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

comments on the eoq model for deteriorating items with conditional trade credit linked to order quantity in the supply chain management abstract ouyang et al 2009 consider an economic order quantity eoq model for deteriorating items with a partially permissible delay in payments linked to order quantity basically their inventory model is practical but there are some defects from the logical viewpoints of mathematics in this paper the functional behaviors of the annual total relevant costs are explored by rigorous methods of mathematics a complete solution procedure is also developed to make up for the shortcomings of ouyang et al 2009 in numerical examples it is proved that the new solution procedure could avoid making wrong decisions and causing cost penalties

optimal pricing and return policies for perishable commodities this paper considers the pricing decision faced by a producer of a commodity with a short shelf or demand life a hierarchical model is developed and the results of the single period inventory model are used to examine possible pricing and return policies the paper shows that several such policies currently in effect are suboptimal these include those where the manufacturer offers retailers full credit for all unsold goods or where no returns of unsold goods are permitted the paper also demonstrates that a policy whereby a manufacturer offers retailers full credit for a partial return of goods may achieve channel coordination but that the optimal return allowance will be a function of retailer demand therefore such a policy cannot be optimal in a multi retailer environment it is proven however that a pricing and return policy in which a manufacturer offers retailers a partial credit for all unsold goods can achieve channel coordination in a multi retailer environment this article was originally published in marketing science volume 4 issue 2 pages 166 176 in 1985

periodic review and continuous ordering abstract many inventory control studies consider either continuous review and continuous ordering or periodic review and periodic ordering mixtures of the two are hardly ever studied however the model with periodic review and continuous ordering is highly relevant in practice as information on the actual inventory level is not always up to date while making ordering decisions this paper will therefore treat this model assuming zero fixed ordering costs and allowing for a non negative lead time and a general demand process we first consider a one period decision problem without salvage cost for inventory remaining at the end of the period in this setting we derive a base line optimal order path described by a simple newsvendor solution with safety stocks increasing towards the end of a review period we then show that for the general multi period problem the optimal policy in a period is to first arrive at this path by not ordering until the excess buffer stock from the previous review period is depleted then follow the path by continuous ordering and stop ordering towards the end to limit excess stocks for the next review period an important managerial insight is that typically no order should be placed at a review moment although this may seem intuitive and is also the standard assumption in periodic review models we illustrate that adhering to the optimal ordering path instead can lead to cost reductions of 30 60 percent compared to pure periodic ordering

pricing and lot sizing polices for perishable goods when the demand depends on selling price displayed stocks and expiration date abstract price is a major factor on the demand based on marketing and economic theory in addition the demand for perishable products also depends on its freshness moreover it is a well known fact that increasing stock display e g fresh fruits vegetables baked goods may encourage consumers to purchase more this paper first proposes an inventory model that stipulates the demand explicitly in a multivariate function of price freshness and displayed stocks it may be profitable to have a closeout sale at a markdown price and always keep on hand displayed stocks fresh and plentiful if the demand is freshness and stock dependent hence the traditional assumption of zero ending inventories is relaxed to a non zero ending inventory as a result the objective is to determine three decision variables i e unit price cycle time and ending inventory level in order to maximize the total profit then it is demonstrated that the total profit is strictly pseudo concave in those three decision variables which reduces the search for solutions to a unique local maximum finally numerical examples to illustrate the theoretical results and to highlight managerial insights are presented

an optimization approach for managing fresh food quality throughout the supply chain one of the most challenging tasks in today s food industry is controlling the product quality throughout the food supply chain in this paper we integrate food quality in decision making on production and distribution in a food supply chain we provide a methodology to model food quality degradation in such a way that it can be integrated in a mixed integer linear programming model used for production and distribution planning the resulting model is applied in an illustrative case study and can be used to design and operate food distribution systems using both food quality and cost criteria

an milp approximation for ordering perishable products with non stationary demand and service level constraints abstract we study the practical production planning problem of a food producer facing a non stationary erratic demand for a perishable product with a fixed life time in meeting the uncertain demand the food producer uses a fifo issuing policy the food producer aims at meeting a certain service level at lowest cost every production run a setup cost is incurred moreover the producer has to deal with unit production cost unit holding cost and unit cost of waste the production plan for a finite time horizon specifies in which periods to produce and how much we formulate this single item single echelon production planning problem as a stochastic programming model with a chance constraint we show that an approximate solution can be provided by an milp model the generated plan simultaneously specifies the periods to produce and the corresponding order up to levels the order up to level for each period is corrected for the expected waste by explicitly considering for every period the expected age distribution of the products in stock the model assumes zero lead time and backlogging of shortages the viability of the approach is illustrated by numerical experiments simulation shows that in 96 4 of the periods the service level requirements are met with an error tolerance of 1

the social costs of monopoly and regulation posner reconsidered focuses on social costs of monopoly and trade regulation in the united states benefit of marginal changes on antitrust activities equality of cost in obtaining monopoly and expected profit of monopolist elasticity of inputs in obtaining monopoly ebsco

age based vs stock level control policies for a perishable inventory system abstract in this study we investigate the impact of modified lotsize reorder control policy for perishables which bases replenishment decisions on both the inventory level and the remaining lifetimes of items in stock we derive the expressions for the key operating characteristics of a lost sales perishable inventory model operating under the proposed age based policy and examine the sensitivity of the optimal policy parameters with respect to various system parameters we compare the performance of the suggested policy to that of the classical q r type policy through a numerical study over a wide range of system parameters our findings indicate that the age based policy is superior to the stock level policy for slow moving perishable inventory systems with high service levels

