inventory of differential items selling from two shops under a single management with periodically increasing demand over a finite time horizon abstract inventories of differential items including the defective ones purchased produced in a lot and sold from two shops primary and secondary shops under a single management are considered here over a finite time horizon a primary shop receives the differential units in a lot but sells only the non defective ones whose demand periodically increases with time and decreases during the shortage period in such a way that it comes back to the initial value at the beginning of the next cycle hence in this shop shortages are allowed and fully backlogged moreover at the beginning of the next cycle the retailer purchases purely non defective units at a higher price to meet up the shortage amount along with the usual lot of differential units for regular sale the defective units identified at the time of selling at the primary shop are continuously transferred to the adjacent secondary shop from which the defective ones are sold at a reduced price after some rework normally the price of a defective item is fixed depending upon the quantum of its defect and people go for these items if they are cheap hence demand for these units is dependent on the selling price which is again inversely proportional to the rate of defectiveness there may be five scenarios for dealing with defective units depending upon the coincidence of the time periods at two shops for all scenarios problems have been mathematically formulated and solved by the use of both parametric study and a gradient based non linear optimisation method the models are illustrated with the help of numerical examples

perishable inventory theory a review this paper reviews the relevant literature on the problem of determining suitable ordering policies for both fixed life perishable inventory and inventory subject to continuous exponential decay we consider both deterministic and stochastic demand for single and multiple products both optimal and sub optimal order policies are discussed in addition a brief review of the application of these models to blood bank management is included the review concludes with a discussion of some of the interesting open research questions in the area

joint pricing and ordering policy for two echelon imperfect production inventory model with two cycles abstract this study deals with an imperfect epq economic production quantity price dependent inventory model over two types of cycles in the first cycle the retailer sells only good product with actual price and in the second he sells the products with a discount price in the production run time the non conforming items are produced at a random rate and they are reworked after the regular production run time and the reworked items are almost perfect as good as original quality items the retailer starts the second cycle when a certain percent of good items are left to him after the completion of regular production the retailer continues simultaneously two cycles up to which both types of the products are available to him now our objective is to find out optimal ordering lot size and optimal price for which the profit of the integrated model is maximum also we check the best strategy of retailer for the time of starting second cycle a numerical example is provided to illustrate the behavior and application of the model

advanced supply chain planning with mixtures of backorders lost sales and lost contract abstract this paper investigates a supply chain system in which a supplier prepares for the selling season by building stock levels prior to the beginning of the season and shortages realized at the beginning of the season are represented as mixtures of backorders and lost sales backlogged items are replenished as soon as possible through an emergency procurement as opposed to waiting until the next scheduled delivery as in many continuous review scenarios and the backorder rate is modeled as a piecewise linear function of the magnitude of the shortage the often intangible cost associated with lost sales and customer goodwill is also quantified in particular the buyer and supplier are engaged in a contractual agreement and the loss of customer goodwill from the supplier s perspective is represented as the expected cost associated with violating the conditions of the contract the likelihood of contract cancellation is also represented as a function of the magnitude of shortage the optimal solution is derived in closed form for the case of exponential demand distribution and an example problem is illustrated with numerical data in order to demonstrate calculation of the optimal solution and corresponding sensitivity analysis for demand distributions in which the solution cannot be expressed in closed form

analysis of an inventory system with exponential partial backordering abstract in this paper we study an inventory model with partial backlogging where unsatisfied demand is partially backlogged according to an exponential function in this model the total cost is the sum of the order cost the holding cost the backorder cost which includes a fixed cost and a cost proportional to the length of time for which the backorder exists and the cost of lost sales a general approach for finding the optimal policy is developed numerical examples are used to illustrate how the approach works

a comparison among various partial backlogging inventory lot size models for deteriorating items on the basis of maximum profit abstract during the past few years there are many researches that deal with different inventory shortage models for deteriorating items and then use minimizing cost as objective to find the optimal replenishment policy over a finite planning horizon in contrast to the other articles we here use maximizing profit as the objective to find the optimal replenishment policy we consider the case of partial backlogging for deteriorating items with four different inventory models not only the opportunity cost due to lost sale but also the purchase cost is taken into account we then make an appropriate comparison among these four alternatives finally some numerical examples are provided

