evaluating jointly constrained order quantity complexities for incremental discounts abstract in this paper we consider the purchasing decisions facing a buying firm which receives incrementally discounted price schedules for a group of items in the presence of constraints such as budgets and space limitations the constraints take the form of upper bounds on positively weighted linear combinations of order size dollar volume unit price and order frequency we adapt the solution procedures from an earlier paper naval res logis 40 2 1993 255 to treat this case the results show that simultaneous order quantities for multiple items offered with separate incremental discounts and subject to joint resource constraints can be calculated efficiently using a combination of lagrangean relaxation and as needed partial enumeration this problem proved to be no more and no less tractable than its counterpart with all units discounts

state lotteries and consumer behavior abstract this paper investigates two central issues regarding state lotteries first analyses of multiple sources of micro level data demonstrate that household lottery spending is financed primarily by a reduction in non gambling expenditures not by a reduction in expenditures on other forms of gambling the introduction of a state lottery is associated with an average decline of 46 per month or 2 4 percent in household non gambling expenditures low income households reduce non gambling household expenditures by 2 5 percent on average 3 1 percent when the state lottery includes instant games these households experience statistically significant declines in expenditures on food and on rent mortgage and other bills second consumer demand for lottery products responds positively to the expected value of the gamble controlling for other statistical moments and product characteristics including the nominal top prize amount this finding is consistent with informed choice among consumers of lottery products although other forms of irrational or misinformed choice cannot be ruled out

e ztax tax salience and tax rates this paper examines whether the salience of a tax system affects equilibrium tax rates i analyze how tolls change after toll facilities adopt electronic toll collection etc drivers are substantially less aware of tolls paid electronically i estimate that in steady state tolls are 20 to 40 percent higher than they would have been without etc consistent with a salience based explanation for this toll increase i find that under etc driving becomes less elastic with respect to the toll and toll setting becomes less sensitive to the electoral calendar alternative explanations appear unlikely to be able to explain the findings

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

reply on comments on a quantity discount pricing model to increase vendor profits professor joglekar is to be thanked for his generally insightful comments 1988 concerning my paper monahan monahan j p 1984 a quantity discount pricing model to increase vendor points management sci 306 june 720 726 he has in my view correctly assessed the limitations of two important production assumptions i made assumptions which need to be rethought in any quantity discount pricing models of the future yet although i find myself in general agreement with joglekar s comments i wish to clarify some points concerning the model and its potential applicability

replenishment decisions under an all units discount schedule and stepwise freight costs in this study we analyze the replenishment decisions under a general replenishment cost structure that includes stepwise freight costs and all units quantity discounts we first formulate a general model that accounts for a larger class of problems and prove several useful properties of the expected profit function we later utilize these properties to develop a computational solution approach to find the optimal order quantity as an application of the general results we study the replenishment decisions in the single period i e the newsboy problem considering several scenarios that model the cost considerations either for the buyer or for both the buyer and the vendor

designing a firm s coordinated manufacturing and supply decisions with short product life cycles in this paper we consider a problem of joint coordination between a firm s manufacturing and supply departments the manufacturing department is responsible for meeting random demand of a product with a short life cycle the supply department s responsibility is to provide the sufficient amount of raw materials so that the required production level can be achieved when coordination prevails both departments decisions are jointly made otherwise decisions are made independently without an exchange of information if the random demand exceeds the amount produced a second production run can be expedited at a substantially higher cost our analysis yields insightful results to such a coordination problem between the two departments we provide conditions under which it is desirable to coordinate resulting in a significant increase in expected profit if coordination is optimal then the supply department would purchase additional reserved material for the second run under this scenario we analyze the effects of joint coordination on the expected profit we also find explicit conditions for which joint coordination is not beneficial i e the supply department should only order sufficient material to meet the first production run requirements we provide a detailed set of numerical examples and generate response surfaces indicating the desirability of coordination for different pairs of parameter combinations

