random yield supply chain with a yield dependent secondary market abstract this paper considers a simple supply chain with one supplier and one retailer where the supplier s production is subject to random yield and the retailer faces uncertain demand there exists a secondary market for acquiring or disposing products by the supplier we study both the centralized and decentralized systems in the decentralized system a no risk sharing contract and a risk sharing minimum commitment contract are analyzed the supply chain with the risk sharing contract is further analyzed with a constant secondary market price and a yield dependent secondary market price we present both the supplier s and the retailer s optimal strategies and provide insights for managers when making decisions under random yield risk and demand uncertainty we find that the secondary market generally has a positive impact on supply chain performance and the actual effect of random yield risk on the supply chain performance depends on cost parameters and supply chain contract settings under certain conditions reducing yield randomness may weaken the double marginalization effect and improve the chain performance from the numerical study we also show that there exists an optimal commitment level for the supply chain

multiperiod sales production decisions under uncertainty abstract this paper studies the behavior of an expected profit maximizing multiperiod firm under uncertainty in output and demand the firm s problem is to determine in each period the level of sales and inventory and the expected output for the coming period the optimal policy is derived in an explicit closed form and is proved to be myopic it is shown that the observed phenomenon of downward price inflexibility can be explained and further specified by using the results of our model

technical note note on myopic heuristics for the random yield problem bollapragada and morton 1999 present several well performing heuristics for solving the periodic inventory problem with random yield and demand their approach is essentially based on a transformation of the single period problem into a standard newsvendor problem with deterministic yield and random demand which however is supply dependent in our note we show that their evaluation of the respective optimality condition is not correct this explains the steady deterioration of their myopic heuristics for parameter constellations that correspond to increasing service levels some computational investigations reveal that the performance of the heuristics can become quite poor if service levels are high and exceed those values for which results are reported in the original study nonetheless up to now these heuristics are still the best ones available for solving the joint random yield problem

the strategic implications of sunk costs a behavioral perspective abstract this paper examines some of the strategic implications of the sunk cost phenomenon in sequential allocation decisions drawing from psychology and behavioral decision theory we first present a taxonomy of possible causes for the sunk cost effect the tendency of many managers to throw good money after bad we then present the analysis of some implications of this behavior in strategic situations a two period strategic game is developed and analyzed to derive optimal allocations as a function of one player s sunk cost behavior we establish when this behavior can be used as a successful precommitment strategy by the sunk cost player and when it is exploitable by an opponent welfare implications are also explored the sunk cost effect constitutes a form of strategic preference manipulation in which a credible preference change can be induced to provide a strategic advantage to one of the players

market forces meet behavioral biases cost misallocation and irrational pricing psychological and experimental evidence as well as a wealth of anecdotal examples suggests that firms may confound fixed sunk and variable costs leading to distorted pricing decisions this article investigates the extent to which market forces and learning eventually eliminate these distortions we envision firms that experiment with cost methodologies that are consistent with real world accounting practices including ones that confuse the relevance of variable fixed and sunk costs to pricing decisions firms follow naive adaptive learning to adjust prices and reinforcement learning to modify their costing methodologies costing and pricing practices that increase profits are reinforced in some market structures but not in others this process of reinforcement causes pricing practices of all firms to systematically depart from standard equilibrium predictions

base stock policies for production inventory problems with uncertain capacity levels abstract in this paper we consider a single item stochastic demand production inventory problem where the maximum amount that can be produced or ordered in any given period is assumed to be uncertain inventory levels are reviewed periodically the system operates under a stationary modified base stock policy the intent of our paper is to present a procedure for computing the optimal base stocl level of this policy under expected average cost per period criterion this procedure would provide guidance as to the appropriate amount of capacity to store in the form of inventory in the face of stochastic demand and uncertain capacity in achieving this goal our main contribution is to establish the analogy between the class of base stock production inventory policies that operate under demand capacity uncertainty and the g g 1 queues and their associated random walks we also present example derivations for some important capacity distributions