modeling customer impatience in a newsboy problem with time sensitive shortages abstract customers across all stages of the supply chain often respond negatively to inventory shortages one approach to modeling customer responses to shortages in the inventory control literature is time dependent partial backlogging partial backlogging refers to the case in which a customer will backorder shortages with some probability or will otherwise solicit the supplier s competitors to fulfill outstanding shortages if the backorder rate i e the probability that a customer elects to backorder shortages is assumed to be dependent on the supplier s backorder replenishment lead time then shortages are said to be represented as time dependent partial backlogging this paper explores various backorder rate functions in a single period stochastic inventory problem in an effort to characterize a diversity of customer responses to shortages we use concepts from utility theory to formally classify customers in terms of their willingness to wait for the supplier to replenish shortages under mild assumptions we verify the existence of a unique optimal solution that corresponds to each customer type sensitivity analysis experiments are conducted in order to compare the optimal actions associated with each customer type under a variety of conditions additionally we introduce the notion of expected value of customer patience information evcpi and then conduct additional sensitivity analyses to determine the most and least opportune conditions for distinguishing between customer behaviors

effects of a hybrid price stock dependent demand on the optimal solutions of a deteriorating inventory system and trade credit policy on re manufactured product abstract this study contributes to formulate a deteriorating inventory model with a hybrid price stock dependent demand with credit for units in stock period in the presence of trade credit policy by using the discounted cash flow approach on re manufactured products in real life the demand function is not always constant or linear or nonlinear the demand rate of any items goes up and down in the real market due to the sum of two different types of demand this study observes that the demand is depending on price and stock of the product time value of money and trade credit policy the objective of this study is to find optimum cycle time optimum selling price and present profit of all future cash flows the model starts with mathematical formulating and thereafter studies the necessary and sufficient conditions for obtaining the unique optimal solution the theoretical solution procedure and case examples have studied for validation of this model moreover the sensitivity analysis is expressed out with respect to main parameters and managerial application is obtained this study uses the different demand functions of a simple pricing inventory system to find out the maximum profit on re manufactured products

haggling over substitutes abstract using a model of substitutable goods i determine generic conditions on tastes which guarantee that fixed prices are not optimal the fully optimal tariff includes lotteries that is a profit maximising seller would employ a haggling strategy we show that the fully optimal selling strategy in a class of cases requires a seller to not allow themselves to focus on one good but to remain haggling over more than one good this throws new light on the selling strategies used in diverse industries these insights are used to provide a counter example to the no lotteries result of mcafee and mcmillan j econ theory 46 1988 335

replenishment and pricing policy for deteriorating items taking into account the time value of money abstract a deteriorating inventory model taking into account the time value of money is developed for a deterministic inventory system with price dependent demand this study applies the discounted cash flows dcf approach for problem analysis a heuristic approach is presented to derive the near optimal replenishment and pricing policy that tries to maximize the total net present value profit a numerical example is implemented to illustrate the theory

an inventory model for deteriorating items with stock dependent consumption rate and shortages under inflation and time discounting this paper derives an inventory model for deteriorating items with stock dependent consumption rate and shortages under inflation and time discounting over a finite planning horizon we show that the total cost function is convex with the convexity a simple solution algorithm is presented to determine the optimal order quantity and the optimal interval of the total cost function the results are discussed with a numerical example and particular cases of the model are discussed in brief a sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out

an economic order quantity model with partial backordering and all units discount abstract the classic economic order quantity model assumes that the unit purchasing cost is not based on the order quantity in practice a supplier may offer purchasers an all units discount we develop a model and solution procedure for the eoq with all unit discounts and partial backordering at a constant rate we show and illustrate with a numerical example how that model can be used to find the solution for the eoq with discount and full backordering a multi factor experiment is used to gain insights into the improvement in performance of the proposed procedure relative to using the basic eoq or the eoq with full backordering and to identify the model parameters that have the greatest impact on the model s performance

an inventory model with partial backordering and unit backorder cost linearly increasing with the waiting time as the implementation of jit practice becomes increasingly popular each echelon in a supply chain tends to carry fewer inventories and thus the whole supply chain is made more vulnerable to lost sales and or backorders the purpose of this paper is to recast the inventory model to be more relevant to current situations where the penalty cost for a shortage occurrence at a downstream stage in a supply chain is continually transmitted to the upstream stages the supplier in this case at the upstream of the supply chain is responsible for all the downstream shortages due to the chain reaction of its backlog the current paper proposes a model in which the backorder cost per unit time is a linearly increasing function of shortage time and it claims that the optimal policy for the supplier is setting the optimal shortage time per inventory cycle to minimize its total relevant cost in a jit environment

foundations of dominant strategy mechanisms wilson 1987 criticizes applied game theory s reliance on common knowledge as sumptions in reaction to wilson s critique the recent literature of mechanism design has adopted the goal of finding detail free mechanisms in order to eliminate this re liance in practice this has meant restricting attention to simple mechanisms such as dominant strategy mechanisms however there has been little theoretical foundation for this approach in particular it is not clear the search for an optimal mechanism that does not rely on common knowledge assumption would lead to simpler mechanisms rather than more complicated ones this paper tries to fill the void in the context of an expected revenue maximizing auctioneer we investigate some foundations for using simple dominant strategy auctions