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

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

a classification of literature on determining the lot size under quantity discounts abstract determining a lot size in the presence of either all units or incremental discounts has represented one of major interests of materials managers it is a common practice that the suppliers offer quantity discount to entice the buyers to purchase more and to achieve economies of scale for transportation and processing costs this paper will classify the literature on lot sizing determination under several types of discount schemes and discuss some of the significant literature in this area over two decades also some future research areas have been identified

quantity discounts under demand uncertainty to motivate buyers to increase their order quantity suppliers often rely on a well established and widely used approach they offer quantity discounts this practice is in large part driven to obtain improved economies in transportation through higher truckload utilization recently transportation rates which are increasing faster than other costs have become a larger portion of total net landed cost placing the traditional quantity discount practices under scrutiny many suppliers are left perplexed as to why their approach is not effective anymore and some are even concerned that their overall profits may have actually decreased due to their discount parameters in this paper we study a multiperiod model with a buyer facing stochastic end item demand and a supplier offering an all units quantity discount to him to understand better the dynamics of such systems we provide guidelines and insights on how to set effective discount parameters and when not to expect much from them we derive the opt

analysis and applications of replenishment problems under stepwise transportation costs and generalized wholesale prices abstract in this study we analyze the replenishment decision of a buyer with the objective of maximizing total expected profits the buyer faces stepwise freight costs in inbound transportation and a hybrid wholesale price schedule given by a combination of all units discounts with economies and diseconomies of scale this general cost structure enables the model and the proposed solution to be also used for the supplier selection of a buyer under the single sourcing assumption we show that the buyer s replenishment problem reduces to finding and comparing the solutions of the following two subproblems i a replenishment problem involving wholesale prices given by an all units discount schedule with economies of scale and a lower bound on the replenishment quantity and ii a replenishment problem involving wholesale prices given by an all units discount schedule with diseconomies of scale and an upper bound on the replenishment quantity we propose solution methods for these two subproblems each of which stands alone as practical problems and utilize these methods to optimally solve the buyer s replenishment problem

a co ordination model combining incentive scheme and co ordination policy for a single vendor multi buyer supply chain abstract incentive scheme and co ordination policy are substantial components for the co ordination of a decentralized supply chain system but there is little work combining the two components as a single decision model li and wang 2007 this paper proposes a model which incorporates both incentive and co ordination issues into a single co ordination model for a single vendor multi buyer supply chain in the proposed model the co ordination is achieved by synchronizing ordering and production cycles while price discount which is based on the buyers order intervals is used as the incentive to motivate buyers to participate in the co ordination while the vendor is benefited from the co ordination by synchronized cycles the proposed price discount scheme can guarantee that a buyer s total relevant cost of co ordination will be reduced when compared with independent optimization more importantly the proposed price discount scheme does not require any cost information from the buyers

on the validity of aggregate models in designing supply chain contracts abstract the vast majority of the existing papers on supply chain contracts analyse these contracts based on a highly aggregate model description of the supply chain recognizing the high complexity of real supply chain systems such models can naturally only be rough approximations of reality out of the many possible ways for aggregating a planning model our study focuses on item aggregation here due to computational informational or organizational reasons a multi product reality is approximated by a model representation with fewer products we explore the aggregation error made when using an aggregate model in order to optimize a supply chain contract which is subsequently applied to a more detailed real system based on a numerical analysis it is shown that the design of supply chain contracts by means of an aggregate planning model may lead to significant suboptimalities

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

kids or cash exploring charter school responses to declining government revenues while the literature is extensive on school districts revenue sources less research has been done on the impact of donations on school district funds in this paper we extend the theoretical literature on crowding out of private donations by government grants for one type of nonprofit firm namely charter schools the theoretical model leads us to focus on the key relationships among fundraising effort enrollment which is tied to federal and state funding and donations using a dataset on texas charter schools we adopt a two stage approach to examine the empirical relationship between changes in nondonor revenues and the donations received by charter schools like the extensive empirical estimates of the effects of government grants on donations for other types of nonprofit firms we find evidence of crowding out with respect to our sample of charter schools we also find a significant positive effect of fundraising on donations with a 1 increase in fundraising associated to a 0 58 increase in donations a pattern consistent with overinvestment in fundraising enrollments exhibit a robust inverse relationship to changes in nondonor revenues jel h00 h32 h50