stochastic comparisons in production yield management manufacturing firms routinely commit resources to increase yield rates through product and process improvement initiatives champions of such yield improvement projects may assume that stochastically larger yield rates are beneficial in this note we show that this need not hold even when the contingent production lot sizes are chosen optimally we employ stochastic comparison techniques to show that a yield rate that is smaller in the convex order ensures higher expected profit and we provide a distribution free bound on the size of increase in expected profit we also identify properties of yield rate distributions that do make stochastically larger yield rates beneficial

on the effect of demand randomness on inventories and costs we explore analytically cardinal effects of the extent of demand randomness on optimal inventory levels and the associated expected costs to model changes in demand randomness we make extensive use of a mean preserving transformation commonly used in probabilistic microeconomics as well as the notion of risk pooling aggregating independent demands for the single period news vendor model the order quantity and associated costs are shown to depend on the randomness parameter in a simple and highly interpretable manner we show by a simple example that in some situations risk pooling might neither reduce inventories nor move them closer to the mean or median demand the managerial relevance of such analyses is discussed

product portfolio management with production flexibility in agribusiness the acquisition of production flexibility is a well documented strategy pursued by many firms to counteract certain operational constraints however these flexibilities can increase the complexity of a production system and the difficulties in managing increased complexity may hinder exploiting the full benefit of flexibility in this paper we consider one such flexibility paradox at an agribusiness firm for an annual 800 million production decision the firm produces a number of products hybrid seeds using limited inventories of several raw materials parent seeds and a production process that is subject to random variations to handle the raw material availability constraint and to partially mitigate the supply risk the firm invests in a costly second production in south america that can be used if the yield in the first production in north america is low we solve this joint problem of raw material allocation and sequential production by reformulating it as a tractable simultaneous optimization

the structure of periodic review policies in the presence of random yield this work provides a comprehensive analysis of a general periodic review production inventory model with random variable yield existence of an order point whose value does not depend on yield being random is proved in the single period case without specifying the yield model and using a very general cost structure when yield is a random multiple of lot size the nonorder up to optimal policy is characterized for a finite horizon model the finite horizon value functions are shown to converge to the solution of an infinite horizon functional equation and the infinite horizon order point is shown to be no smaller than when yield is certain

sunk costs uncertainty and market exit a real options perspective in this article we examine whether the option value of keeping an operation alive will deter firms from exiting an industry we find that uncertainty dissuades firms from exiting an industry but only when the sunk costs of entering and exiting that industry are sizeable moreover we argue and find that sunk costs can be influenced by the technological intensity of an industry by the extent to which a firm competes on the basis of innovation and by the firm s diversification strategy copyright 2009 the author 2009 published by oxford university press on behalf of associazione icc all rights reserved oxford university press

a single period stocking and pricing problem involving stochastic emergency supply abstract we develop a model for determining jointly optimal price and production policy of products with short life cycles subject to partially uncertain supply capacity within the price setting newsvendor framework we consider that demand in excess of the stocking quantity can be met by an emergency order due to the randomness of emergency supply capacity it may not always be possible to satisfy the demand completely assuming that all customers are charged the same price we explore the optimal sourcing and pricing decisions in the commonly used additive and multiplicative demand scenarios the first order conditions imply that the optimal price in the problem with random emergency supply is less than the optimal price associated with the deterministic demand problem when demand uncertainty is additive and it is greater than the optimal price associated with the deterministic demand problem when demand uncertainty is multiplicative we also find that the same type of comparative static applies in the multiplicative uncertainty case when there exists a dual source emergency system consisting of a perfectly reliable supplier and a second supplier with a stochastic capacity

the value of real time yield information in multi stage inventory systems exact and heuristic approaches abstract we consider a random yield inventory system where a company has access to real time information about the actual yield realizations to contribute to a better understanding of the value of this information we develop a mathematical model of the inventory system and derive structural properties we build on these properties to develop an optimal solution approach that can be used to solve small to medium sized problems to solve large problems we develop two heuristics we conduct numerical experiments to test the performances of our approaches and to identify conditions under which real time yield information is particularly beneficial our research provides the approaches that are necessary to implement inventory control policies that utilize real time yield information the results can also be used to estimate the cost savings that can be achieved by using real time yield information the cost savings can then be compared against the required investments to decide if such an investment is profitable