an integrated mixture of local experts model for demand forecasting abstract demand forecasting is an important issue in the supply chain planning process due to its usage for efficiently managing different planning tasks the common techniques adopted to perform such task are easy to use forecasting methods performed in computerised systems with minimum human intervention such as the simple exponential smoothing concerning the drawbacks of these modelling approaches past evidence suggests that they have been less successful in predicting short term fluctuations on demand in this work the simple exponential smoothing method is employed to build an integrated mixture of local experts model imlem for demand forecasting using as independent variable a lagged gross domestic product gdp indicator the imlem is usually employed to deal with rapidly changing situations and it is used in this work to improve the performance of the forecasts by providing a way to take into account short term fluctuations on demand due to changes on economic activity growth within an easy to use forecasting method the proposed method was applied on one step ahead demand forecasting for a brazilian beverage manufacturer for 130 non seasonal stock keeping units skus and the accuracy of the generated forecasts allowed to reduce the forecasting errors the obtained results also supported the decision making process by aiding demand planners concerning how to react to short term fluctuations on demand

robust auctions for revenue via enhanced competition in robust auctions for revenue via enhanced competition t roughgarden i talgam cohen and q yan revisit the classic bulow klemperer result this result compares the revenues of two well know

bundling as an optimal selling mechanism for a multiple good monopolist abstract multiple objects may be sold by posting a schedule consisting of one price for each possible bundle and permitting the buyer to select the price bundle pair of his choice we identify conditions that must be satisfied by any price schedule that maximizes revenue within the class of all such schedules we then provide conditions under which a price schedule maximizes expected revenue within the class of all incentive compatible and individually rational mechanisms in the n object case we use these results to characterize environments mainly distributions of valuations where bundling is the optimal mechanism in the two and three good cases

on the stock control performance of intermittent demand estimators the purpose of this paper is to assess the empirical stock control performance of intermittent demand estimation procedures the forecasting methods considered are the simple moving average single exponential smoothing croston s method and a new method recently developed by the authors of this paper we first discuss the nature of the empirical demand data set 3000 stock keeping units and we specify the stock control model to be used for experimentation purposes performance measures are then selected to report customer service level and stock volume differences the out of sample empirical comparison results demonstrate the superior stock control performance of the new intermittent demand forecasting method and enable insights to be gained into the empirical utility of the other estimators

deteriorating inventory model with quantity discount pricing and partial backordering inventory models with quantity discount pricing and partial backordering although common in practice have received very little attention from researchers the objective of this study is to develop a deterministic inventory model with quantity discount pricing and partial backordering when the product in stock deteriorates with time most retailers make pricing decisions of their products at certain times of the year and these decisions affect demand in this study the demand rate is assumed to decrease as price for the product increases unlike traditional inventory models that seek to minimize cost the objective of this study is to maximize profit the findings of this study are particularly relevant to retailers of deteriorating products in a competitive environment a numerical example is given to illustrate the theory

forecasting and inventory performance in a two stage supply chain with arima 0 1 1 demand theory and empirical analysis the arima 0 1 1 demand model has been analysed extensively by researchers and used widely by forecasting practitioners due to its attractive theoretical properties and empirical evidence in its support however no empirical investigations have been conducted in the academic literature to analyse demand forecasting and inventory performance under such a demand model in this paper we consider a supply chain formed by a manufacturer and a retailer facing an arima 0 1 1 demand process the relationship between the forecasting accuracy and inventory performance is analysed along with an investigation on the potential benefits of forecast information sharing between the retailer and the manufacturer results are obtained analytically but also empirically by means of experimentation with the sales data related to 329 stock keeping units skus from a major european superstore our analysis contributes towards the development of the current state of knowledge in the areas of inventory forecasting and forecast information sharing and offers insights that should be valuable from the practitioner perspective

integrating deterioration and lifetime constraints in production and supply chain planning a survey abstract items with short lifetimes that are subject to deterioration are important in the business world research has a long tradition in integrating deterioration and value loss effects into mathematical models for inventory planning and control where such effects are understood as a general loss or shrinkage of inventory however there has been little work in the modeling of lifetime restrictions of items to prevent wastage and disposals especially in a dynamic planning context globalization and other trends extend the consideration of single companies to whole supply chains implying increased coordination and information needs this is important as planning decisions impact lead times and thus the quality of items in the whole supply chain products that exceed their useful lifetime can impose high costs due to inventory loss or the need to rework them this implies increased utilization of scarce resources e g machine time metals and or energy thereby increasing co 2 levels we survey the state of the art regarding depreciation effects and the modeling of lifetime constraints as well as a classification of models following business planning functions of the value chain a critical evaluation of approaches and their limitations is provided highlighting directions for future research

