inventory models with managerial policy independent of demand abstract this paper is an extension of two papers the first of these published in european journal of operational research 2007 112 120 is by deng et al 2007 and concerns inventory models for deteriorating items with ramp type demand the second published in computer industrial engineering 2009 1296 1300 is by cheng and wang 2009 and concerns inventory models for deteriorating items with trapezoidal type demand the purpose of this paper is threefold first this paper will show that the optimal solution is independent of the demand considered in the two previous papers second several replenishment cycles were considered during the finite time horizon to balance the set up cost with the sum of the deteriorated cost holding cost and shortage cost third this paper will examine the same numerical example in cheng and wang 2009 to show that this new approach will result in the saving of 84 39

a note on the inventory models for deteriorating items with ramp type demand rate abstract in this research we study the inventory models for deteriorating items with ramp type demand rate we first clearly point out some questionable results that appeared in mandal b pal a k 1998 order level inventory system with ramp type demand rate for deteriorating items journal of interdisciplinary mathematics 1 49 66 and wu k s ouyang l y 2000 a replenishment policy for deteriorating items with ramp type demand rate short communication proceedings of national science council roc a 24 279 286 and then resolve the similar problem by offering a rigorous and efficient method to derive the optimal solution in addition we also propose an extended inventory model with ramp type demand rate and its optimal feasible solution to amend the incompleteness in the previous work moreover we also proposed a very good inventory replenishment policy for this kind of inventory model we believe that our work will provide a solid foundation for the further study of this sort of important inventory models with ramp type demand rate

an optimal replenishment policy for deteriorating items with effective investment in preservation technology abstract in this paper considering the amount invested in preservation technology and the replenishment schedule as decision variables we formulate an inventory model with a time varying rate of deterioration and partial backlogging the objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time for any given preservation technology cost we first prove that the optimal replenishment schedule not only exists but is unique next under given replenishment schedule we show that the total profit per unit time is a concave function of preservation technology cost we then provide a simple algorithm to figure out the optimal preservation technology cost and replenishment schedule for the proposed model we use numerical examples to illustrate the model

the proper scope of government theory and an application to prisons when should a government provide a service in house and when should it contract out provision we develop a model in which the provider can invest in improving the quality of service or reducing cost if contracts are incomplete the private provider has a stronger incentive to engage in both quality improvement and cost reduction than a government employee has however the private contractor s incentive to engage in cost reduction is typically too strong because he ignores the adverse effect on noncontractible quality the model is applied to understanding the costs and benefits of prison privatization

optimal retailer investments in green operations and preservation technology for deteriorating items abstract this paper examines the impact of dynamic retailer investments in green operations while considering the reference price effect a replenishment problem based on joint pricing dynamic investment in green operations preservation technology and optimal replenishment times for deteriorating items is considered as a way to maximize retailer profit in this problem the demand rate depends on the sales and reference prices as well as green concern level optimal control theory is employed to obtain a dynamic investment rate and a simulated annealing algorithm is used to find the solution of the nonlinear constraint optimization problem which determines the price preservation technology investment and replenishment cycle time in addition computational simulations and sensitivity analyses are carried out to offer managerial insights the findings suggest that continuous investment in green operations and preservation technology can significantly improve the retailer s financial performance the consumer reference price is an important influence on the retailer s decision to invest in green operations furthermore results show that the higher price sensitivity of the market always discourages the retailer from investing in green operations the retailer needs to invest more in green operations for products with relatively high unit value

contractual solutions to the hold up problem this paper considers a general version of the hold up problem where n agents first make relation specific investments and then must agree on some collective action it is shown that first best solutions exist under a variety of different assumptions about the nature of information asymmetries

simple contracts renegotiation under asymmetric information and the hold up problem abstract in this article it is demonstrated that voluntary bargaining over a collective decision under asymmetric information may well lead to ex post efficiency if the default decision is non trivial it is argued that the default decision may be interpreted as a simple contract that the parties have written ex ante this result is used in order to show that simple unconditional contracts which are renegotiated may allow the hold up problem to be solved even if the parties valuations are private information