evaluation of cycle count policies for supply chains with inventory inaccuracy and implications on rfid investments inventory record inaccuracy leads to ineffective replenishment decisions and deteriorates supply chain performance conducting cycle counts i e periodic inventory auditing is a common approach to correcting inventory records it is not clear however how inaccuracy at different locations affects supply chain performance and how an effective cycle count program for a multi stage supply chain should be designed this paper aims to answer these questions by considering a serial supply chain that has inventory record inaccuracy and operates under local base stock policies a random error representing a stock loss such as shrinkage or spoilage reduces the physical inventory at each location in each period the errors are cumulative and are not observed until a location performs a cycle count we provide a simple recursion to evaluate the system cost and propose a heuristic to obtain effective base stock levels for a two stage system with identical error distributions and counting costs we prove that it is more effective to conduct more frequent cycle counts at the downstream stage in a numerical study for more general systems we find that location proximity to the customer error rates and counting costs are primary factors that determine which stages should get a higher priority when allocating cycle counts however it is in general not effective to allocate all cycle counts to the priority stages only one should balance cycle counts between priority stages and non priority stages by considering secondary factors such as lead times holding costs and the supply chain length in particular more cycle counts should be allocated to a stage when the ratio of its lead time to the total system lead time is small and the ratio of its holding cost to the total system holding cost is large in addition more cycle counts should be allocated to downstream stages when the number of stages in the supply chain is large the analysis and insights generated from our study can be used to design guidelines or scorecard systems that help managers design better cycle count policies finally we discuss implications of our study on rfid investments in a supply chain

an approximate policy for a dual sourcing inventory model with positive lead times and binomial yield this paper studies the inventory system of a retailer who orders his products from two supply sources a local one that is responsive and reliable but expensive and a global one that is low cost but less reliable the deliveries from the global source only partially satisfy the quality requirements we model this situation with a dual sourcing inventory model with positive lead times and random yield we propose a dual index order up to policy dop based on approximating the inventory model with an unreliable supplier by a sequence of dual sourcing models with reliable suppliers and suitably modified demand distributions numerical results show that the performance of this heuristic is close to that of the optimal dop moreover we extend the heuristic to models with advance yield information and study its impact on the total inventory costs

a unified theory of the dynamics of closed loop supply chains we investigate the dynamics of a closed loop supply chain with first order auto regressive ar 1 demand and return processes we assume these two processes are cross correlated the remanufacturing process is subject to a random triage yield remanufactured products are considered as goodas new and used to partially satisfy market demand newly manufactured products make up the remainder we derive the optimal linear policy in our closed loop supply chain setting to minimise the manufacturer s inventory costs we show that the lead time paradox can emerge in many cases in particular the auto and cross correlation parameters and variances of the error terms in the demand and the returns as well as the remanufacturing lead time all influence the existence of the lead time paradox finally we propose managerial recommendations for manufacturers

exploring the effect of cap and trade mechanism on firm s production planning and emission reduction strategy abstract cap and trade mechanism has a significant effect on firm s production and operation decisions and carbon emissions this study develops a mathematical model to examine the effect of cap and trade mechanism on firm s production planning and emission reduction strategy based on the model the firm s critical production planning decisions such as the optimal production quantity optimal allowance selling price and the maximum profit under the cap and trade mechanism are derived firstly then based on the cost benefit analysis the conditions under which the firm makes the optimal emission reduction strategy between buying carbon allowance from the carbon trading market and conducting low carbon processing are identified the result suggests that when the low carbon processing cost is greater than the potential opportunity benefit the firm is inclined to purchase carbon allowance from the carbon trading market and vice versa finally a numerical analysis is conducted to investigate the effects of relevant factors such as carbon quotas carbon emission rate low carbon processing cost and transaction cost on firm s production and operation decisions the results indicate that under the cap and trade mechanism the transaction cost has a positive effect on allowance selling price the firm s optimal production quantity and maximum profit is positively related to carbon quotas while negatively related to carbon emission rate and low carbon processing cost this research contributes to enrich related literature and knowledge with regard to carbon emissions reduction at the firm level and highlight the critical importance of cap and trade mechanism in reducing carbon emissions

