentralized information however factor suppliers may threaten to withhold private signals in order to secure side payments from the potential beneficiaries of this information j harsanyi s theory of the n person cooperative game is applied to a model where both physical inputs and information can be withheld by factor owners for the special case of a binary decision problem the central limit theorem is used to approximate the harsanyi solution by a linear combination of are as under the standard normal curve copyright 1988 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

on the instability of mixed strategy nash equilibria abstract what behavior processes will lead to a nash equilibrium of an n person game two very general processes are examined for finite games with finite horizon generalized fictitious play strict mixed strategy nash equilibria are shown to be unstable for almost all finite games with discrete or continuous time generalized gradient processes mixed strategy nash equilibria are shown to be unstable

a differential game model of the marketing operations interface in the development of their dynamic strategies the marketing and operations functions within a firm have differing objectives and conflict between the two functions is common the strategic interdependence involving marketing and operations decisions is modeled as a noncooperative differential game demand is assumed to be a function of price and advertising goodwill and marketing controls price and advertising to maximize its discounted stream of revenue net of advertising costs backlogging is allowed and operations controls production to minimize its discounted stream of production and backlog costs a feedback nash equilibrium is derived for the game which allows a solution of the system of differential equations for goodwill and backlog and is analyzed to study the nature of the dynamic strategies for price advertising and production

production inventory and pricing under cost and demand learning effects abstract the paper considers a monopolist firm that plans its production inventory and pricing policy over a fixed and finite horizon the problem is represented by an optimal control model which combines elements from three streams of literature the first of these is a classical or area and deals with optimal production and inventory under exogenously given demand conditions the second is an area of marketing science which studies dynamic pricing under demand learning effects demand learning refers to the situation where current demand for a product is influenced by past demand the third area belongs to microeconomics and industrial organization and is concerned with the effects of learning by doing in a firm s production process learning is reflected in a unit production cost that decreases with cumulative production using a path synthezising procedure we obtain closed form characterizations of optimal production pricing and inventory policies

on intrabrand and interbrand competition the strategic role of fees and royalties abstract we examine oligopolistic markets with both intrabrand and interbrand competition we characterize equilibrium contracts involving a royalty or wholesale price and a fee when each upstream firm contracts with multiple downstream firms royalties control competition between own downstream firms at the expense of making them passive against rivals when the number of downstream firms is endogenous each upstream firm chooses to have only one downstream firm this result is in sharp contrast to previous literature where competitors benefit by having a larger number of independent downstream firms under only fixed fee payments we discuss why allowing upstream firms to charge per unit payments in addition to fixed fees dramatically alters their strategic incentives

competition under industry stock driven prevailing market price environmental consequences and the effect of uncertainty abstract we address competition between several firms that cause pollution when producing fully substitutable products these firms comprise the industry and each individual firm charges for its products the market price determined by the difference between cumulative market supply and demand i e by the industry s stock we find that although the greater the number of firms competing for the same primary market the lower the market price and the higher the industry inventory surplus the reduction in price at market equilibrium is insufficient to stimulate greater aggregate sales that is greater competition does not necessarily induce higher industry output and pollution furthermore we show that commitment production pollution strategies compared to contingent strategies do not necessarily result in lower pollution especially when the number of competing firms is not high market uncertainty is low and proportional pollution taxation is high

marketing production coordination in channels of distribution abstract in this paper we analyze the effects of functional horizontal decentralization by a channel member on the performance of an industrial channel of distribution we use the model of eliashberg j steinberg r 1987 management science 33 981 1000 which describes a channel of distribution consisting of a manufacturer and a value adding distributor we allow the distributor to decentralize decision making between his marketing and production functions our results show that functional decentralization at the distributor level increases the price sensitivity of the distributor concerning the price he faces from the manufacturer causes a shift in the distributor s demand curve increases the distributor s inventory activities in terms of both quantity and time frame and under certain conditions increases the manufacturer s inventory as expected the decentralized distributor has a less coordinated pricing policy vis a vis the production policy using numerical means we show that functional decentralization can improve the overall channel profitability i e for both manufacturer and distributor this counter intuitive result suggests that in our non repeated perfect information game setting functional decentralization can yield a pareto dominant equilibrium outcome where both the distributor and manufacturer are better off even though it is only the distributor who is changing his organizational decision making