optimal investment in setup reduction in manufacturing systems with wip inventories abstract a number of models have been proposed to predict optimal setup times or optimal investment in setup reduction in manufacturing cells these have been based on the economic order quantity eoq or economic production quantity epq model formulation and have a common limitation in that they neglect work in process wip inventories which can be substantial in manufacturing systems in this paper a new model is developed that predicts optimal production batch sizes and investments in setup reduction this model is based on queuing theory which permits it to estimate wip levels as a function of the decisions variables batch size and setup time optimal values for batch size and setup time are found analytically even though the total cost model was shown to be strictly non convex

unforeseen contingencies and incomplete contracts we scrutinize the conceptual framework commonly used in the incomplete contract literature this literature usually assumes that contractual incompleteness is due to the transaction costs of describing or of even foreseeing the possible states of nature in advance we argue however that such transaction costs need not interfere with optimal contracting i e transaction costs need not be relevant provided that agents can probabilistically forecast their possible future payoffs even if other aspects of the state of the nature cannot be forecast in other words all that is required for optimality is that agents be able to perform dynamic programming an assumption always invoked by the incomplete contract literature the foregoing optimality result holds very generally provided that parties can commit themselves not to renegotiate moreover we point out that renegotiation may be hard to reconcile with a framework that otherwise presumes perfect rationality however even if renegotiation is allowed the result still remains valid provided that parties are risk averse

information gathering transaction costs and the property rights approach the property rights approach to the theory of the firm suggests that ownership structures are chosen in order to provide ex ante investment incentives while bargaining is ex post efficient in contrast transaction cost economics emphasizes ex post inefficiencies in the present paper a party may invest and acquire private information about the default payoff that it can realize on its own inefficient rent seeking can overturn prominent implications of the property rights theory in particular ownership by party b may be optimal even though only the indispensable party a makes an investment decision

an eoq model with partial backordering and advance payments for an evaporating item abstract in the classic economic order quantity model the purchasing cost of an order is paid at the time of its receipt in some cases retailers ask purchasers to pay all or a fraction of the purchasing cost in advance and may allow them to divide the prepayment into several equal sized parts in this paper an economic order quantity model for an evaporating item with partial backordering and partial consecutive prepayments is developed with a real case study of a gasoline station real numerical examples illustrate the proposed model and the solution method

an inventory model with generalized type demand deterioration and backorder rates abstract this study is motivated by the paper of skouri et al skouri konstantaras papachristos ganas european journal of operational research 192 1 2009 79 92 we extend their inventory model from ramp type demand rate and weibull deterioration rate to arbitrary demand rate and arbitrary deterioration rate in the consideration of partial backorder we demonstrate that the optimal solution is actually independent of demand that is for a finite time horizon any attempt at tackling targeted inventory models under ramp type or any other types of the demand becomes redundant our analytical approach dramatically simplifies the solution procedure

classical unemployment accommodation policies and the adjustment of real wages a model of wage formation and stabilization policy in economies with strong trade unions is developed the analysis provides a theoretical underpinning for the assertion that accommodation policies may cause wage inflation and ultimately reduce employment various methods of accomplishing a real wage adjustment are discussed i a policy of complete nonaccommodation 2 continued accommodation policies but with lower employment targets 3 social contracts and 4 tax based incomes policies tip

a resource portfolio model for equipment investment and allocation of semiconductor testing industry profitable but risky semiconductor testing market has led companies in the industry to carefully seek to maximize their profits by developing a proper resource portfolio plan for simultaneously deploying resources and selecting the most profitable orders various important factors such as resource investment alternatives trade offs between the price and speed of equipment and capital time value further increase the complexity of the simultaneous resource portfolio problem this study develops a simultaneous resource portfolio decision model as a non linear integer programming and proposes a genetic algorithm to solve it efficiently the proposed method is employed in the context of semiconductor testing industry to support decisions regarding equipment investment alternatives including new equipment procurement rent and transfer by outsourcing and phasing outing for simultaneous resources such as testers and handlers and task allocation experiments have showed that our approach in contrast to an optimal solution tool obtains a near optimal solution in a relatively short computing time