a periodic review lot sizing problem with random yields disruptions and inventory capacity this paper examines a periodic reviewed lot sizing problem with random yields disruptions and limited inventory capacity to characterise the continuous production an additive random yield model is considered rather than a multiplicative one disruptions cause breakdowns to production inventory capacity is included since the production has to be shut down when the inventory buffer is full both disruptions and shutdowns lead to a start up cost and a stochastic lead time to recover the production these compound factors of uncertainty are encountered in practical planning decisions in process industries we review the existing random yield models which are then compared with the additive model with a linear production cost the additive model has an order up to policy to be optimal disruptions deteriorate the expected actual production quantity and the fill rate dramatically even though the optimal order up to level increases compared with the cases of no disruption considering inventory capacity makes the problem to be a non convex dynamic programming problem numerical analysis shows that the performance is dramatically deteriorated when the inventory capacity is rather tight which indicates the importance of selecting a proper inventory capacity to reduce the negative impacts and avoid redundant investment on capacity moreover the start up cost plays an important role in determining the level of inventory capacity

the rational effect of price promotions on sales and consumption we explore the rational effect of price variation on sales and consumption in markets where consumers are uncertain about the future price of goods we first derive an optimal ordering policy which expresses the amount a consumer should purchase and consume in a given period as a function of the observed price of the good the distribution of future prices and the nature of his or her inventory this policy extends previous normative models of inventory control such as those by golabi 1985 and kalymon 1970 to the case where the amount to consume in a given period is an explicit decision variable and prices follow a first order stochastic process we then use this model to explore how changes in the long run frequency and temporal correlations of price promotions should normatively affect the contemporaneous relationship between purchase consumption and price among the predictions which follow from the model are that consumption should rationally increase with the size of existing inventories the short term sensitivity of sales to prices should be greater than that of consumption to price and this discrepancy increases with decreases in the temporal correlation of price deals and the long term relative frequency of price deals

lost sales problems with stochastic lead times convexity results for base stock policies we consider a single location inventory system with periodic review and stochastic demand it places replenishment orders to raise the inventory position that is inventory on hand plus inventory in transit to exactly s at the beginning of every period the lead time associated with each of these orders is random however the lead time process is such that these orders do not cross demand that cannot be met with inventory available on hand is lost permanently we state and prove some sample path properties of lost sales inventory on hand at the end of a period and inventory position at the end of a period as functions of s the main result is the convexity of the expected discounted sum of holding and lost sales costs as a function of s this result justifies the use of common search procedures or linear programming methods to determine optimal base stock levels for inventory systems with lost sales and stochastic lead times it should be noted that the class of base stock policies is suboptimal for such systems and we are primarily interested in them because of their widespread use

a theory of rational addiction we develop a theory of rational addiction in which rationality means a consistent plan to maximize utility over time strong addiction to a good requires a big effect of past consumption of the good on current consumption such powerful complementarities cause some steady states to be unstable they are an important part of our analysis because even small deviations from the consumption at an unstable steady state can lead to large cumulative rises over time in addictive consumption or to rapid falls in consumption to abstention our theory also implies that cold turkey is used to end strong addictions that addicts often go on binges that addicts respond more to permanent than to temporary changes in prices of addictive goods and that anxiety and tensions can precipitate an addiction

