optimal joint pricing and lot sizing with fixed and variable capacity this paper examines previously unexplored fixed and variable capacity problems of jointly determining an item s price and lot size for a profit maximizing firm facing constant but price dependent demands over a planning horizon we apply geometric programming to these constrained nonlinear maximization problems with nonconcave objective functions and obtain global optimal solutions using kuhn tucker condition marginal and sensitivity analyses we investigate model interactions provide managerial implications on the optimal capacity decisions and explore the postoptimal behavior of the price lot size and capacity expansion and reduction size some findings cast interesting insights different from previous just in time management studies without pricing consideration

an inventory model of immediate and delayed delivery this paper considers the long run profit maximizing strategy of a distributor that holds a good good 1 in inventory for immediate delivery and that offers a second good good 2 for delayed delivery when the two goods are substitutes an out of stock situation for good 1 will cause some consumers walkers to seek the good elsewhere other consumers waiters to accept a raincheck for later delivery of good 1 and others still switchers to place an order for good 2 it is shown that a profit maximizing strategy may entail setting a price for the delayed delivery item so as to encourage switching behavior the rationale is that the distributor can hold a smaller inventory thereby incurring lower holding costs because out of stock situations are less costly than they would be without some consumers being willing to switch

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

integrating distribution strategy and tactics a model and an application designing distribution systems requires two decisions one strategic i e the number of levels between the producer and the customer and the other tactical i e channel management policies such as trade discounts and rebates while the modeling literature focuses on one or the other evidence from the field indicates that the two decisions are in fact interactive in this paper we develop and then apply an integrated model that solves the strategic issue of channel levels and the tactical issue of price rebates simultaneously

a dynamic programming approach for pricing options embedded in bonds abstract we propose a dynamic programming dp approach for pricing options embedded in bonds the focus being on call and put options with advance notice an efficient procedure is developed for the cases where the interest rate process follows the vasicek cox ingersoll ross cir or generalized vasicek models our dp methodology uses the exact joint distribution of the interest rate and integrated interest rate at a future date conditional on the current value of the interest rate we provide numerical illustrations for the vasicek and cir models comparing our dp method with finite difference methods our procedure compares quite favorably in terms of both efficiency and accuracy an important advantage of the our dp approach is that it can be applied to more general models calibrated to capture the term structure of interest rates e g the generalized vasicek model

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

a 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

residential energy efficiency and distributed generation natural partners or competition abstract residential energy efficiency and distributed generation seem to be natural partners in our journey towards a more sustainable energy future a growing range of energy efficient consumer technologies and extraordinary declines in photovoltaics system prices has seen household electricity demand fall whilst a growing proportion of the remaining load is provided by household self generation australia is a particularly interesting example of these developments with around 15 of households now possessing a pv system while per capita household demand has also fallen markedly however existing retail electricity tariffs and regulatory arrangements can create mixed incentives for households contemplating both pv and energy efficiency options and for their network service providers this is certainly the case in australia with net metering arrangements that value self consumption of pv far more than pv exports to the grid there are also complex benefits for the electricity network created by these household energy resources that can be significant in this paper we use real household load and pv data from sydney households to model the potential implications of existing electricity tariff arrangements on the financial attractiveness of pv and energy efficiency we model these options separately and in combination for both households implementing these options and their network service providers our results highlight how inappropriate tariffs may well adversely impact on the value that the combination of energy efficiency and pv offers not only to households but also to their network service providers and suggest ways that such impacts might be ameliorated by acknowledging the benefits that these resources can offer to the electricity network