inventory and investment in setup and quality operations under return on investment maximization in this paper we construct and analyze a return on investment roi maximization model for inventory and capital investment in setup and quality operations under an investment budget constraint specifically we show how such an roi maximization model can be formulated and derive analytical results such as the conditions under which the inventory is reduced and for the determination of the unique global optimal solution in addition by applying the reformulation linearization technique rlt we show via numerical examples how this nonconvex optimization model can be solved effectively and how rlt may produce superior results to those from the conventional cut across the board rule cabr various managerial insights are provided throughout the paper for example as the investment budget increases or decreases a fundamental shift of investment strategies setup cost reduction vs quality improvement may be necessary so as to maximize roi

inventory models with ramp type demand rate partial backlogging and weibull deterioration rate in this paper an inventory model with general ramp type demand rate time dependent weibull deterioration rate and partial backlogging of unsatisfied demand is considered the model is studied under the following different replenishment policies a starting with no shortages and b starting with shortages the model is fairly general as the demand rate up to the time point of its stabilization is a general function of time the backlogging rate is any non increasing function of the waiting time up to the next replenishment the optimal replenishment policy for the model is derived for both the above mentioned policies

cooperative investments and the value of contracting recent articles have shown that contracts can support the efficient outcome for bilateral trade even in the face of specific investments and incomplete contracting these studies typically considered selfish investments that benefit the investor e g the seller s investment reduces her production costs the authors find very different results for cooperative investments that directly benefit the investor s partner e g the seller s investment improves the buyer s value of the good most importantly if committing not to renegotiate the contract is impossible then contracting has no value i e the parties cannot do better than to abandon contracting altogether in favor of ex post negotiation

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

information and the hold up problem we examine situations in which a party must make a sunk investment prior to contracting with a second party to purchase an essential complementary input we study how the resulting hold up problem is affected by the seller s information about the investing party s likely returns from its investment our principal focus is on the effects of the investment s being observable by the non investing party contrary to popular intuition we find that an improvement in the seller s information e g the investment s being observable rather than not can benefit the buyer and harm the seller we also find that other popular intuitions about this problem are either false incomplete or require strong assumptions to be valid

note on inventory model with a mixture of back orders and lost sales abstract competitiveness is an important means of determining whether a company will prosper business organizations compete with one another in a variety of ways among these competitive methods are time and cost factors the purpose of this paper is to examine the inventory models presented by padmanabhan and vrat international journal of systems sciences 21 1990 1721 with a mixture of back orders and lost sales we develop the criterion for the optimal solution for the total cost function if the criterion is not satisfied this model will degenerate into one cycle inventory model with a finite inventory period this implies an extension of shortage period as long as possible to produce lower cost however we know that time is another important factor in company competitiveness customers will not indefinitely wait for back orders a tradeoff will be made between the two most important factors time and cost the minimum total cost is evaluated under the diversity cycle time and illustrations are applied to explain the calculation process this work provides a reference for decision makers

a deteriorating inventory model with time varying demand and shortage dependent partial backlogging abstract recently chu et al p chu k l yang s k liang t niu note on inventory model with a mixture of back orders and lost sales european journal of operational research 159 2004 470 475 presented the necessary condition of the existence and uniqueness of the optimal solution of padmanabhan and vrat g padmanabhan p vrat inventory model with a mixture of back orders and lost sales international journal of systems science 21 1990 1721 1726 however they included neither the purchase cost nor the cost of lost sales into the total cost in this paper we complement the shortcoming of their model by adding not only the cost of lost sales but also the non constant purchase cost and then extend their model from a constant demand function to any log concave demand function we also provide a simple solution procedure to find the optimal replenishment schedule further we use a couple of numerical examples to illustrate the results and conclude with suggestions for future research