escalation errors and the sunk cost effect an explanation based on reputation and information asymmetries this paper is concerned with explaining a paradox of human behavior consider the following example a department manager makes a large investment in new production equipment and soon after learns of different equipment that could perform the same operations at lower cost incremental analysis favors switching but the manager refuses saying he does not want to waste the investment already made such real world examples have been extensively documented and studied by social scientists see thaler 1980 and staw 1981 in these examples the decision maker having commited to a course of action subsequently discovers new information that indicates that continuing the earlier commitment would likely result in worse consequences than switching in spite of this he clings to and even escalates his earlier

procrastination and obedience in this lecture i shall focus on situations involving repeated decisions with time inconsistent behavior although each choice may be close to maximizing and therefore result in only small losses the cumulative effect of a series of repeated errors may be quite large thus in my examples decision makers are quite close to the intelligent well informed individuals usually assumed in economic analysis but cumulatively they make seriously wrong decisions that do not occur in standard textbook economics this lecture discusses and illustrates several pathological modes of individual and group behavior procrastination in decision making undue obedience to authority membership of seemingly normal individuals in deviant cult groups and escalation of commitment to courses of action that are clearly unwise in each case individuals choose a series of current actions without fully appreciating how those actions will affect future perceptions and behavior the standard assumption of rational forwardlooking utility maximizing is violated the nonindependence of errors in decision making in the series of decisions can be explained with the concept from cognitive psychology of undue salience or vividness for example present benefits and costs may have undue salience relative to future costs

stockpiling under price uncertainty and storage capacity constraints abstract a model is presented for the operation of an agent whose responsibility is to purchase and perhaps stockpile sufficient quantities of a certain commodity in order to satisfy an exogenous constant demand per time period this is the situation faced by a state agency which is responsible for the purchasing of oil products to satisfy the demand of a country in which demand for energy has stabilized at a certain level an important feature of the model is that the price of the commodity is described by a stochastic process this reflects the volatility of prices of oil products furthermore the model takes storage capacity constraints explicitly into account and thus can help to assess the optimal level of storage capacity expansion the relevant stochastic dynamic programming equations are derived and solved for the least cost function which turns out to be piecewise linear in the inventory level the storage capacity enters only in the computation of the constant term of the value function the solution of the dynamic programming equation leads also to the optimal purchasing strategy of agencies with different levels of flexibility in their policy in the model an agency can be allowed or not to resell from the stock and it can have finite or infinite storage capacity

optimal joint inventory and transshipment control under uncertain capacity in this paper we address the optimal joint control of inventory and transshipment for a firm that produces in two locations and faces capacity uncertainty capacity uncertainty e g due to downtime quality problems yield etc is a common feature of many production systems but its effects have not been explored in the context of a firm that has multiple production facilities we first characterize the optimal production and transshipment policies and show that uncertain capacity leads the firm to ration the inventory that is available for transshipment to the other location and characterize the structure of this rationing policy then we characterize the optimal production policies at both locations which are defined by state dependent produce up to thresholds we also describe sensitivity of the optimal production and transshipment policies to problem parameters and in particular explain how uncertain capacity can lead to counterintuitive behavior such as produce up to limits decreasing for locations that face stochastically higher demand we finally explore through a numerical study when the optimal policy is most likely to yield significant benefits compared to simple policies

infinite horizon strategies for replenishment systems with a general pool of suppliers we consider a general infinite horizon inventory control model that combines demand and supply risks and the firm s ability to mitigate the supply risks by diversifying its procurement orders among a set of n potential suppliers supply risks arise because only a random percentage of any given replenishment order is delivered as useable units the suppliers are characterized by the price they charge and the distribution of their yield factor assuming unsatisfied demand is backlogged the firm incurs as in standard inventory models three types of costs i procurement costs ii inventory carrying costs for units carried over from one period to the next and iii backlogging costs we establish the existence of an optimal stationary policy under both the long run discounted and average cost criteria and characterize its structure assuming each period s inventory level distribution can be approximated as a normal we develop an efficient solution method identifying additional structural properties finally we identify a simple class of heuristic policies that come close to being optimal