optimal control of a single stage production system subject to random process shifts we consider a single stage production system with poisson demand and exponential processing times after producing a good item the production process can shift to an out of control state with a given probability and start producing bad items the state of the process is known only when the next stage or customer receives the item once an out of control process is detected process correction is instantaneous customers arriving to an empty system get backlogged in this framework we examine fifo first in first out and lifo last in first out issuing policies the objective is to minimize the total expected discounted or average costs over an infinite time horizon we characterize the structure of the optimal production policy for fifo and lifo show that lifo is better than fifo and in general better than a large class of issuing policies a numerical example illustrates that savings up to 20 percent can be obtained from using lifo over fifo we also derive conditions under which maintaining z

a new age based replenishment policy for supply chain inventory optimization of highly perishable products abstract a simulation optimization framework is proposed for supply chain inventory management of highly perishable products a new replenishment policy based on old inventory ratio is developed hence called oir policy it is an age based policy using only partial age information to measure the freshness of the entire inventory the efficiency of the new policy is evaluated in detail for a single vendor multi buyer platelet with a limited shelf life of 5 days supply chain the inventory objective is to minimize the expected system outdate rate under a predetermined maximal allowable shortage level the new oir policy is compared with two existing order up to policies one is the order up to policy without age consideration the other one is the ewa policy developed by broekmeulen and van donselaar 2009 the three policies are compared under both decentralized and centralized controls for different levels of the fillrate constraint the computational results show that adopting centralized control over the whole platelet supply chain greatly helps in reducing the system expected outdate rate from 19 6 down to 1 04 on average while keeping sufficiently high fill rate at each entity the two policies with age consideration are generally better than the policy without age consideration under both control strategies this is particularly true for decentralized control the new oir policy is recommended because it is the best among all three consistently yielding good results in all cases studied

inventory models with shelf age and delay dependent inventory costs in this paper we show how any model with a general shelf age dependent holding cost and delay dependent backlogging cost structure may be transformed into an equivalent model in which all expected inventory costs are level dependent we develop our equivalency results first for periodic review models with full backlogging of stockouts these equivalency results permit us to characterize the optimal procurement strategy in various settings and to adopt known algorithms to compute such strategies for models in which all or part of stockouts are lost we show that the addition of any shelf age and delay dependent cost structure does not complicate the structure of the model beyond what is required under the simplest i e linear holding and backlogging costs we proceed to show that our results carry over to continuous review models with demands generated by compound renewal processes the continuous review models with shelf age and delay dependent carrying and backlogging costs are shown to be equiva

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

optimal discounting and replenishment policies for perishable products abstract we consider a retailer selling a perishable product with short shelf life and uncertain demand facing these key decisions a whether to discount old er items b how much discount to offer and c what should be the replenishment policy in order to better understand the impact of consumer behavior and shelf life on these decisions we consider four models in model a the product has a shelf life of two periods and the retailer decides whether or not to offer a discount the amount of discount is exogenous and assumed to be large enough so that all the customers prefer the old product to the new one when a discount is offered based on several numerical examples we find that a threshold discounting policy in which a discount is offered if and only if the inventory of old product is below a threshold is optimal in model b the retailer also decides how much discount to offer model c extends model b and considers a new pool of customers who are willing to purchase from the retailer when a discount is offered in both models b and c the product has a shelf life of two periods while model d explores what happens with longer shelf life we analyze and compare these models to present different managerial insights

an order level lot size inventory model with inventory level dependent demand and deterioration abstract many inventory models have been developed for various deteriorating items with constant demand rate it is a common experience that for perishable consumer goods the age of inventory has a negative impact on the demand due to the loss of consumer confidence on such product consumers tend to keep off perishable items which have reached closer to their expiry dates this paper describes an inventory model in which the demand is considered as a composite function consisting of a constant component and a variable component which is proportional to the inventory level in the periods when there is a positive inventory buildup the rate of production is considered finite and the decay rate as exponential the total cost function is composed of four cost components of all phases of the cycle backorder replenishment inventory buildup inventory depletion and shortage this cost function is later reduced to a two variable function using boundary relations to determine iteratively the set of values of the variables that resulted in minimum cost per cycle the optimum lot size and order level were then obtained with relations established previously results are demonstrated for an instance of the model

dynamic economic lot size model with perishable inventory this paper considers an economic lot size els model for perishable products where an inventory stock s deterioration rate and its carrying cost in each period depend on the age of the stock we discuss situations where the traditional els models are not applicable and propose a new model with general concave production and inventory cost functions we explore the structural properties of the optimal solutions and use them to develop a dynamic programming algorithm which solves the problem in polynomial time we also consider special cases of the general model which are solvable with reduced computational complexities

evaluation of stock allocation policies in a divergent inventory system with shipment consolidation in this paper we consider a one warehouse n retailer inventory system characterized by access to real time point of sale data and a time based dispatching and shipment consolidation policy at the warehouse more precisely inventory is reviewed continuously while a consolidated shipment for example a truck to all retailers is dispatched from the warehouse at regular time intervals the focus is on investigating the cost benefits of using state dependent myopic allocation policies instead of a simple fcfs first come first serve rule to allocate shipped goods to the retailers the analysis aims to shed some light on when if ever fcfs is a reasonable policy to use in this type of system the fcfs allocations of items to retailers are determined by the sequence in which retailer orders or equivalently customer demands arrive to the warehouse applying the myopic policy enables the warehouse to postpone the allocation decision to the moment of shipment from the warehouse or the moments of delivery to the different retailers and to base it on the inventory information available at those times the myopic allocation method we study is often used in the literature on periodic review systems