renegotiation and optimality in agency contracts we analyse renegotiation in a hidden action principal agent model contract renegotiation offers are made by the agent a refinement is imposed on the principal s beliefs if precisely one action is optimal with respect to both the principal s and the agent s contracts the principal believes that that action has been taken with the refinement imposed perfect bayesian equilibrium allocations are identical to the second best in the classical principal agent model without renegotiation when renegotiation is led by the agent and when equilibria satisfy the refinement equilibrium allocations are ex ante efficient incentive contracting is a common mechanism for promoting ex ante investments and for avoiding ex post opportunistic behaviour in a long term or continuing economic relationship the classical principal agent model holmstrom 1979 grossman and hart 1983 is a natural framework for this class of problem in such a model a risk averse agent performs an action on behalf of a risk neutral principal the agent s action is unobservable and affects the principal s revenue in a random fashion the derivation and characterization of efficient compensation schemes have been the major focus in the principal agent literature generally the incentives to motivate a costly action from the agent take the form of profit sharing the agent s reward is made contingent on his random performance outcomes

ex ante investment ex post adaptation and joint ownership abstract this study extends the property rights theory prt model by introducing an ex post adaptation to changes in trade circumstances we show that if uncertainty is sufficiently high joint ownership can facilitate both ex ante investment and ex post adaptation

the loss averse newsvendor model with backordering abstract in this paper we study the optimal order quantity in the loss averse newsvendor model with backordering we first obtain the optimal order quantity to maximize the expected utility to hedge against the risk arising from the uncertainty of market demand we introduce the conditional value at risk cvar measure and derive the optimal order quantity to maximize the cvar objective about utility it is found that the optimal order quantity with the cvar objective is decreasing in the confidence level and thus is smaller than the optimal order quantity to maximize the expected utility it is proved that under the optimal order quantity with the cvar objective the loss averse newsvendor s expected utility is decreasing in the confidence level it further confirms that high risk implies high return and low risk comes with low return

preservation technology investment for deteriorating inventory abstract the objective of this study is to develop a deteriorating inventory policy when the retailer invests on the preservation technology to reduce the rate of product deterioration a solution procedure is presented to determine an optimal replenishment cycle shortage period order quantity and preservation technology cost such that the total profit per unit time is maximized a numerical example and sensitivity analysis are presented to illustrate the model

incomplete contracts the hold up problem and asymmetric information abstract given symmetric information in a standard hold up problem a buyer s investment incentives are always increasing in his bargaining power while this result is robust under one sided private information it can be overturned under two sided private information

energy security externalities and policies abstract in this paper we review conceptual arguments and empirical evidence related to two potential sources of market failure involving energy security in doing so we consider several questions involving the distinction between externality and market inefficiency and the distinction between market failures that are amenable or not amenable to correction given our current understanding of the workings of an economy several conclusions follow from our analysis regarding the potential sources of market failure and possible remedies the problem of excess wealth transfer from exporter market power may be an issue but current knowledge of oil market behaviour is too weak to support a strong conclusion other supposed costs of oil import dependence also are not well grounded including externalities related to the vulnerability of the economy to energy price shocks

impact of product pricing and timing of investment decisions on supply chain co opetition abstract in supply chain co opetition firms simultaneously compete and co operate in order to maximize their profits we consider the nature of co opetition between two firms the product supplier invests in the technology to improve quality and the purchasing firm buyer invests in selling effort to develop the market for the product before uncertainty in demand is resolved we consider three different decision making structures and discuss the optimal configuration from each firm s perspective in case 1 the supplier invests in product quality and sets the wholesale price for the product the buyer then exerts selling effort to develop the market and following demand potential realization sets the resale price in case 2 the supplier invests in product quality followed by the buyer s investment in selling effort then after demand potential is observed the supplier sets the wholesale price and the buyer sets the resale price finally in case 3 both firms simultaneously invest in product quality and selling effort respectively subsequently observing the demand potential the supplier sets the wholesale price and the buyer sets the resale price we compare all configuration options from both the perspective of the supplier and the buyer and show that the level of investment by the firms depends on the nature of competition between them and the level of uncertainty in demand our analysis reveals that although configuration 1 results in the highest profits for the integrated channel there is no clear dominating preference on system configuration from the perspective of both parties the incentives of the co opetition partners and the investment levels are mainly governed by the cost structure and the level of uncertainty in demand we examine and discuss the relation between system parameters and the incentives in desiging the supply contract structure