quality improvement vs advertising support which strategy works better for a manufacturer abstract we consider a marketing channel with a single manufacturer and a single retailer where both advertising and quality improvement contribute to the build up of goodwill in a non coop scenario the retailer controls the advertising efforts while the manufacturer controls the quality improvements and wholesale price although improving quality positively contributes to goodwill it also increases the production cost thereby reducing the manufacturer s profit in a coop scenario the manufacturer supports the retailer s advertising while decreasing his investments in quality we investigate the conditions under which a coop program is beneficial when such a trade off occurs our results demonstrate that only when advertising significantly contributes to goodwill the manufacturer has an incentive to cooperate and a coop program turns out to be pareto improving conversely the retailer is always better off with a coop program moreover the channel is operational and marketing driven when quality effectiveness is high independent of advertising effectiveness or when both quality and advertising effectiveness are large in all other cases the channel is marketing driven

simultaneous and dynamic price production inventory and capacity decisions abstract this paper concerns a profit maximizing firm that derives the optimal price for its output level of output level of inventory and composition of productive capacity over time first it is assumed that capacity may be acquired to either increase or replace the firm s existing productive capacity second it is assumed that the acquisition of new capacity causes a reduction in the firm s production cost lastly it is assumed that demand which is expressed as a function of time and price must be met either from current production or from inventory clearly the level of production cannot exceed the productive capacity at any time the optimal control model formulated requires the solution of a two point boundary value problem so that a discrete approximation numerical procedure is presented numerical results indicate that due to anticipated technological improvement the acquisition of new capacity is postponed and occurs in greater magnitude later in the planning horizon in addition as a result of upgrading productive capacity through the acquisition of new technology numerical results show that a firm lowers its per unit production cost and thereby reduces the optimal price charged for output which increases demand furthermore since the level of capacity is increased due to the purchase of new technology less reliance on inventory is necessary to meet peak demand lastly it is shown that a larger firm optimally acquires a greater level of new capacity over the planning horizon to reduce its operating costs and thereby further its competitive advantage

interactions between members of a marketing production channel under seasonal demand abstract key decisions in a marketing production channel faced with a seasonal demand include production and pricing decisions for the manufacturer and processing and pricing decisions for the retailer in such situations a variety of contracts are possible including contracts under which the manufacturer charges a constant price throughout the season or the retailer processes at a constant rate throughout the season also possible are channel structures in which the manufacturer and retailer cooperate to make decisions jointly the main objective of the present paper is to compare optimal policies under all the situations described above we show that having a constant manufacturer s price or a constant processing rate does not have a significant impact upon the retailer s price or inventory decisions however if the demand is not highly seasonal a constant processing rate contract will result in higher production and processing rates and a lower manufacturer s price compared to a constant manufacturer s price contract also a centralized channel involving joint decision making will lead to a lower price at the retail level and higher production and processing rates hence issues such as channel coordination and contracts between manufacturers and retailers which have received significant attention in the marketing literature have implications for the production area as well

competition and cooperation in marketing channel choice theory and application this paper discusses the problem of choosing a vertical marketing channel in a product differentiated duopolistic market firms choose product price and the form of the marketing channel to maximize profits it is shown that integration of the marketing function results in greater price competition and lower prices than does the use of independent marketing middlemen the profitability of reducing price competition by using such middlemen is investigated two hypotheses that integration is negatively associated with the products substitutability and that symmetric channel structures are stable are tested in a preliminary way and supported with survey data from the international semiconductor industry

a stochastic production planning model with a dynamic chance constraint abstract this paper deals with the optimal production planning for a single product over a finite horizon the holding and production costs are assumed quadratic as in holt modigliani muth and simon hmms 7 model the cumulative demand is compound poisson and a chance constraint is included to guarantee that the inventory level is positive with a probability of at least at each time point the resulting stochastic optimization problem is transformed into a deterministic optimal control problem with control variable and of the optimal solution is presented the form of state variable inequality constraints a discussion the optimal control production rate is obtained as follows if there exists a time t 1 such that t 1 o t where t is the end of the planning period then i produce nothing until t 1 and ii produce at a rate equal to the expected demand plus a correction factor between t 1 and t if t 1 is found to be greater than t then the optimal decision is to produce nothing and always meet the demand from the inventory