supply chain networks with corporate financial risks and trade credits under economic uncertainty abstract the focus of this paper is to provide an analytical framework which can be used to investigate how financial risks affect the values of interconnected supply chain firms from a network perspective and how financial risks affect the supply chain firms profitability as well as the cash and credit transactions in particular we develop a variational inequality equilibrium model in conjunction with capital asset pricing model capm and the net present value npv to determine the optimal supply chain prices profits and implicit equity values of supply chain firms under financial risks and economic uncertainty we illustrate the analytical framework with computational studies which yield interesting managerial implications to the following questions 1 how do financial risks and economic uncertainty affect the values of interconnected supply chain firms from a network perspective 2 how do financial risks and economic uncertainty affect the supply chain firms profitability as well as the cash and credit transactions 3 how does the effect of financial risks change under different competition scenarios

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

application of multi steps forecasting for restraining the bullwhip effect and improving inventory performance under autoregressive demand recent research suggests that the bullwhip effect or increasing variability of inventory replenishment orders as one moves up a supply chain illustrates inventory management inefficiencies this paper quantifies the bullwhip effect in the case of serially correlated external demand if autoregressive models are applied to obtain multiple steps demand forecasts a materials requirements planning mrp based inventory management approach is proposed to reduce the order variance simulation modeling is used to investigate the impact of the forecasting method selection on the bullwhip effect and inventory performance for the most downstream supply chain unit the mrp based approach is shown to reduce magnitude of the bullwhip effect while providing the inventory performance comparable to that of a traditional order up approach the application of autoregressive models compares favorably to other forecasting methods considered according to both the bullwhip effect and inventory performance criteria

revisiting the value of information sharing in two stage supply chains abstract there is a substantive amount of literature showing that demand information sharing can lead to considerable reduction of the bullwhip effect inventory costs the core argument analysis underlying these results is that the downstream supply chain member the retailer quickly adapts its inventory position to an updated end customer demand forecast however in many real life situations retailers adapt slowly rather than quickly to changes in customer demand as they cannot be sure that any change is structural in this paper we show that the adaption speed and underlying unknown demand process crucially affect the value of information sharing for the situation with a single upstream supply chain member manufacturer and a single retailer we consider two demand processes stationary or random walk these represent two extremes where a change in customer demand is never or always structural respectively the retailer and manufacturer both forecast demand using a moving average where the manufacturer bases its forecast on retailer demand without information sharing but on end customer demand with information sharing in line with existing results the value of information turns out to be positive under stationary demand one contribution though is showing that some of the existing papers have overestimated this value by making an unfair comparison our most striking and insightful finding is that the value of information is negative when demand follows a random walk and the retailer is slow to react slow adaptation is the norm in real life situations and deserves more attention in future research exploring when information sharing indeed pays off

supply chain forecasting when information is not shared the operations management literature is abundant in discussions on the benefits of information sharing in supply chains however there are many supply chains where information may not be shared due to constraints such as compatibility of information systems information quality trust and confidentiality furthermore a steady stream of papers has explored a phenomenon known as downstream demand inference ddi where the upstream member in a supply chain can infer the downstream demand without the need for a formal information sharing mechanism recent research has shown that under more realistic circumstances ddi is not possible with optimal forecasting methods or single exponential smoothing but is possible when supply chains use a simple moving average sma method in this paper we evaluate a simple ddi strategy based on sma for supply chains where information cannot be shared this strategy allows the upstream member in the supply chain to infer the consumer demand mathematically rather than it being shared we compare the ddi strategy with the no information sharing nis strategy and an optimal forecast information sharing fis strategy in the supply chain the comparison is made analytically and by experimentation on real sales data from a major european supermarket located in germany we show that using the ddi strategy improves on nis by reducing the mean square error mse of the forecasts and cutting inventory costs in the supply chain

on the equivalence of bayesian and dominant strategy implementation we consider a standard social choice environment with linear utilities and independent one dimensional private types we prove that for any bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus the short proof is based on an extension of an elegant result due to gutmann kemperman reeds and shepp 1991 we also show that the equivalence between bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed or when the equivalence concept is strengthened to apply to interim expected allocations

information distortion in a supply chain the bullwhip effect this article originally appeared in management science april 1997 volume 43 number 4 pp 546 558 published by the institute of management sciences consider a series of companies in a supply chain each of whom orders from its immediate upstream member in this setting inbound orders from a downstream member serve as a valuable informational input to upstream production and inventory decisions this paper claims that the information transferred in the form of orders tends to be distorted and can misguide upstream members in their inventory and production decisions in particular the variance of orders may be larger than that of sales and distortion tends to increase as one moves upstream a phenomenon termed bullwhip effect this paper analyzes four sources of the bullwhip effect demand signal processing rationing game order batching and price variations actions that can be taken to mitigate the detrimental impact of this distortion are also discussed