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

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

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

a learning curve model with knowledge depreciation abstract empirical studies in several industries have verified that unit costs decline as organizations gain experience or knowledge in production which is referred to as the learning curve effect in the past two decades there has also been analytical work on the relationship between a firm s learning curve effects and its pricing and output decisions learning rates differ significantly across firms in the same industry and recent empirical evidence has shown that knowledge depreciation may be an important reason for these differences we propose and analyze a learning curve model with knowledge depreciation and provide several new insights first we show that there exists a steady state where knowledge level and unit cost remain constant over time and there exists an optimal path to this steady state many empirical researchers have observed this plateau phenomenon whereby unit costs decline but reach saturation after some time while this has been traditionally modeled exogenously in the learning curve literature by assuming that cost reduction stops at some level of knowledge through a convex decreasing unit cost function we provide an alternative endogenous explanation we are also able to show that unlike in the model without knowledge depreciation the production rate along the optimal path to the steady state may decrease over time also the knowledge level along the optimal path may actually decline over time finally we show that the optimal production rate decreases at higher interest rates and increases at higher knowledge depreciation rates in turn this implies that a high interest rate environment discourages firms from achieving high knowledge levels and results in higher prices on the other hand higher knowledge depreciation rates result in higher production rates and lower prices

the value of marketing expertise this paper has three objectives 1 to construct a theoretical model that aids in evaluating marketing expertise 2 to use that theoretical model to identify factors influencing the value of marketing expertise and 3 to empirically test the model by observing how different market conditions influence whether companies emphasize marketing expertise we accomplish these objectives as follows first we use decision theory to find an expression for the expected value of marketing expertise we do not use decision analysis in the normative tradition nor do we assume that firms actually use formal decision analysis rather we assume that firms are rational and that decision theory describes their actions given that assumption we predict how firms should evaluate marketing here marketing expertise helps a firm make better marketing decisions at least on average hence the value of marketing expertise increases as marketing decisions become more important second consistent with decision theory

pulsation in a competitive model of advertising firm s cost interaction the literature reveals contradiction between theoretical results superiority of uniform policy under a concave advertising response function and empirical results concavity of the advertising response function and the superiority of a pulsation policy to reconcile the above difference this paper offers a resolution based on 1 the concavity of the advertising response function 2 the convexity of the firm s cost function and 3 over advertising the resolution is reached upon maximizing the net profit per unit time over the infinite planning horizon subject to an exogenous advertising budget constraint theoretical results for monopolistic markets are found mostly generalized to competitive markets a numerical example is introduced to gain more insight into the theoretical findings and an approach is introduced and implemented to empirically assess the shape of a firm s cost function and the advertising policy to be employed

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

clearance pricing and inventory policies for retail chains clearance pricing and end of season inventory management are challenging and important problems in retailing sales rates depend upon price seasonal effects and the remaining assortment of items available to customers there is little time to react to observed sales and pricing errors result in either loss of potential revenue or excess inventory to be liquidated this paper develops optimal clearance prices and inventory management policies that take into account the impact of reduced assortment and seasonal changes on sales rates versions of these policies have been tested and implemented at three major retail chains and these applications are summarized and discussed

coordinating advertising and pricing in a manufacturer retailer channel abstract cooperative advertising is a practice that a manufacturer pays retailers a portion of the local advertising cost in order to induce sales cooperative advertising plays a significant role in marketing programs of channel members nevertheless most studies to date on cooperative advertising have assumed that the market demand is only influenced by advertising expenditures but not by retail price this paper addresses channel coordination by seeking optimal cooperative advertising strategies and equilibrium pricing in a two member distribution channel we establish and compare two models a non cooperative leader follower game and a cooperative game we develop propositions and insights from the comparison of these models the cooperative model achieves better coordination by generating higher channel wide profits than the non cooperative model with these features a the retailer price is lower to consumers and b the advertising efforts are higher for all channel members we identify the feasible solutions to a bargaining problem where the channel members can determine how to divide the extra profits

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

the impact of competitive entry in a developing market upon dynamic pricing strategies this paper analyzes dynamic pricing strategies for new durable goods in a two period context the first period is characterized as a monopoly market structure for a new product having dynamic demand the second period begins when a new firm enters the market and thereby changes the market structure to a duopolistic one we begin by analyzing the pricing strategies of three types of monopolists nonmyopic myopic and surprised a nonmyopic monopolist is a first entrant who perfectly predicts the competitive entry a myopic monopolist totally discounts the duopolistic period and a surprised monopolist is a first entrant who has the longer time horizon of the nonmyopic monopolist but who does not foresee the competitive entry our results indicate that the nature of these pricing strategies may be quite different it is optimal for the nonmyopic firm to price its product at a higher level than the myopic monopolist additional results indicate under what circumstances the surprised monopolist will p