simulation study of the price differentiation effect in a stochastic deteriorating inventory with heterogeneous consumers freshness sensitivity a fixed price policy regardless of expiration date may result in unsold inventory and sales loss price reduction over time as the expiration date approaches motivates customers to purchase all items including the ones that are left with only a short interval until their expiration we conduct a discrete event simulation that captures the main characteristics of this phenomenon results show that a moderate differentiation of price increases profits by 6 a larger differentiation reduces profits profits are the highest for freshness oriented customers a fixed price policy is preferred in an environment of large variance and expected near term expirations

approximation algorithms for perishable inventory systems we develop the first approximation algorithms with worst case performance guarantees for periodic review perishable inventory systems with general product lifetime for both backlogging and lost sales models the demand process can be nonstationary and correlated over time capturing such features as demand seasonality and forecast updates the optimal control policy for such systems is notoriously complicated thus finding effective heuristic policies is of practical importance in this paper we construct a computationally efficient inventory control policy called the proportional balancing policy for systems with an arbitrarily correlated demand process and show that it has a worst case performance guarantee less than 3 in addition when the demands are independent and stochastically nondecreasing over time we propose another policy called the dual balancing policy which admits a worst case performance guarantee of 2 we demonstrate through an extensive numerical study that both policies perform consistently close to optimal

an s 1 s inventory system with emergency orders in this paper we develop an approximate model of an inventory control system in which there exist two options for resupply with one having a shorter lead time we assume that demand and the fixed ordering costs are small relative to the holding cost so that a one for one ordering policy is appropriate we consider a policy for placing emergency orders that uses information about the age of outstanding orders we derive the steady state behavior of this policy and present some computational results

a new class of stock level dependent ordering policies for perishables with a short maximum shelf life many perishables such as fresh food and blood platelet concentrates are characterized by a short maximum shelf life as demand is often highly uncertain the outdating and shortages figures can be very high especially when frequent replenishment is not possible or inefficient due to fixed ordering cost we present a new class of stock level dependent ordering policies the s s q q policy which is a periodic review s s policy with the order quantity restricted by a minimum q and maximum q optimal weekday dependent parameter values are derived by dynamic programming and simulation the s s q q policy performs nearly optimal and improves the s s policies in many cases by 4 25

managing blood donations with marketing blood banks rely on marketing to encourage donors to give blood many if not most blood banks in the united states are community based not for profit organizations with limited marketing budgets as a result blood banks increasingly use novel and inexpensive online media i e paid owned and earned poe media in their marketing efforts we propose a dynamic model to help blood bank marketing managers understand how blood donations can be managed via online poe media we analytically characterize the optimal forward looking paid media strategies taking into account the asymmetric costs related to shortage and excess of blood as well as the possibility of a cost free target donation zone we detail new advertising resource allocation rules for blood banks and show when traditional allocation recommendations do not apply additionally we discover that under certain circumstances owned earned media activities hurt the blood bank s performance despite being predominantly free we validate our analytical model by using daily donation data from a community based blood bank and measure the effects of poe media activities on the level of blood donated

blood platelet inventory management with protection levels abstract we consider a discrete time inventory system for a perishable product where demand exists for product of different ages an example of such a product is blood platelets in addition to the classical costs for inventory holding outdating and shortage our model includes substitution mismatch costs incurred when a demand for a certain aged item is satisfied by a different aged item we propose a simple inventory replenishment and allocation heuristic to minimize the expected total cost over an infinite time horizon in our heuristic inventory of the newest items is replenished in fixed quantities and the newest items are protected for future use by limiting some substitutions when making allocation decisions according to a critical level policy we model our problem as a markov decision process mdp derive the costs of our heuristic policy and computationally compare this policy to extant near optimal policies in the literature our extensive computational study shows that our policy leads to superior performance compared to existing heuristics in the literature particularly when supplies are limited

blood platelet production with breaks optimization by sdp and simulation abstract the production and inventory management of blood products at blood banks and hospitals is a problem of general human interest as a shortage may put lives at risk shortages are to be kept to a minimum as the supply is voluntary and costly any spill of unused blood products is also to be minimized blood platelets thrombocytes which are the most expensive and perishable blood product have the complication of a limited shelf life of only 5 7 days a general figure in the western world the usa and western europe for the spill of blood platelets is in the order of 15 20 a combined new approach is therefore presented which combines stochastic dynamic programming sdp and simulation to provide i practical simple order up to rules that are nearly optimal ii formal theoretical support the approach has been applied to a dutch regional blood bank numerical results show a significant reduction of the figures from 1 to 1 for shortages 20 to 1 for spill a practical question for blood bank managers that still remains is how to anticipate irregular production breaks like at easter and christmas the present paper therefore will extend the combined sdp simulation approach to include such breaks the main findings are also for these breaks a simple order up to rule remains to be nearly optimal also for these breaks the outdating and shortages can be kept less than 1 the stationary periods with production and the non stationary breaks without can be integrated the approach thus seems suitable for practical implementation

blood inventory management an overview of theory and practice blood inventory management has attracted significant interest from the operations research profession during the last 15 years a number of methodological contributions have been made in the areas of inventory theory and combinatoric optimization that can be of use to other products or systems these contributions include the development of exact and approximate ordering and issuing policies for an inventory system the analysis of lifo or multi product systems and various forms of distribution scheduling in addition many of these results have been implemented either as decision rules for efficient blood management in a hospital or as decision support systems for hierarchical planning in a regional blood center in this paper we attempt a review of the recent operations research contributions to blood inventory management theory and practice whereas many problems have been solved others remain open and new ones keep being created with advances in medical technology and practices our approach is not to present an exhaustive review of all the literature in the field but rather to address several important issues from a unified perspective of theory and practice and point out new areas for further research