discounted costs obsolescence and planned stockouts with the eoq formula abstract in this paper we propose a simple economic order quantity for a class of inventory management problems concerning items with a short and stochastic lifetime the analysis is relevant to the management of items in industries subject to fast technological progress where the obsolescence rate is large the approach is performed in the framework of the total discounted cost criterion a new economic order quantity is computed it may turn out to be significantly smaller than the one given by wilson formula finally we show that a policy maker who faces the risk of obsolescence can plan stockouts if sufficiently many customers accept late delivery

optimal price and order size under partial backordering incorporating shortage backorder and lost sale costs abstract in this paper we consider the pricing and lot sizing problem for a product subject to general rate of deterioration and partial backordering we use impatience functions to model backlogging of demand we show that even when lost sale and backorder costs are present the problem is well posed in the reduced space we provide an iterative procedure for solving the overall problem we describe structural properties of the solution for the new model and comment on the recent work incorporating backorder cost we illustrate the solution procedure for the new model with examples

reduction of the value of information sharing as demand becomes strongly auto correlated information sharing has been identified in the academic literature as one of the most important levers to mitigate the bullwhip effect in supply chains a highly cited article on the bullwhip effect has claimed that the percentage inventory reduction resulting from information sharing in a two level supply chain when the downstream demand is autoregressive of order one is an increasing function of the autoregressive parameter of the demand in this paper we show that this is true only for a certain range of the autoregressive parameter and there is a maximum value beyond which the bullwhip ratio at the upstream stage is reduced and the percentage inventory reduction resulting from information sharing decreases towards zero we also show that this maximum value of the autoregressive parameter can be as high as 0 7 which represents a common value that may be encountered in many practical contexts this means that large benefits of information sharing cannot be assumed for those stock keeping units skus with highly positively auto correlated demand instead equally careful analysis is needed for these items as for those skus with less strongly auto correlated demand

an arima supply chain model this paper presents a multistage supply chain model that is based on autoregressive integrated moving average arima time series models given an arima model of consumer demand and the lead times at each stage it is shown that the orders and inventories at each stage are also arima and closed form expressions for these models are given the paper also discusses the causes of the bullwhip effect a phenomenon in which variation in demand produces larger variations in upstream orders and inventory this discussion reveals how different modeling can lead to different insights because they make different assumptions about the cause of the bullwhip effect these observations are used to develop managerial insights about reducing the bullwhip effect

an ascending vickrey auction for selling bases of a matroid consider selling bundles of indivisible goods to buyers with concave utilities that are additively separable in money and goods we propose an ascending auction for the case when the seller is constrained to sell bundles whose elements form a basis of a matroid it extends easily to polymatroids applications include scheduling allocation of homogeneous goods and spatially distributed markets among others our ascending auction induces buyers to bid truthfully and returns the economically efficient basis unlike other ascending auctions for this environment ours runs in pseudopolynomial or polynomial time furthermore we prove the impossibility of an ascending auction for nonmatroidal independence set systems

buy it now or take a chance price discrimination through randomized auctions increasingly detailed consumer information makes sophisticated price discrimination possible at fine levels of aggregation demand may not obey standard regularity conditions we propose a new randomized sales mechanism for such environments bidders can buy it now at a posted price or take a chance in an auction where the top d 1 bidders are equally likely to win the randomized allocation incentivizes high valuation bidders to buy it now we analyze equilibrium behavior and apply our analysis to advertiser bidding data from microsoft advertising exchange in counterfactual simulations our mechanism increases revenue by 4 4 and consumer surplus by 14 5 compared to an optimal second price auction this paper was accepted by assaf zeevi stochastic models and simulation

on bullwhip in a family of order up to policies with arma 2 2 demand and arbitrary lead times a number of papers have recently appeared that investigate the bullwhip effect the variance amplification of ordering decisions in the supply chain produced by the order up to replenishment policy an adapted policy with a proportional inventory position feedback controller has shown improved bullwhip behaviour the dynamic behaviour of this so called proportional order up to policy has been investigated for arbitrary lead times and several demand models such as i i d demand and autoregressive moving average ar 1 and arma 1 1 models it has been shown that for a correct choice of the feedback parameter the bullwhip effect can always be avoided however less attractive properties of this policy have also become clear herein we investigate the behaviour of the proportional order up to policy for arma 2 2 demand with arbitrary lead times in order to compensate for possible weaknesses of the proportional out policy we propose another replenishment rule that accounts for the characteristics of the demand in a superior manner the characteristics of both policies are compared for several parameter settings of the arma 2 2 model finally the consequences of our full state feedback order up to policy are discussed