note comments on a quantity discount pricing model to increase vendor profits monahan monahan j p 1984 a quantity discount pricing model to increase vendor profits management sci june 720 726 adapted the quantity discount model of inventory theory to the problem of determining an optimal quantity discount schedule from a vendor s point of view and opened up an important direction of research however his one item one customer one vendor model is based on several implicit assumptions that must be judged unreasonable monahan must account for the vendor s inventory carrying charges and redefine his variable s2 it is shown that a rational vendor s manufacturing frequency would not be identical to the buyer s ordering frequency if the vendor s manufacturing setup costs are substantially larger than the buyer s ordering costs a numerical example presented in this note also questions the practical usefulness of monahan s model even after its theoretical inaccuracies axe corrected monahan s model may explain discounts that are a fraction of 1 of the price of an item but it fails to explain commonly observed magnitudes of quantity discounts such as 10 of the unit price

optimal lot sizing integration policy under learning and rework effects in a manufacturer retailer chain abstract most research in economic manufacturing order quantity management assumes that all products are of perfect quality and are produced at a constant production rate one result of this assumption is that the number of units produced in a given period is constant which is not the case in real life most production systems produce items which are of perfect quality along with some that are of imperfect quality defective items as well as the learning effect affect production and inventory costs thereby shaping the performance of the manufacturer retailer chain the present study uses the nash stackelberg and cooperation games to model an imperfect production system to investigate the combined effects of lot sizing size integration the learning effect imperfect production and the rework process on a manufacturer retailer channel this study also demonstrates the optimal properties of the proposed models develops a search algorithm for obtaining optimal solutions and conducts a numerical study to seek structural and quantitative insights into the structure of the proposed models in addition it analyzes the sensitivity of the solutions in relation to the major parameters

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

the coordinated replenishment dynamic lot sizing problem with quantity discounts abstract in the classical coordinated replenishment dynamic lot sizing problem the primary motivation for coordination is in the presence of the major and minor setup costs in this paper a separate element of coordination made possible by the offer of quantity discounts is considered a mathematical programming formulation for the extended problem under the all units discount price structure and the incremental discount price structure is provided then using variable redefinitions tighter formulations are presented in order to obtain tight lower bounds for reasonable size problems more significantly as the problem is np hard we present an effective polynomial time heuristic procedure for the incremental discount version of the problem that is capable of solving reasonably large size problems computational results for the heuristic procedure are reported in the paper

discount pricing decisions in distribution channels with price sensitive demand abstract in this paper we evaluate the effectiveness of quantity discounts and volume discounts as coordination mechanisms in distribution channels with demand that is price sensitive we consider a single vendor single retailer distribution channel demand for the product arises only at the retailer the demand faced by the retailer is assumed to be deterministic but price elastic the retailer in turn buys the product from the vendor the vendor and the retailer act independently and rationally each maximizing their own respective profit the equilibrium point that specifies the vendor s and buyer s inventory and pricing policy is determined by the solution to a stackelberg game we consider the cases when quantity discount and volume discount respectively are offered we develop methods to determine the optimal discount policy for these cases we then consider the case where both volume and quantity discounts are offered simultaneously and develop a method to determine the optimal simultaneous discount offer the relative performance of the alternative discount schemes is then evaluated through a numerical study the results of the study demonstrate that the effectiveness of volume discount as a coordination mechanism is higher when the sensitivity of demand to price changes is higher the effectiveness of quantity discount on the other hand is higher with lower price sensitivity of demand finally the results also demonstrate that perfect coordination is achieved when volume and quantity discounts are offered simultaneously