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

coordinating pricing and production decisions in the presence of price competition abstract in this paper we study the effects of coordinating pricing and production decisions on the improvement of a firm s position in a price competitive environment assuming duopolistic market conditions we use game theoretic concepts and models to analyze two scenarios a firm s marketing and production departments may vertically coordinate their pricing and production quantity decisions and the two firms may horizontally compete for price sensitive random demand the two scenarios include i no coordination and ii coordination in both firms we show that by coordinating their pricing and production decisions competing firms can increase their profitability especially when conditions are unfavourable i e with smaller market sizes higher unit costs and lower unit revenues while it may be intuitive to expect that coordination will outperform non coordination our models provide a means for formalizing and quantifying the differences between the two policies

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

multiple lot sizing and value of probabilistic information in production to order of an uncertain size abstract a make to order batch manufacturer knows that an order for items with some particular specifications is forthcoming but does not yet know the exact size of the order due to production lead times work needs to start immediately but some units produced may fail to meet required tolerances that is the yield of each batch is random each new run involves a costly setup and each unit attempted involves material and other variable costs if a subjective probability distribution for the order size can be formed the following related questions arise 1 a what is the optimal run size 2 b when should production stop to answer these questions this paper formulates a new model whose main new feature is the ability to handle uncertain demand within a multiple lot sizing setting it is proved that the optimal policy for this scenario is one of control limit stop if and only if the stock of good units is larger than some critical value a computer program was developed for solving the problem for binomial yields and optimal policies for several examples are reported due to the effort required to form and communicate probabilistic forecasts a common practice is to express a forecast as a single number corresponding perhaps to the mean or median of the unarticulated distribution we compute the extra profit expected from forming and using probabilistic forecasts we also show how to compute the profit s variance for any policy

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

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

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

the impact of dynamic pricing on the economic order decision this paper analyzes the impact of dynamic pricing on the single product economic order decision of a monopolist retailer items are procured from an external supplier according to the economic order quantity eoq model and are sold to customers on a single market without competition following the simple monopolist pricing problem coordinated decision making of optimal pricing and ordering is influenced by operating costs including ordering and inventory holding costs and the demand rate obtained from a price response function the retailer is allowed to vary the selling price either in a fixed number of discrete points in time or continuously while constant and continuous pricing have received much attention in the literature problems with a limited number of price changes are rather rare this paper illustrates the benefit of dynamically changing prices to achieve operational efficiency in the eoq model that is to trigger high demand rates when inventories are high we provide structural properties of the optimal time instants when the price should be changed taking into account costs for changes in price it provides numerical guidance on number timing and size of price changes during an order cycle numerical examples show that the benefits of dynamic pricing in an eoq framework can be achieved with only a few price changes and that products being unprofitable under static pricing may become profitable under dynamic pricing

dynamic version of the economic lot size model this article originally appeared in management science october 1958 volume 5 number 1 pp 89 96 published by the institute of management sciences a forward algorithm for a solution to the following dynamic version of the economic lot size model is given allowing the possibility of demands for a single item inventory holding charges and setup costs to vary over n periods we desire a minimum total cost inventory management scheme which satisfies known demand in every period disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full n periods

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

chapter 17 marketing strategy models publisher summary despite the advances in the sophistication and proliferation of marketing science models relatively few true marketing strategy models have been developed and those that have been developed generally had limited impact on management the gap between management needs for models that help them generate evaluate and implement better marketing strategies and the available models especially non traditional is narrowing as the environment and the characteristics of successful businesses are changing the nature of the marketing paradigm and the nature of desired marketing strategy models is changing as well

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