optimal pricing mechanisms with unknown demand the standard profit maximizing multi unit auction intersects the submitted demand curve with a preset reservation supply curve which is determined using the distribution from which the buyers valuations are drawn however when this distribution is unknown a preset supply curve cannot maximize monopoly profits the optimal pricing mechanism in this situation sets a price to each buyer on the basis of the demand distribution inferred statistically from other buyers bids the resulting profit converges to the optimal monopoly profit with known demand as the number of buyers goes to infinity and convergence can be substantially faster than with sequential price experimentation

an inventory model with deteriorating items quantity discount pricing and time dependent partial backlogging abstract wee international journal of production economics 59 1999 511 in his interesting paper presented a deterministic inventory model with the following characteristics quantity discount schemes for the unit cost partial backlogging at a fixed rate deterioration of stock in time and demand rate being a linear function of the selling price in this article we generalize the work of wee 1999 more specifically we consider a model where the demand rate is a convex decreasing function of the selling price and the backlogging rate is a time dependent function which ensures that the rate of backlogged demand increases as the waiting time to the following replenishment point decreases

inventory models with variable lead time and present value the figures for inventory make up a huge proportion of a company s working capital because of this we formulated the optimal replenishment policy considering the time value of money to represent opportunity cost in this article we provide a mixed inventory model in which the distribution of lead time demand is normal to consider the time value first the study tries to find the optimal reorder point and order quantity at all lengths of lead time with components crashed to their minimum duration secondly we develop a method to insure the uniqueness of the reorder point to locate the optimal solution finally some numerical examples are given to illustrate our findings

a comparison between two pricing and lot sizing models with partial backlogging and deteriorated items abstract recently abad 2003 optimal pricing and lot sizing under conditions of perishability finite production and partial backordering and lost sale european journal of operational research 144 677 685 studied the pricing and lot sizing problem for a perishable good under finite production exponential decay partial backordering and lost sale in this article we extend his model by adding not only the backlogging cost but also the cost of lost goodwill we then analytically compare the net profits per unit time between abad s 2003 model and goyal and giri s 2003 the production inventory problem of a product with time varying demand production and deterioration rates european journal of operational research 147 549 557 model in abad s model the cycle starts with an instant production to accumulate stocks then stops production to use up stocks and finally restarts production to meet the unsatisfied demands by contrast in goyal and giri s model the cycle begins with a period of shortages then starts production until accumulated inventory reaches certain level and finally stops production and uses up inventory our theoretical results show that there is no dominant one between these two models furthermore we provide certain conditions under which one model has more net profit per unit time than the other finally we give several numerical examples to illustrate the results

an optimal replenishment policy for non instantaneous deteriorating items with stock dependent demand and partial backlogging abstract in this study we consider a problem of determining the optimal replenishment policy for non instantaneous deteriorating items with stock dependent demand in the model shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment the necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown as the special cases the results for the models with instantaneous or non instantaneous deterioration rate and with or without shortages are derived further we analytically identify the best circumstance among these special cases based on the minimum total relevant cost per unit time sensitivity analysis of the optimal solution with respect to major parameters is carried out finally four numerical examples are presented to demonstrate the developed model and the solution procedure

optimal pricing strategy for new products robinson and lakhani 1975 initiated a long research stream in marketing when they used the bass model 1969 to develop optimal pricing path for a new product a careful analysis of the extant literature reveals that the research predominantly suggests that the optimal price path should be largely based on the sales growth pattern however in the real world we rarely find new products that have such pricing pattern we observe either a monotonically declining pricing pattern or an increase decrease pricing pattern that does not seem close to the sales path in this paper we use a variation of the generalized bass model called gbm developed by bass et al 1994 that yields optimal pricing policies that are consistent with empirical data

an integrated production inventory model with imperfect production processes and weibull distribution deterioration under inflation abstract this study develops an integrated production and inventory model from the perspectives of both the manufacturer and the retailer the model assumes a varying rate of deterioration partial backordering inflation imperfect production processes and multiple deliveries the elapsed time until the production process shift is assumed to be arbitrarily distributed the discounted cash flow and classical optimization technique are used to derive the optimal solution a numerical example including the sensitivity analysis is given to validate the results of the production inventory model the integrated decision results in lower optimal joint cost compared with an independent decision by the manufacturer and the retailer

joint pricing and replenishment policy for deteriorating inventory with declining market abstract this study deals with a deteriorating inventory model where demand decreases linearly with time and cost of items planning horizon is assumed to be finite the replenishment cycles are constant and shortages are partially back ordered the net profit maximizing ordering policy and price are determined for different degree of partial back ordering the reduction in revenue resulted from lost sale is expressed in the lost sale shortage penalty in the total cost formulation a solution method based on nonlinear programming code and the hessian matrix guarantees global optimality of the solution a numerical example is provided to illustrate the theory