economic order quantity for growing items abstract economic order production quantity eoq epq models have generally been presented for manufacturing products incorporating some important features of a specific category of products different eoq epq models have been proposed in literature this study proposes a new class of inventory models i e a model for a specific type of inventory items growing items poultry and livestock are good examples of growing inventory items we begin by proposing a general mathematical model which can be used for different types of growing items followed by a particular mathematical model for a specific type of poultry we calculate the optimal order quantity of the growing items at the start of a growing cycle the optimal length of the growing cycle and the optimal total profit numerical examples are provided for a type of poultry to illustrate the model a sensitivity analysis is presented to study the effect of the main parameters of the model in terms of its decision variables and objective function the results of the sensitivity analysis suggest that production costs are the most crucial parameter

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

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

the newsvendor problem in a global market optimal centralized and decentralized control policies for a two market stochastic inventory system the global markets of today offer to the style goods producer more selling opportunities and pose new challenges in production planning and coordination from a production management standpoint the opportunity to exploit the difference in timing of the selling season of geographically dispersed markets for style goods is important for improving the firm s profitability in this paper we examine the above issue with an insightful model of a producer of style goods selling the goods to two markets a primary and a secondary market with nonoverlapping selling seasons we refer to this problem as the global newsvendor problem for the above two market stochastic inventory systems we first develop optimal centralized control policies then we demonstrate the suboptimality of decentralized production control policies with the production centers at each market treated as independent profit centers and a constant transfer price being used to coordinate their production we propose as an effective alternative a decentralized production control structure with a nonlinear pricing scheme for production coordination among centers administered through an intermediate organizational unit in our modeling we explicitly consider the effects of exchange rate uncertainty on the production planning decisions

eoq models for continuously deteriorating products using linear and exponential penalty costs abstract we present eoq models for perishable products which consider continuous deterioration of the utility of a product and introduce an exponential penalty cost function as a measurement of the utility deterioration the approach proposed is simple and can be used to obtain easily the closed forms of the economic order quantities which have not previously been derived these forms describe the effect of the penalty cost clearly and are a natural extension of economic order quantities for non perishable products our results are shown to be consistent with reported eoq models with exponential decay but derived more elaborately our approach has the added advantage that it can be easily extended to the economic lot scheduling problem for multi item perishable products

integrated supply chain management for perishable products dynamics and oligopolistic competition perspectives with application to pharmaceuticals abstract we propose an integrated supply chain management framework that allows us to explicitly consider the impact of product perishability on a broad scale that includes manufacturers distribution centers wholesalers and demand markets the framework proposed herein also makes it possible to consider the oligopolistic competition across wholesalers that drives price and demand fluctuations furthermore the supply chain decision rules are derived from necessary conditions in the framework the inclusion of such salient features allows the framework to generate outcomes that suggest realistic managerial insights we provide a numerical example in which two multi national pharmaceutical firms producing a homogeneous medicinal drug and four oligopolistic wholesalers are considered

the application of queueing theory to continuous perishable inventory systems this paper develops two distinct models for studying inventory systems with continuous production and perishable items the perishable items have a deterministic usable life after which they must be outdated for each of the models analytical expressions derived from queueing theory are found for the steady state distribution of system inventory knowledge of this steady state behavior may be used for evaluation of system performance and for consideration of alternatives for improving system performance both models assume that inventory is replenished by a continuous production process the first model assuming continuous inventory units has poisson demand requests with the size of each request distributed as an exponential random variable the second model has poisson demand requests with all demands being for a single unit the analysis for both models exploits the similarity of the inventory system with a single server queueing system

an allocation and distribution model for perishable products this paper presents an allocation model for a perishable product distributed from a regional center to a given set of locations with random demands we consider the combined problem of allocating the available inventory at the center while deciding how these deliveries should be performed two types of delivery patterns are analyzed the first pattern assumes that all demand points receive individual deliveries the second pattern subsumes the frequently occurring case in which deliveries are combined in multistop routes traveled by a fleet of vehicles computational experience is reported

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

note an application of the eoq model with nonlinear holding cost to inventory management of perishables abstract in this note we consider a variation of the economic order quantity eoq model where cumulative holding cost is a nonlinear function of time this problem has been studied by weiss weiss h 1982 economic order quantity models with nonlinear holding costs european journal of operational research 9 56 60 and we here show how it is an approximation of the optimal order quantity for perishable goods such as milk and produce sold in small to medium size grocery stores where there are delivery surcharges due to infrequent ordering and managers frequently utilize markdowns to stabilize demand as the product s expiration date nears we show how the holding cost curve parameters can be estimated via a regression approach from the product s usual holding cost storage plus capital costs lifetime and markdown policy we show in a numerical study that the model provides significant improvement in cost vis a vis the classic eoq model with a median improvement of 40 this improvement is more significant for higher daily demand rate lower holding cost shorter lifetime and a markdown policy with steeper discounts

batch size and stocking levels in multi echelon repairable systems in multi echelon repairable inventory systems with high set up cost for order and or high demand rates the use of batch ordering may be more cost effective than the common s 1 s ordering policy this paper addresses the issue of determining the optimal order batch size and stocking levels at the stocking locations in such a system a power approximation is used to estimate the total system stock and backorder levels from which the optimal batch size can be readily determined a search routine involving one pass searches are then followed to obtain the stocking levels at the depot and the local sites of the system this procedure has been evaluated using 900 test cases and has been found to be very effective the power approximation approach also results in a simple analytical relationship to test whether or not s 1 s is an optimal ordering policy for repairable items in a multi echelon environment