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

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

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

coordination and profit sharing between a manufacturer and a buyer with target profit under credit option several studies have focused on buyer vendor coordination through quantity discount credit option mechanism but few quantitative models and investigations are available that have explored the mechanism for transfer of surplus generated due to coordination in this paper we develop a coordination mechanism through credit option such that both the parties can divide the surplus equitably after satisfying their own profit targets two situations are explored here in the first situation both the parties have no individual profit target from the business whereas in the second situation there are individual profit target for both the parties the proposed mechanism for division of surplus is studied through a numerical study and the impact of different parameter values on the results are examined

concurrent pricing and lot sizing for make to order contract production abstract this paper develops a model for the simultaneous i e concurrent determination of the inventory and pricing policies of a supplier which produces and supplies a product to a buyer on the basis of a contractual agreement calling for the delivery of a specific quantity periodically assuming that the customer is rational i e it follows its own optimal purchasing policy the objective of the supplier is to determine the product s selling price in conjunction with an appropriate production inventory policy so that a predetermined gross profit level is achieved it is further assumed that the supplier s production batch size is an integer multiple of the buyer s order quantity in formulating a mathematical model of this situation the interactions between the product s price the buyer s economic order quantity and the supplier s selling price costs and profit are taken into account for solving this model a simple iterative algorithm is proposed which is illustrated through a numerical example sensitivity analysis performed on the model demonstrates that it is relatively robust and quite insensitive to errors in estimating the buyer s ordering to carrying cost ratio on the part of the producer

revisiting foundations in lot sizing connections between harris crowther monahan and clark abstract while many review articles exist on deterministic lot sizing models used in the context of price and quantity discounts buyer vendor coordination supply chain management and joint economic lot sizing problems they do not convey the impact of important findings which date back to at least 2002 or in hindsight to 1984 as a result many recent articles still model the financial implications of lot sizing decisions without having the assurance that these models would help the firm s involved in maximising the net present value npv this paper therefore reviews these findings while adding also its own contributions as to convey the general importance to lot sizing theory we show that the underlying principles used in the four key articles that have led to a division in modelling approaches are in fact all in line with npv and argue that therefore there should not be these discrepancies that currently persist in the literature we establish the connections between these four strands of the literature using the solution to a simple variation of harris eoq model deriving thereby results from boyaci and gallego 2002 and beullens and janssens 2011 but showing their general applicability to any type of supply chain structure the breath of implications to deterministic lot sizing theory is illustrated using practical examples we present a stochastic version of the model of crowther 1964 which is arguably the least understood and applied model but on the other hand the most important one in realising how these modelling strands can be unified

towards a more economic production and just in time delivery system abstract we study a system in which a batch production supplier participates in just in time jit delivery of its products to a jit buyer firm we demonstrate that under certain conditions a small adjustment of previously agreed product selling price can result in a more economic production and jit delivery system with reduced delivery quantity and hence increased delivery frequency in the case when both buyer and supplier share equal profit margin optimal levels of adjustment for price and delivery frequency can be obtained that maximize the profit margin a numerical example is used to illustrate the results

a fuzzy mathematical model for the joint economic lot size problem with multiple price breaks abstract this paper applies fuzzy mathematical programming to solve the joint economic lot size problem with multiple price breaks in order to entice the buyer to increase the order quantity it is a common practice for the seller to offer quantity discounts to the buyer from the system viewpoint the joint cost for the seller and buyer can be minimized only when the buyer increases his economic order quantity the problem is how to determine the number of price breaks as well as the quantity discount and order quantity at each price break to achieve the optimal joint cost fuzzy mathematical programming provides a very efficient algorithm to solve the above problem simultaneously from the perspectives of the seller and the buyer another common problem in joint economic lot size model is how to split the system profit between the seller and the buyer whereas the traditional approach to this problem is to divide the profit based on a certain ratio determined by the bargaining power of both parties fuzzy mathematical programming can achieve the same satisfaction level to both parties based on their respective cost functions

order variability in perishable product supply chains abstract empirical research has shown that the degree of order variability in supply chains is significantly influenced by product and industry specific factors this paper analyzes the impact of perishability on order variability and the bullwhip effect in supply chains we decompose the ordering process of a retailer into a sales and an outdating process and quantify their short and long term variability and correlation we find differences to non perishable product supply chains driven by the impact of the inventory depletion policy stock out management and retailers service level requirement these three factors significantly affect the retailer s order variability and thus the decision making process and the profitability of the upstream supply stage for the majority of instances the perishable nature of a product results in the ordering process having a lower variability than the demand process only when inventory depletion is dominated by last in first out in high service level environments variability amplification can be observed we propose a dynamic ordering policy for the upstream supply stage taking into account negative correlation of retailer orders between periods this dynamic policy may lead to substantial performance improvements in a sensitivity analysis we investigate the impact of shelf life lead time and demand correlation