an application of tournament genetic algorithm in a marketing oriented economic production lot size model for deteriorating items abstract the goal of this research is to discuss an application of tournament genetic algorithm tga for solving an economic production lot size epl model in this model the production rate of the item is finite and it is assumed to be a decision variable the demand rate is also a deterministic function of selling price and the marketing cost the selling price per unit item is determined by a mark up over the unit production cost the deterioration rate at any instant is a linear increasing decreasing function of time partial backlogging shortages are allowed with a variable rate dependent on the length of the waiting time up to the starting of next production this model is formulated as a highly non linear constrained optimization problem to solve this problem a tga with steady state selection whole arithmetic crossover and non uniform mutation has been developed and applied the model has been illustrated with three numerical examples finally sensitivity analyses have been shown graphically to study the variations of the average profit with respect to the different parameters

sustainable inventory system with controllable non instantaneous deterioration and environmental emission rates abstract in today s environment it is difficult to be successful without considering sustainability the effects of global warming are becoming more observable in daily life supply chain activities are important sources of environmental emissions this effect increases concerns to control emissions through the development of a supply chain inventory model a replenishment problem based on joint pricing dynamic investment in environmental cost order cost preservation technology cost and optimal replenishment times for a non instantaneous deteriorating item is considered as a way to maximize retailer profit in this problem the demand rate depends on the stock and selling price an algorithm is used to find the optimum solution of the supply chain inventory problem which determines the selling price preservation technology investment cost environmental emission cost order cost and replenishment cycle time theoretical analysis of the optimal properties of the proposed model is provided and then solution methods are proposed numerical analysis is conducted to show the application of the model managerial implications are given to practitioner this study demonstrates that the proposed model could be applied under real world situations

after you sir hold up direct externalities and sequential investment we propose a solution to the hold up problem the parties in a contract can avoid the inefficiencies caused by the possibility of opportunistic behaviour and implement the first best level of investment if they make their investment decision sequentially one party observing the choice made by the other party before making his own choice unlike the existing literature the proposed solution leads to the efficient choice of investment even when there are two sided direct externalities journal of economic literatureclassification numbers d23 d82

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 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

renegotiation proof implementation and time preferences this paper explores how the requirement that the implementation of contracts be renegotiation proof affects the set of contracts that can be implemented in a seller buyer scenario in which the information regarding the agents valuations is nonverifiable this paper explicitly adds a time dimension to an implementa tion problem and introduces a natural criterion of renegotiation proofness for the case of time consuming renegotiation the main insight gained is that the addition of the time dimension enlarges significantly the set of contracts that can be implemented in a renegotiation proof manner jel c70 d23 this paper explores how the requirement that the implementation of contracts be renegotiation proof affects the set of con tracts that can be implemented in a seller buyer scenario in which the informa tion regarding the agents valuations is non verifiable the paper s main contributions are that first it explicitly adds a time di mension to an implementation problem and second it introduces a natural criterion of renegotiation proofness for the case of time consuming renegotiation for concreteness the discussion will be conducted in the context of the following example there are two agents a seller and a buyer who sign a contract for the sale of one unit in the future their valuations for the unit denoted by s and b respectively are not known when they sign the contract they become known to both parties after the contract is signed and before it is imple mented thus when it comes to implement ing the contract the parties information is complete but it is assumed to be nonverifi able i e not observable to third parties such as a court 1 when they sign the con tract the parties want to specify for any possible realization of the valuations s b whether or not there will be trade and the price p s b at which it will take place the contract describes the procedure that will be followed after the valuations are real ized the purpose of this procedure is to make sure that the original intentions of the parties are indeed carried out the idea is that the steps laid out in the contract are independent of s b and hence are en forceable by a third party or by a social convention in game theoretic terms a contract specifies a game form that imple ments the function p in the sense that for all s and b p s b is the resulting game s unique subgame perfect equilibrium out come in the context of this scenario we shall investigate the set of price functions p s b that can be so implemented by a contract and examine how this set is affected by the requirement that the contract be renegotia