modeling an inventory routing problem for perishable products with environmental considerations and demand uncertainty the transition to sustainable food supply chain management has brought new key logistical aims such as reducing food waste and environmental impacts of operations in the supply chain besides the traditional cost minimization objective traditional assumptions of constant distribution costs between nodes unlimited product shelf life and deterministic demand used in the inventory routing problem irp literature restrict the usage of the proposed models in current food logistics systems from this point of view our interest in this study is to enhance the traditional models for the irp to make them more useful for the decision makers in food logistics management therefore we present a multi period irp model that includes truck load dependent and thus route dependent distribution costs for a comprehensive evaluation of co2 emission and fuel consumption perishability and a service level constraint for meeting uncertain demand a case study on the fresh tomato distribution operations of a supermarket chain shows the applicability of the model to a real life problem several variations of the model each differing with respect to the considered aspects are employed to present the benefits of including perishability and explicit fuel consumption concerns in the model the results suggest that the proposed integrated model can achieve significant savings in total cost while satisfying the service level requirements and thus offers better support to decision makers

inventory dynamics and supply chain coordination this paper extends the theory of supply chain incentive contracts from the static newsvendor framework of the existing literature to the simplest dynamic setting a manufacturer distributes a product through retailers who compete on both price and fill rates we show that inventory durability is the key factor in determining the underlying nature of incentive distortions and their contractual resolutions when the product is highly perishable retailers are biased toward excessive price competition and inadequate inventories vertical price floors or inventory buybacks subsidies for unsold inventory can coordinate incentives in both pricing and inventory decisions when the product is less perishable the distortion is reversed and vertical price ceilings or inventory penalties can coordinate incentives

optimization of order up to s policies for two level inventory systems with compound poisson demand abstract we consider a two level inventory system with one warehouse and n retailers leadtimes are constant and the retailers face different compound poisson demand processes all facilities apply order up to s replenishment policies we show how to evaluate holding and shortage costs exactly

two stage perishable inventory models in this paper we consider perishable inventory systems with two types of demand demand may be for either fresh items or for somewhat older items we model the system with two inventory stages the first stage holds fresh items and the second stage holds the older items we approximate the performance of the two stage inventory system and compare two managerial policies

an economic ordering policy model for deteriorating items with time proportional demand abstract a t i s i inventory policy model for deteriorating items is presented in this paper the model is developed based on the assumptions that 1 demand rate is deterministic and linearly changes with time 2 deterioration rate is constant 3 planning horizon is finite and known and 4 replenishment periods are not equal the model is solved using a dynamic programming method the result is applicable to the case where the demand is either increasing or decreasing a numerical example is provided to illustrate the model and solution procedure

perishable inventory management with stochastic leadtime and different selling prices abstract this paper discusses a model for a perishable product with stochastic procurement leadtime and different selling prices this model is a generalization of the one period horizon model of nahmias 4 5 ishii et al 3 and nose et al 7 for the model the optimal ordering policy and its properties are derived

an approximation to the continuous review inventory model with perishable items and lead times a continuous review perishable inventory model based on approximations to the expected outdating the expected shortage quantity and the expected inventory level is developed to determine a best q r ordering policy under a positive order leadtime when the total expected average cost per unit time is minimized the approximation method is simple and verified by a comparison with the weiss model the results reveal that the mean absolute deviation from the optimal total expected average cost per unit time is only 0 58 this paper also compares the proposed model to the conventional model with no perishability a value is given to the item lifetime indicating when an approximate answer approaches closely to the conventional ordering policy finally a simulation model written in simscript ii 5 is used to validate the approximate results

the profitability of canadian defence contractors abstract in this paper we employ a simultaneous equations approach to test the hypothesis that firm profitability is affected by or affects the degree to which a firm is involved in defence contracting we find no evidence of any link between corporate profitability and defence contracting activity in canada moreover our data do not support the hypothesis that a positive effect of defence contracting is offset by the government pursuing a bailout contract award strategy based on the nature of the canadian defence procurement system we argue that our results indicate that the government has used its monopsony powers to restrict the rate of return earned on defence contracts to equal that earned in commercial operations thus firms which earn excess profits in commercial markets will also earn excess profits in defence markets

inferring shortfall costs and integrating environmental costs into optimal production levels for an all you care to eat food service operation abstract this study examines how optimal food production policies at an all you care to eat aycte facility would change were life cycle cost estimates of embodied co2 included in the disposal costs associated with overproduction in an aim to study production planning possibilities in a situation that places increased emphasis on the environmental impacts of overproduction aycte operations exhibit a lack of revenue associated with each item served since there is no per item lost sales value incurred when demand exceeds supply accordingly the second objective of this research is to present a novel method for estimating shortfall costs in a setting with no marginal revenue per satisfied unit of demand we examine empirical data from aycte operations at the university of missouri s campus dining services cds to infer the per item shortfall costs that are implied by cds management s historical production decisions consistent with cds management s stated aversion to shortfalls we estimate shortfall values which are between 1 6 and 2 7 times larger than the procurement cost and between 30 and over 100 times larger than the disposal cost utilizing published estimates of life cycle co2 and the social cost of carbon we identify a per portion environmental cost we incorporate the environmental costs associated with wasted overproduction and the inferred shortfall cost estimates into a newsvendor model formulation to identify new optimal production levels illustrating this approach with application to a set of food items served by cds we find that optimal production levels are decreased significantly 18 25 for food items with high environmental impacts such as beef and reduced less for foods with less embodied co2