strong duality for a multiple good monopolist we characterize optimal mechanisms for the multiple good monopoly problem and provide a framework to find them we show that a mechanism is optimal if and only if a measure derived from the buyer s type distribution satisfies certain stochastic dominance conditions this measure expresses the marginal change in the seller s revenue under marginal changes in the rent paid to subsets of buyer types as a corollary we characterize the optimality of grand bundling mechanisms strengthening several results in the literature where only sufficient optimality conditions have been derived as an application we show that the optimal mechanism for n independent uniform items each supported on c c 1 is a grand bundling mechanism as long as c is sufficiently large extending pavlov s result for two items pavlov 2011 at the same time our characterization also implies that for all c and for all sufficiently large n the optimal mechanism for n independent uniform items supported on c c 1 is not a grand bundling mechanism

planning for shortages net present value analysis for a deteriorating item with partial backlogging abstract this paper develops inventory models to help answer strategic questions concerning whether planning for shortages offers financial benefits a production inventory system producing a deteriorating product in batches at a finite production rate with partial backordering is considered customers pay a deposit when placing a backorder backordered items receive a discount on the sales price as lost sales may lead to customers not returning the demand rate may depend on the fraction of lost sales we develop a cash flow based profit maximising net present value npv model without the inventory cost parameters commonly used in this context unit holding cost unit backorder cost unit deterioration cost and unit lost sales cost the model finds the optimal inventory policy just like npv models that discount the traditional parameters but has the advantage of not needing to estimate the value of the traditional parameters it is shown that in models based on discounting the traditional parameters the parameters are not exogenously determinable but are non trivial functions of non financial endogenous system parameters such as the production rate annual demand rate and backorder rate extensive numerical experiments illustrate how cash flow npv models provide insights into the value of planning for shortages and strategic choices about the design of the production inventory system it also provides insight into the classical problem of how to interpret unit backorder cost and unit lost sales cost the study indicates that these insights cannot be reliably obtained from npv models based on discounting unit backorder costs and unit lost sales costs

an inventory model for perishable items in a lot size system with quantity discounts abstract an inventory model continuous in units and time is developed for perishable items in a lot size system that allows partially backlogging and partially lost saling the model is developed under deterministic demand instantaneous delivery with quantity discounts and any well behaved probability distribution for the time to perishables an example is given to illustrate the model

demand forecasting with four parameter exponential smoothing abstract exponential smoothing methods are powerful tools for denoising time series predicting future demand and decreasing inventory costs in this paper we develop a smoothing and forecasting method that is intuitive easy to implement computationally stable and can satisfactorily handle both additive and multiplicative seasonality even when time series contain several zero entries and large noise component we start with the classical additive holt winters method and introduce an additional smoothing parameter in the level recurrence equation all parameters are required to lie within 0 1 and estimated by minimizing the one step ahead forecasting errors in the sample doing so the errors decrease substantially especially for the time series with strong trends the newly developed method produces more accurate short term out of sample forecasts than the classical holt winters methods and the holt winters methods with damped trend the performance of the method is evaluated using a battery of real quarterly and monthly time series from the m3 competition a simulation study is conducted for further in depth analysis of the method under different demand patterns we developed and justified the use of a symmetric relative efficiency measure that allows researchers ad practitioners to evaluate the performance of different smoothing and forecasting methods

effects of inflation and time value of money on an inventory model with time dependent demand rate and shortages abstract in a recent paper datta and pal investigated the effects of inflation and time value of money on an inventory model with linearly increasing demand and finite shortage cost however their models are formulated under the assumption of equal inventory carrying time during each replenishment cycle in this paper we redevelop the models of datta and pal by relaxing this assumption and modifying their mathematical formulations our models can be applicable to both growing and declining markets with general continuous time dependent demand rates numerical examples are provided to illustrate the developed models

an epq model of ramp type demand with weibull deterioration under inflation and finite horizon in crisp and fuzzy environment abstract this paper deals with an economic production model for deteriorating items with ramp type demand rate a single item is produced and the finite rate of production is proportional to the demand rate the deterioration rate of the item is taken as two parameter weibull s distribution we also have considered the effect of inflation when there is no shortage in the stock and the model is under finite time horizon the inventory model is solved under crisp and fuzzy environment to evaluate the optimum solution of the model in different cases we illustrate the model with an example by taking various number of replenishment we present sensitivity analysis to illustrate the example under crisp and fuzziness thus the objective of the paper is to find the optimal solution of production time so as to minimize the present value of total cost of the whole replenishment cycle and to check which environment crisp or fuzzy is desirable

multi item auctions a collection of items is to be distributed among several bidders and each bidder is to receive at most one item assuming that the bidders place some monetary value on each of the items it has been shown that there is a unique vector of equilibrium prices that is optimal in a suitable sense for the bidders in this paper we describe two dynamic auction mechanisms one achieves this equilibrium and the other approximates it to any desired degree of accuracy