quality improvement and setup reduction in the joint economic lot size model abstract the co maker concept has become accepted practice in many successful global business organizations this fact has resulted in a class of inventory models known as joint economic lot size jels models heretofore such models assumed perfect quality production on the part of the vendor this paper relaxes this assumption and proposes a quality adjusted jels model in addition classical optimization methods are used to derive models for the cases of setup cost reduction quality improvement and simultaneous setup cost reduction and quality improvement for the quality adjusted jels numerical results are presented for each of these models comparisons are made to the basic quality adjusted model results indicate that all three policies exhibit significantly reduced total cost however the simultaneous model results in the lowest cost overall and the smallest lot size this suggests a synergistic impact of continuous improvement programs that focus on both setup and quality improvement of the vendor s production process sensitivity analysis indicates that the simultaneous model is robust and representative of practice

the theory of the firm as governance structure from choice to contract the propositions that organization matters and that it is susceptible to analysis were long greeted by skepticism by economists one reason why this message took a long time to register is that it is much easier to say that organization matters than it is to show how and why the prevalence of the science of choice approach to economics has also been an obstacle as developed herein the lessons of organization theory for economics are both different and more consequential when examined through the lens of contract this paper examines economic organization from a science of contract perspective with special emphasis on the theory of the firm

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

inspection policy for inventory system with deteriorating products abstract typical inventory models usually focus on screening out the deteriorating items not much attention is paid to the situation that a proportion of deteriorated items are sold to consumers together with serviceable items during a replenishment cycle this paper first presents a model to formulate the process of such kind of mixed sales a simple closed form solution is obtained for maximizing the net profit per unit time under the assumption of small deterioration rate the effect of shortage back ordering is then considered and closed form solutions of optimal ordering quantity and replenishment time are obtained under similar assumption we further study the effect of inspection policies on optimal decisions for a deteriorating inventory system a dynamic programming approach is proposed for solving the optimal policy numerical examples are then provided to demonstrate our conclusions and results

an economic production and remanufacturing model with learning effects abstract managing inventory in reverse logistics has been receiving much attention in recent years one inventory problem that has been of interest to researchers is the production and remanufacturing model where used items are collected and remanufactured to satisfy customer demand the available models in the literature do not discuss the learning effects in production and remanufacturing processes this may not be true in industries where labour costs and learning costs are expensive by modelling these learning effects management may use established learning models to better utilize capacity manage inventories and coordinate production and distribution throughout the chain this paper extends the production remanufacture and waste disposal model by assuming learning to occur in both production and remanufacturing processes however this paper also assumes that improvements due to learning require capital investment mathematical models are developed numerical examples are provided and results are discussed

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

optimal replenishment policies for non instantaneous deteriorating items with stock dependent demand abstract wu et al 2006 an optimal replenishment policy for non instantaneous deteriorating items with stock dependent demand and partial backlogging international journal of production economics 101 369 384 established an inventory model for non instantaneous deteriorating items with stock dependent demand and obtained the optimal replenishment policy in this paper we first amend wu et al s model by changing the objective to maximizing the total profit secondly we set a maximum inventory level in the model to reflect the facts that most retail outlets have limited shelf space thirdly we relax the restriction of zero ending inventory when shortages are not desirable we then establish the theoretical results and provide an algorithm to find the optimal solution finally we present some numerical examples to illustrate the results

public goods and the hold up problem under asymmetric information an agent can make an observable but non contractible investment a principal then offers to collaborate with the agent to provide a public good private information of the agent about his valuation may either decrease or increase his investment incentives depending on whether he learns his type before or after the investment stage