emergency lateral transshipments in a two location inventory system with positive transshipment leadtimes abstract we consider a single echelon continuous review inventory system for spare parts with two parallel locations each location faces independent poisson demand and backorders are allowed in this paper we consider the possibility of lateral transshipments between the locations the transshipment leadtime is positive and deterministic and there is an additional cost for making a transshipment we suggest a transshipment policy which is based on the timing of all outstanding orders and develop and solve a heuristic model by using theory and concepts from doubly stochastic poisson processes and also partial differential equations a simulation study indicates that our heuristic works very well and that the relative cost increase of disregarding the transshipment leadtime may be quite high our results also indicate that it is in general worth the effort of reducing the transshipment leadtime even if it is already relatively short

spare parts management linking distributional assumptions to demand classification spare parts are known to be associated with intermittent demand patterns and such patterns cause considerable problems with regards to forecasting and stock control due to their compound nature that renders the normality assumption invalid compound distributions have been used to model intermittent demand patterns there is however a lack of theoretical analysis and little relevant empirical evidence in support of these distributions in this paper we conduct a detailed empirical investigation on the goodness of fit of various compound poisson distributions and we develop a distribution based demand classification scheme the validity of which is also assessed in empirical terms our empirical investigation provides evidence in support of certain demand distributions and the work described in this paper should facilitate the task of selecting such distributions in a real world spare parts inventory context an extensive discussion on parameter estimation related difficulties in this area is also provided

deterministic models of perishable inventory with stock dependent demand rate and nonlinear holding cost this paper deals with an extended eoq type inventory model for a perishable product where the demand rate is a function of the on hand inventory the traditional parameters of unit item cost and ordering cost are kept constant but the holding cost is treated as i a nonlinear function of the length of time for which the item is held in stock and ii a functional form of the amount of the on hand inventory the approximate optimal solution in both the cases are derived computational results are presented indicating the effects of nonlinearity in holding costs

analysis of a sampling control scheme for a perishable inventory system we consider an inventory system in which both the arrival of items and the demand for those items are poisson processes the stored items have two phases of shelf life if the item has not been taken by a demand during the first phase it is inspected with probability q it is removed and with probability p 1 q it is transferred to the second phase the blood bank model inspired this study we compute ergodic limits for the number of items in the system the lost demands and the two types of outdating

an eoq model with ramp type demand rate time dependent deterioration rate unit production cost and shortages an order level inventory system for deteriorating items has been developed with demand rate as a ramp type function of time the finite production rate is proportional to the demand rate and deterioration rate is time proportional the unit production cost is inversely proportional to the demand rate the model with no shortage case in inventory is first solved the inventory shortage is discussed next results are illustrated with two numerical examples for two models along with its sensitivity

joint product durability and lot sizing models this paper concerns the simultaneous selection of product durability and order quantity for items that deteriorate over time choices of product durability are modelled as the values of a single design parameter that affects the distribution of the time to onset of deterioration tod once deterioration has begun individual items are assumed to have exponential remaining lifetimes we analyze two scenarios in the first case items are guaranteed to be good if used prior to an expiry date therefore tod is a constant and the store manager may choose an appropriate value at cost in the second case tod is a random variable then the design parameter can affect tod distribution in either mean preserving or variance preserving or mixed manner we report insightful numerical examples for each case and derive highly plausible conditions which when true imply that the corresponding expected cost per unit time is strictly quasi convex

optimal inventory policies for perishable items with time dependent demand abstract this paper presents two computationally efficient solution methods that determine the optimal replenishment schedules for exponentially deteriorating items and perishable products with fixed lifetime for both models the inventoried items have general continuous time dependent demand the models are formulated under the assumption of discrete opportunities for replenishment over a fixed planning horizon numerical examples are included to illustrate the models

the economies of massed reserves the economy of massed reserves first mentioned by e a g robinson 1958 pp 26 27 is now firmly established in the industrial organization literature as an example of a potential plant level scale economy the massing of reserves results in a savings in the proportion of required reserves to expected output as the scale of a facility increases examples of such reserves are bank tellers specialized tools and equipment repairmen inventories spare parts and checkout lines the potential economies from massing reserves are dependent on the underlying stochastic processes governing the supply and or demand of the service provided theoretical justification for the economies of massed reserves has usually been based on an appeal to the law of large numbers for example donald hay and derek morris wrote the law of large numbers makes the number of breakdowns more predictable in a plant using a large number of machines so that the number of stand by maintenance staff need not be increased in proportion to size 1979 p 44 this paper demonstrates that the law of large numbers does not provide a theoretical explanation of massed reserves scale economies instead it is shown that the expected economies of massed reserves can be calculated from the steady state properties of well known queuing models queuing models apply to any case where a servicing input is held in reserve to cope with the stochastic nature of the market or production process in addition a method for quantifying the expected economies of queuing processes is developed the magnitude of these expected economies is shown to be significant and calculable for example the expected economies inherent in a widely applied queuing model are shown to exceed 23 percent in some cases section i establishes the irrelevance of the law of large numbers as a theory of scale economies section ii provides a formal method for determining the scale economies inherent in the most often mentioned massed reserves example machine repair section iii shows that the same method can be used to calculate scale economies for the remaining massed reserves examples specialized repair tools and equipment checkout counter clerks bank tellers and other service personnel capacity and inventories and spare parts in addition it is demonstrated that the same method can be used to calculate scale economies for some multiproduct operations