a stackelberg game and its improvement in a vmi system with a manufacturing vendor vendor managed inventory vmi is an inventory management strategy to let a vendor manage his retailers inventories which makes the vendor have the opportunity to obtain some inventory and market related information of his retailers this paper discusses how the vendor can take advantage of this information for increasing his own profit by using a stackelberg game in a vmi system the vendor here is a manufacturer who procures raw materials to produce a finished product and supplies it at the same wholesale price to multiple retailers the retailers then sell the product in independent markets at retail prices solution procedures are developed to find the stackelberg game equilibrium that each enterprise is not willing to deviate from for maximizing his own profit the equilibrium makes the manufacturer benefited and the retailers profits maximized the equilibrium can then be improved for further benefiting the manufacturer and his retailers if the retailers are willing to cooperate with the manufacturer by using a cooperative contract finally a numerical example and the corresponding sensitivity analysis are given to illustrate that 1 the manufacturer can benefit from his leadership and monopolize the added profit of the vmi system in some cases 2 the manufacturer can further improve his own profit and then the retailers profits by the cooperative contract as compared to the stackelberg equilibrium 3 market and raw material related parameters have significant influence on every enterprise s net profit

the bullwhip effect progress trends and directions the bullwhip effect refers to the phenomenon where order variability increases as the orders move upstream in the supply chain this paper provides a review of the bullwhip literature which adopts empirical experimental and analytical methodologies early econometric evidence of bullwhip is highlighted findings from empirical and experimental research are compared with analytical and simulation results assumptions and approximations for modelling the bullwhip effect in terms of demand forecast delay replenishment policy and coordination strategy are considered we identify recent research trends and future research directions concerned with supply chain structure product type price competition and sustainability

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

modeling quantity discounts under general price sensitive demand functions optimal policies and relationships this paper presents models for determining optimal all unit and incremental quantity discount policies and investigates the effect of quantity discounts on increasing demand and ensuring pareto efficient transactions under general price sensitive demand functions the paper develops optimal quantity discount policies investigates their interrelationships and their benefits to both the supplier and the buyer and gains managerial insights for the scenarios of maximizing the supplier s profit and the joint profit we develop simple and efficient solution approaches for determining the all unit and the incremental optimal decision policies for general price sensitive demand functions we have three main findings first with price sensitive demand there are two incentives in offering quantity discounts increasing demand and ensuring pareto efficient transactions in most cases increasing demand dominates in justifying the offering of quantity discounts second using a single lot size associated with all efficient transactions as with the constant demand case does not hold with the price sensitive demand case third the optimal all unit quantity discount policy is equivalent to the optimal incremental quantity discount policy in benefiting both the supplier and the buyer

a supplier s optimal quantity discount policy under asymmetric information in the supply chain literature an increasing body of work studies how suppliers can use incentive schemes such as quantity discounts to influence buyers ordering behaviour thus reducing the supplier s and the total supply chain s costs various functional forms for such incentive schemes have been proposed but a critical assumption always made is that the supplier has full information about the buyer s cost structure we derive the optimal quantity discount policy under asymmetric information and compare it to the situation where the supplier has full information

coordinating ordering and pricing decisions in a two stage distribution system with price sensitive demand through short term discounting abstract we consider a short term discounting model in which the distributor offers a discounted price for the retailers orders placed at the beginning of its replenishment cycle in a non cooperative distribution system with one distributor and multiple retailers each facing price sensitive demand we examine the value of the price discount strategy as a mechanism for the distributor to coordinate the retailers ordering and pricing decisions under two common types of demand linear demand in price and constant elasticity demand in price our numerical study reveals that in the presence of homogeneous retailers namely retailers with identical demand rates the distributor s profit improvement due to coordination generally decreases as the number of retailers or the inventory holding cost rate increases but increases as price elasticity increases although an increase in the inventory holding cost rate has a negative effect on the distributor s profit it may have a positive effect on the retailers profits we further find that with heterogeneous retailers namely retailers with different demand rates offering a discounted price under linear demand benefits the distributor when both the inventory holding cost rate and the variation in demand are either small or large this cross effect however is absent under constant elasticity demand