holding costs under push or pull conditions the impact of the anchor point holding costs are traditionally determined from the investment in physical stock during a cycle an alternative approach instead derives holding costs from net present value npv functions it is known that applying both frameworks to the same system can lead to different holding cost valuations but little explanation has been offered by introducing the anchor point in a model this paper shows for four different systems that traditional holding cost models implicitly assume pull conditions while current npv approaches model push conditions this explains in part the differences between the methods it is shown that the anchor point concept allows the construction of npv models under pull conditions giving results in better correspondence with traditional models the traditional framework is restricted to pull conditions and important considerations could be easily overlooked leading to wrong valuations of holding costs npv seems superior as such considerations are automatically incorporated the application to multi echelon inventory systems provides interesting insights on the roles of echelon stocks and lead times and offers potential for future research

the effects of integrating management judgement into intermittent demand forecasts empirical research suggests that quantitatively derived forecasts are very frequently judgementally adjusted nevertheless little work has been conducted to evaluate the performance of these judgemental adjustments in a practical demand sales context in addition the relevant analysis does not distinguish between slow and fast moving items currently there are neither conceptual developments nor empirical evidence on the issue of integrating judgements and statistical forecasts for slow intermittent demand items moreover no results have ever been reported on the stock control implications of these human judgements our work analyses monthly intermittent demand forecasts for the uk branch of a major international pharmaceutical company the company relies upon a commercially available statistical forecasting system to produce forecasts that are subsequently judgementally adjusted based on marketing intelligence gathered by the company forecasters the benefits of the intervention are evaluated by comparing the actual sales to system and final forecasts using both forecast accuracy and inventory control accuracy implication metrics our study allows insights to be gained on potential improvements to intermittent demand forecasting processes and subsequently the design effectiveness of forecasting support systems

auctions versus negotiations which is the more profitable way to sell a company an auction with no reserve price or an optimally structured negotiation with one less bidder we show under reasonable assumptions that the auction is always preferable when bidders signals are independent for affiliated signals the result holds under certain restrictions on the seller s choice of negotiating mechanism the result suggests that the value of negotiating skill is small relative to the value of additional competition the paper also shows how the analogies between monopoly theory and auction theory can help derive new results in auction theory jel d44 g34 there are close analogies between standard price theory and the theory of auctions in an absolute english auction in which the price rises continuously until only one bidder remains and the seller is required to accept the final bid the sale price equals the lowest competitive price at which supply equals demand in the theory of optimal auctions the seller is treated as a monopolist who can choose any

optimal pricing and lot sizing under conditions of perishability and partial backordering we formulate a generalized model of dynamic pricing and lot sizing by a reseller who sells a perishable good we assume that when it is economic to backlog demand the reseller can plan for periods of shortage during which demand can be partially backordered when the good is highly perishable the reseller may need to backlog demand in order to market the good at a reasonable price we present a simple solution procedure for solving the optimization problem the procedure entails solving first a single nonlinear equation and then if required two nonlinear equations

a survey of deterministic models for the eoq and epq with partial backordering models for the basic deterministic eoq or epq problem with partial backordering or backlogging make all the assumptions of the classic eoq or epq model with full backordering except that only a fraction of the demand during the stockout period is backordered in this survey we review deterministic models that have been developed over the past 40 years that address the basic models and extensions that add other considerations such as pricing perishable or deteriorating inventory time varying or stock dependent demand quantity discounts or multiple warehouses

measuring and avoiding the bullwhip effect a control theoretic approach an important contributory factor to the bullwhip effect i e the variance amplification of order quantities observed in supply chains is the replenishment rule used by supply chain members first the bullwhip effect induced by the use of different forecasting methods in order up to replenishment policies is analysed variance amplification is quantified and we prove that the bullwhip effect is guaranteed in the order up to model irrespective of the forecasting method used thus when production is inflexible and significant costs are incurred by frequently switching production quantities up and down order up to policies may no longer be desirable or even achievable in the second part of the paper a general decision rule is introduced that avoids variance amplification and succeeds in generating smooth ordering patterns even when demand has to be forecasted the methodology is based on control systems engineering and allows important insights to be gained about the dynamic behaviour of replenishment rules

effects of inflation and the time value of money on order quantity and allowable shortage abstract this paper investigates the effects of inflation and time value of money on the optimal ordering quantities and the maximum allowable shortage in a finite replenishment inventory system the present value of total cost incurred in this inventory system is developed first then an optimal order quantity and maximum allowable shortage are obtained by using a search procedure the effect of inflation and time value of money was investigated under given sets of values of inflation and discount rates this study shows that the optimal order quantity and maximum allowable shortage vary with the change in difference between inflation and time discount computational results indicate that this effect on the system becomes more significant with the increase of the difference between inflation rate and time discount rate