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

eoq models for perishable items under stock dependent selling rate this paper presents inventory models for perishable items with stock dependent selling rate the selling rate is assumed to be a function of current inventory level and rate of deterioration is taken to be constant under instantaneous replenishment with zero lead time the model incorporates aspects such as complete partial and no backlogging eoq is determined for maximizing the total profit in each of the situations the models developed are illustrated through numerical examples and sensitivity analysis is reported

controlling inventories in divergent supply chains with advance order information this paper considers a generic one warehouse multiple retailer inventory system under continuous review where customers provide perfect advance order information more specifically each customer order entails a due date specifying when the customer wants the item delivered the information is perfect in the sense that a placed order cannot be revised with the intent of using the advance order information fully throughout the supply chain each installation replenishes its stock using order base stock policies see hariharan and zipkin 1995 as for stock allocation the presence of advance order information at the central warehouse raises important questions regarding when reservations should be made for different retailers i e how to make best use of the available temporal information to allocate items to retailers exact and approximate cost evaluation techniques are presented for the general case the general reservation policy as well as for the two special cases of reserving as early as possible the complete reservation policy and as late as possible the last minute allocation policy a numerical study illustrates the performance of the proposed heuristics and provides insights on the value of using advance order information in supply chain inventory control

operating characteristics of the s 1 s inventory system with partial backorders and constant resupply times in this paper we consider an s 1 s inventory system with poisson demand and constant resupply times an arriving customer facing stockout will either backorder or withdraw its order expressions describing steady state operating characteristics of the system and the expected total cost rate are developed furthermore the behavior of the expected total cost rate as the function of the relevant parameters is explored

optimal production planning utilizing leftovers for an all you care to eat food service operation abstract food service operations in an all you care to eat environment need to consider two conflicting objectives a desire to reduce overproduction food waste and its corresponding environmental impacts and an aversion to shortfalls in which some customer demands go unsatisfied a particular challenge in such buffet style operations is the absence of any lost marginal revenue associated with lost sales that can be used to measure the shortfall cost complicating any attempt to determine a minimum cost solution this research presents a multi criteria optimization approach to identify the efficient frontier of points lying between the minimum waste and minimum shortfall solutions in particular we identify optimal production adjustments relative to demand forecasts demand thresholds for utilization of leftovers and percentages of demand to be satisfied by leftovers considering two alternative metrics for overproduction waste mass and greenhouse gas emissions to account for the embodied chemical usage during farming transportation and landfill decomposing of overproduced food waste a statistical analysis of the changes in decision variable values across each of the efficient frontiers can then be performed to identify the key variables that could be modified to reduce the amount of wasted food at minimal increase in shortfalls or alternatively to reduce the amount of shortfalls at minimal increase in waste we illustrate our approach with an application to empirical data from campus dining services operations at the university of missouri our analysis suggests that targeted production level modifications rather than blanket increases or decreases can allow food service providers to reduce overproduction food waste without significant increases in demand shortfalls

analysis of postponement strategy for perishable items by eoq based models abstract this paper develops economic order quantity model eoq based models with perishable items to evaluate the impact of a form postponement strategy on the retailer in a supply chain we formulate models for a postponement system and an independent system to minimize the total average cost function per unit time for ordering and keeping n perishable end products an algorithm is given to derive the optimal solutions of the proposed models the impact of the deterioration rate on the inventory replenishment policies is studied with the help of theoretical analysis and numerical examples our theoretical analysis and computational results show that a postponement strategy for perishable items can give a lower total average cost under certain circumstances

an optimal procurement policy for items with an inventory level dependent demand rate and fixed lifetime abstract this paper investigates an optimal procurement policy for items with an inventory level dependent demand rate and fixed lifetime the demand rate is assumed to be a function of current inventory level and each unit has its fixed expiry date so any units which remain unused by their expiry date are considered outdated and must be disposed of for the system presented a mathematical model and solution methodology were developed sensitivity of the decision variables to changes in the parameter values is examined and future research needs are discussed in brief

production control in the face of storable raw material random supply and an outside market we study a periodic review production inventory control problem where both the supply of raw material and demand for the finished product are exogenous and random the raw material can be stored for future use can be purchased from or sold to an outside market we study both the lost sales and backlogging cases under both strict convex and linear raw material purchasing selling costs convexity of the purchasing selling cost implies that the more the firm purchases from or sells to the outside market the more expensive or less valuable the raw material becomes for all cases we find the partial characterizations for the optimal policies which all turn out to be very intuitively appealing in particular for each of the linear cost cases the optimal policy degenerates into a combination of two base stock policies one for the raw material inventory and the other for the finished product inventory

an inventory model with exogenous failures this note introduces a model where inventory is repeatedly wiped out due to exogenous failure processes the difference between this model and perishable inventory models is pinpointed by two sample examples relevant applications are also mentioned

a coordinated multi item inventory system for perishables with random lifetime abstract this paper considers the continuous review can order s c s policy for coordinating the replenishment of multiple perishable items with random lifetimes for zero lead time we model this inventory system as a markov process an iterative procedure is proposed to solve the joint replenishment problem for perishable items under positive lead time we investigate the impact of perishability and cost parameters on the performance of the can order policy and compare it to the optimal periodic review s s policy

coordinating inventory control and pricing strategies for perishable products we analyze a joint pricing and inventory control problem for a perishable product with a fixed lifetime over a finite horizon in each period demand depends on the price of the current period plus an additive random term inventories can be intentionally disposed of and those that reach their lifetime have to be disposed of the objective is to find a joint pricing ordering and disposal policy to maximize the total expected discounted profit over the planning horizon taking into account linear ordering cost inventory holding and backlogging or lost sales penalty cost and disposal cost employing the concept of l concavity we show some monotonicity properties of the optimal policies our results shed new light on perishable inventory management and our approach provides a significantly simpler proof of a classical structural result in the literature moreover we identify bounds on the optimal order up to levels and develop an effective heuristic policy numerical results show that our heuristic policy performs well in both stationary and nonstationary settings finally we show that our approach also applies to models with random lifetimes and inventory rationing models with multiple demand classes