equilibrium returns policies in the presence of supplier competition the pioneering pasternack returns policy model analyzed channel coordination with a single supplier catering to a retailer facing stochastic demand for a perishable product with a fixed price and the model showed that giving partial returns of unsold stock to the retailer is the optimal policy for the entire supply chain the result thus begs the question as to why manufacturers of perishable commodities widely accept full returns of unsold stock as the norm we model the environment as one where two capacity constrained manufacturers compete for shelf space with the same retailer and we show that a complete credit returns policy is in fact the only possible equilibrium of the game our results obviate the need for knowing the exact functional form of the demand distribution in order to compute the returns credit as pasternack s results would require from a retailer s standpoint we establish a simple procurement strategy and show that it is optimal the same game with price only contracting has a pure strategy equilibrium when the supplier capacities are below a threshold value and a mixed strategy equilibrium when the supplier capacities cross this threshold but are still so limited that no single supplier can with certainty supply all the quantity demanded

on the economics of state lotteries s tate lotteries can be evaluated from either of two perspectives familiar to economists as a consumer commodity or as a source of public revenue l as a commodity the lottery is notable for its broad market penetration and rapid growth sixty percent of the adults in lottery states play at least once in a year the annual growth in real per capita sales in lottery states has averaged 12 percent rising in 1989 dollars from 22 in 1975 to 108 in 1989 as a source of public revenue lotteries account for a rather modest fraction of revenue in states that run them 3 3 percent in 1986 but they are nonetheless one of the most visible state government activities lottery sales exceed those of all other products sold directly by state governments to the public and are larger than all but three major activities of state government education public welfare and highways clotfelter and cook 1989 table 2 5 moreover lotteries are a qualitatively new activity for state governments in that they are a business operated in effect for profit state liquor stores are perhaps the closest analog but they were created to encourage temperate drinking practices and do not engage in the sales promotion and marketing activities that are characteristic of the lotteries lotteries enjoy an honored place in american history as a device for raising funds for public purposes funding for such institutions as the jamestown settlement harvard college and the continental army as well as hundreds of bridges fire houses and schools came from lotteries but after the

quantity discounts managerial issues and research opportunities marketing managers frequently administer pricing policies involving substantial quantity discounts however our understanding of the precise role of these discounts and their design is quite limited this paper reviews and integrates the economics and marketing literature and presents a detailed analysis of the policies of four firms in order to i specify the variety of motivations for quantity discounts ii provide guidelines to managers in designing quantity discount schedules and iii set out the most fruitful directions for future research

government growth and private contributions to charity we exploit the time series properties of charitable giving to provide additional insights into the relationship between charitable contributions and government spending cointegration tests reveal a significant long run relationship between several categories of charitable giving and government spending granger causality tests provide evidence on the short run giving and spending relationship evidence suggests that charitable contributions to education respond quite differently to state and local government education expenditures versus federal government expenditures we argue that the government spending and charitable giving relationship depends on the source of government revenue how this revenue is used and the rational ignorance of private donors

multi buyer discount pricing abstract this article gives an exact optimal solution to the problem of finding the optimal discount price and price break quantity for a seller dealing with one buyer it also gives a method for solving the problem when one seller offers a single quantity discount schedule to many buyers the discount is of the all quantity type and the model of the cost structure was originally proposed by crowther

improving buyer seller system cooperation through inventory control abstract much of the literature pertaining to inventory control systems assumes a perfectly competitive market in which increases or decreases in the buyer s purchase costs affect neither the final retail price nor consumer demand this paper attempts to contribute results to the more recent literature characterized by the buyer seller in a monopolistic market the focus is on issues and advantages of improving buyer seller cooperation in an inventory control system two inventory models are structured in a game framework in the first model a noncooperative relationship transaction is assumed in which the seller as the leader makes the first decision and then the buyer as the follower makes its decision the unique equilibrium of the game is obtained and found to coincide with the classical eoq result in the second model the leader follower relationship is relaxed and a scenario is examined in which the seller and the buyer cooperatively maximize their joint system profit comparison of the two models reveals that 1 a the total system profit is higher at cooperation than at noncooperation 2 b the optimal order quantity of the buyer is higher at cooperation than at noncooperation 3 c the wholesale price of the seller to the buyer is lower at cooperation than at noncooperation it is also demonstrated that a quantity discount approach is an effective mechanism for achieving system cooperation

a one vendor multi buyer integrated inventory model abstract we consider a one vendor multi buyer integrated inventory model the vendor seeks to minimize his total annual cost subject to the maximum costs which buyers are prepared to incur in order to implement this model the vendor only needs to know buyer s annual demand and previous order frequency which can be inferred from buyer s past ordering behavior we find the optimal solution for the one vendor one buyer case and present a heuristic approach for the one vendor multi buyer case

an incremental discount pricing schedule with multiple customers and single price break abstract this paper analyzes how a supplier can formulate the terms of a quantity discount pricing schedule assuming a single incremental discount system a model is developed from which an algorithm is derived for an optimal discount schedule the cases are investigated in which both the discount rate and the break point are unknown and either one is prescribed a numerical example is presented to illustrate the algorithm developed

an optimization approach for supply chain management models with quantity discount policy abstract owing to the difficulty of treating nonlinear functions many supply chain management scm models assume that the average prices of materials production transportation and inventory are constant this assumption however is not practical vendors usually offer quantity discounts to encourage the buyers to order more and the producer intends to discount the unit production cost if the amount of production is large this study solves a nonlinear scm model capable of treating various quantity discount functions simultaneously including linear single breakpoint step and multiple breakpoint functions by utilizing the presented linearization techniques such a nonlinear model is approximated to a linear mixed 0 1 program solvable to obtain a global optimum

production lot sizing with work in process considerations in response to periodic demand abstract this paper develops two separate models for simultaneous determination of a product s manufacturing batch size and the order quantities of the input items that are used in the production process in response to periodic fixed purchase orders from a single customer the effects of work in process inventories resulting from a finite rate of production on the producer s cost function is explicitly taken into consideration in the model development process the first of these models assumes that all input items are procured lot for lot based on the production schedule of the output item this assumption is relaxed in the second model where multiple procurement lots for any input during a production cycle are allowed while an optimization procedure is outlined for solving the first model for the more generalized case an iterative heuristic solution algorithm is proposed due to the associated computational burden particularly for a large number of input items these concepts are illustrated through a numerical example

education s gambling problem earmarked lottery revenues and charitable donations to education i examine the impact that lotteries introduced to support education have on voluntary contributions to education state lotteries and the causes they are introduced to support are highly publicized this provides the opportunity to assess whether donors are crowded out by government spending of which they are almost certainly aware using donor level survey data and nonprofits tax returns i find that donations to education related organizations fall with the introduction of a lottery this result is driven by donors response to the new highly publicized government revenue source rather than a decrease in nonprofit fundraising efforts jel d64 h3 h75

single supplier multiple buyer supply chain coordination incorporating buyers expectations under vertical information sharing abstract we address the coordination problem in a single supplier multiple buyer supply chain the supplier wishes to coordinate the supply chain by offering quantity discounts to obtain their complete cost information the supplier exchanges his own cost parameters with buyers leading to vertical information sharing the supplier thinks that the buyers as they have access to supplier s setup and holding cost information may demand a portion of the anticipated coordination savings based on the partial information they hold about the cost structure of the entire supply chain we model each buyer s expectations based on her limited view of the entire supply chain which consists of herself and the supplier only these expectations are then incorporated into the modeling of the supply chain which results in a generalization of the traditional stackelberg type models we discuss alternative efficiency sharing mechanisms and propose methods to design the associated discount schemes that take buyers expectations into account in designing the discount schemes we consider both price discriminatory and non price discriminatory approaches the study adds to the existing body of work by incorporating buyers expectations into a constrained stackelberg structure and by achieving coordination without forcing buyers to explicitly comply with the supplier s replenishment period in choosing their order quantities the numerical analysis of the coordination efficiency and allocation of the net savings of the proposed discount schemes shows that the supplier is still able to coordinate the supply chain with high efficiency levels and retain a significant portion of the net savings