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

exact and approximate evaluation of batch ordering policies for two level inventory systems we consider a two level inventory system with one warehouse and n identical retailers lead times transportation times are constant and the retailers face independent poisson demand in a previous paper we derived a recursive procedure for determining the policy costs for an average item in case of one for one replenishment policies in this paper we show how these results can be used for the exact or approximate evaluation of more general policies where both the retailers and the warehouse order in batches we compare our methods to the method recently suggested by a svoronos and p zipkin

s 1 s policies for perishable inventory we consider s 1 s policies for a single item whose lifetime is fixed and known with certainty demands are generated by a stationary poisson process and there is a positive leadtime for replenishment we believe this study gives the only analysis for perishables with a positive order leadtime the analysis involves the derivation of the stationary distribution of the s dimensional stochastic process corresponding to the time elapsed since the last s orders were placed this distribution is then used to obtain an expression for the expected cost rate of operating the system in steady state as a function of s a computer program has been developed to compute optimal s values and expected annual costs we report a computation for a variety of system parameters which show some of the unusual features of the problem finally we show how this model can be used in the context of a problem of optimizing availability of operating equipment subject to scheduled maintenance as well as random failure

evaluation of installation stock based r q policies fortwo level inventory systems with poisson demands we consider a two level inventory system with one warehouse and n retailers leadtimes transportation times are constant and the retailers face different poisson demand processes all facilities apply continuous review installation stock r q policies with different reorder points and batch quantities we show how to evaluate holding and shortage costs exactly in case of two retailers in case of more than two retailers we use the same methodology as an approximation when evaluating costs at a certain retailer the other retailers are then aggregated into a single retailer

optimal inventory policy for a perishable item with demand function sensitive to price and time abstract we formulate a model for determining the optimal pricing order quantity and replenishment period for perishable items with price dependent and time dependent demand the items have a fixed shelf life and the demand rate decreases linearly in the selling price and polynomially over the time after replenishment until it vanishes either at the reservation price or at expiration time we prove that the three variable profit maximization problem can be reduced into a single variable problem in which the variable is the duration of the replenishment period we show that the profit function is strictly pseudo concave and provide means of obtaining the optimal policy three numerical examples are presented to demonstrate the model accompanied by a sensitivity analysis

production planning for a deteriorating item with stochastic demand and consumer choice abstract this paper concerns inventory control of a deteriorating product with non negligible procurement lead time that perishes after a known number of periods demand for fresh products during each period is represented as a random variable with known probability distribution but only a fraction of this demand is satisfied during any given period due to item deterioration we derive the expected profit function for a two period problem with one production opportunity before the selling season begins and a single product type with two period shelf life for the case in which demand during both periods is uniform independent and identically distributed we identify sufficient conditions for the existence of an optimal solution and present a straightforward procedure for obtaining the solution

approximations for the relative outdating of perishable products by combining stochastic modeling simulation and regression modeling abstract in this paper we derive approximations for the expected amount of outdating waste in an inventory system with perishable products periodic review positive lead time fixed case pack sizes and a first in first out withdrawal policy demand is discrete and stochastic demand which is not met from inventory on hand will be lost the approximations can be used to evaluate how the amount of outdating can be reduced by changing the safety stock and or the product and demand characteristics we first derive approximations in an analytical way and then use regression to improve these approximations the final approximation is very fast and performs very well the mean and standard deviation of the approximation error are equal to 0 01 and 0 78 moreover the approximation is applicable in situations with parameter settings which are frequently encountered in practice and for which no other approximations have been derived in the literature before

a perishable inventory model with markovian renewal demands abstract in the inventory model people usually assume that the inter demand time is independently identical distributed which may not be true in reality here we study an s s continuous review model for items with an exponential random lifetime and a general markovian renewal demand process by constructing markovian renewal equations we derive the mean and the variance of the reorder cycle time and lead to a simple expression for the total expected long run cost rate the numerical results illustrate the system behavior and lead to managerial insights into controlling such inventory systems

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

inventory problems with perishable items fixed lifetimes and backlogging our model deals with a single product and a single stock location with poisson demand the replenishment leadtime from the external supplier is fixed the lifetime of the product is also fixed and aging is assumed to begin when the order is placed when the age of a unit has reached its lifetime the unit is useless and thus discarded from the system the replenishment policy is assumed to be an order up to s policy demand that cannot be met immediately is backordered we consider three different cases where the service requirements are represented by 1 backorder costs per unit 2 a service level constraint 3 backorder costs per unit and time unit cases 1 and 2 are solved exactly while an approximation is developed for case 3 we show how the results from an earlier paper assuming lost sales can be used to solve the considered problems our results are compared to the results in a related paper considering q r policies c 2009 elsevier b v all rights reserved less

dynamic pricing and ordering decisions by a monopolist this paper considers the relationship between pricing and ordering decisions for a monopolistic retailer facing a known demand function where over the inventory cycle the product may exhibit i physical decay or deterioration of inventory called wastage and ii decrease in market value called value drop associated with each unit of inventory on hand the retailer is allowed to continuously vary the selling price of the product over the cycle we introduce a notion of instantaneous margin and use it to derive profit maximizing conditions for the retailer the model explains the markdown of retail goods subject to decay it also provides guidance in determining when price changes during the cycle are worthwhile due to product aging how often such changes should be made and how such changes affect ordering intervals and quantities