two echelon supply chain coordination through the unified number of annual orders abstract this paper studies the problem of how to coordinate a one supplier multi retailer supply chain by requiring retailers to adopt the unified number of annual orders proposed by the supplier the paper presents two coordination models one considering a small number of retailers the other considering a large number of retailers in the proposed models the supplier views all retailers or some selected retailers if more beneficial in the supply chain as one group then offers a price discount to entice the retailers in this group placing their orders only with the specific number of annual orders a heuristic is developed for each model to let the supplier know which retailers will be selected to implement the common number of annual orders and how to determine the corresponding optimal number of annual replenishments and price discount by using a numerical study we evaluate the benefit of the proposed coordination strategy

discount pricing for a family of items the supplier s optimal decisions abstract consider a family of skus for which the supplier will offer a quantity discount according to the aggregate purchases of the product group management of those items is based on the modified periodic policy from the supplier s point of view what are the optimal parameters breakpoint and discount percentage for deterministic demand we discuss the cases in which demand is both constant and price sensitive first as a noncooperative stackelberg game and then when the two parties make the discount and replenishment decisions jointly we illustrate the impact of price sensitivity and joint decision making on the supplier s discount policy

a cooperative game theory model of quantity discounts quantity discounts offered by a monopolist are considered in the context of a bargaining problem in which the buyer and the seller negotiate over the order quantity and the average unit price all units and incremental quantity discounts that permit transaction at a negotiated outcome are described the effects of risk sensitivity and bargaining power on quantity discounts are discussed for alternative bargaining models

pricing strategy for deteriorating items using quantity discount when demand is price sensitive abstract this study develops an optimal pricing and ordering policy for a deteriorating item with price sensitive demand since it usually benefits the vendor more than the buyer when both the buyer and the vendor are integrated a quantity discount pricing strategy is necessary to entice the buyer to accept the alliance a negotiation factor is incorporated to balance the profit sharing between both players sensitivity analysis with the numerical example shows that the integrated total cost is very sensitive to the deterioration rate and the price sensitive parameter the analysis resulted in an increase in the total joint profit therefore it is significant to consider the integrated vendor buyer strategy with quantity discount

note the role of returns policies in pricing and inventory decisions for catalogue goods manufacturers often use returns policies to encourage retailers to stock and price items more aggressively we focus on the effect that such policies have on both a retailer s and a manufacturer s profits when the retailer must commit prior to the selling season to both a stocking quantity and a price at which to sell an item such a commitment is often necessary for retailers who sell primarily through catalogues

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

earmarking lottery proceeds for public goods empirical evidence from u s lotto expenditures this study examines motives for lottery play using a state level panel of lottery expenditures we find that expenditures per capita are greater in states that earmark proceeds for public goods further we find that casino gambling only impacts lotto play in general fund states

supplier pricing and lot sizing when demand is price sensitive abstract the problem of co ordination between a vendor and a buyer is formulated as a two person fixed threat bargaining game the vendor decides on his lot size and the price schedule he is to offer to the buyer the buyer decides upon his lot size and the selling price in the market we have characterized pareto efficient solutions and the nash bargaining solution for the problem we have also proposed two pricing schedules for the vendor who is supplying to a large population of buyers the first one is based upon profit sharing the second one resembles the classical all unit quantity discount schedule we have thus provided for the supplier a procedure for setting all unit quantity discount schedule

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

game theoretic pricing and ordering decisions with partial lost sales in two stage supply chains abstract few papers have studied the optimal pricing and ordering with partial lost sales from a two stage game theoretic perspective this paper considers a supply chain game with a buyer and a seller through pricing and ordering models with partial lost sales we evaluate the optimal solutions for the buyer and the seller and provide insights into both the deterministic and stochastic demand models we also propose search algorithms to obtain the global optimum when convexity and concavity conditions are not satisfied

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