optimality of myopic policies for dynamic lot sizing problems in serial production lines with random yields and autoregressive demand we study lot size policies in a serial multistage manufacturing inventory system with two key generalizations namely 1 random yields at each production stage and 2 an autoregressive demand process previous research shows that the optimal policies in models with random yields even in models with a single installation lack the familiar order up to structure and are not myopic thus dynamic programming algorithms are needed to compute optimal policies and one encounters the curse of dimensionality this is exacerbated here by the need to expand the size and dimension of the state space to accommodate the autoregressive demand feature nevertheless although our model is more complex we prove that there is an optimal policy with the order up to feature and more importantly that the optimal policy is myopic this avoids the computational burden of dynamic programming our results depend on two assumptions concerning the stochastic yield namely that the expected yield at a work station is proportional to the lot size and the distribution of the deviation of the yield from its mean does not depend on the lot size we introduce the concept of echelon like variables a generalization of clark and scarf s classical concept of echelon variables to derive the structure of optimal policies furthermore we show that the same kind of policy is optimal for several criteria infinite horizon discounted cost infinite horizon long run average cost and finite horizon discounted cost with the appropriate choice of the salvage value function

myopic heuristics for the random yield problem we consider a single item periodic review inventory problem with random yield and stochastic demand the yield is proportional to the quantity ordered with the multiplicative factor being a random variable the demands are stochastic and are independent across the periods but they need not be stationary the holding penalty and ordering costs are linear any unsatisfied demands are backlogged two cases for the ordering cost are considered the ordering cost can be proportional to either the quantity ordered e g in house production or the quantity received e g delivery by an external supplier random yield problems have been addressed previously in the literature but no constructive solutions or algorithms are presented except for simple heuristics that are far from optimal in this paper we present a novel analysis of the problem in terms of the inventory position at the end of a period this analysis provides interesting insights into the problem and leads to easily implementable and highly accurate myopic heuristics a detailed computational study is done to evaluate the heuristics the study is done for the infinite horizon case with stationary yields and demands and for the finite horizon case with a 26 period seasonal demand pattern the best of our heuristics has worst case errors of 3 0 and 5 0 and average errors of 0 6 and 1 2 for the infinite and finite horizon cases respectively

environmental safety stock the impacts of regulatory and voluntary control policies on production planning inventory control and environmental performance abstract this paper analyzes the impacts of different pollution control policies on a firm s decisions of production planning and inventory control based on a stochastic model with both demand and environmental uncertainties we derive the optimal policies of production planning and inventory control under both regulatory and voluntary pollution control approaches and investigate their operational and environmental effects we establish that the conventional wisdom which suggests that reduction of environmental waste at the end of a production process also decreases the stock and throughput levels of a production system is not necessarily true rather a regulatory environmental standard that limits the total amount of waste may induce the firm to raise its planned stock level which would lead to a higher expected amount of environmental wastes before the standard is enforced as well as environmental risks at other stages of the production process the additional planned stock level which is termed environmental safety stock can be reversed by using the voluntary control approach that provides the firm with the flexibility to occasionally exceed the environmental standard we also conduct numerical experiments to analyze the effects of different values of model parameters under different control approaches the analytical results provide new insights to the impacts of a firm s production and inventory decisions on the natural environment as well as to the choices of pollution control approaches by decision makers in both the private and public sectors

a bargaining model for a first time interaction under asymmetric beliefs of supply reliability we consider the case of a first time interaction between a buyer and a supplier who is unreliable in delivery the supplier declares her estimate of the ability to meet the order obligations but the buyer may have a different estimate which may be higher or lower than the suppliers estimate we derive the nash bargaining solution and discuss the role of using a down payment or nondelivery penalty in the contract for the case of buyer overtrust the down payment contract maximizes channel profits when the suppliers estimate is public information if the suppliers estimate is private information a nonsymmetric contract is shown to be efficient and incentive compatible for the case of buyer undertrust the contract structure is quite different as both players choose not to include down payments in the contract when delivery estimates are public information a nondelivery penalty contract is able to maximize channel profits if the buyer uses the suppliers estimate in making the ordering decision if estimates are private information channel profits are maximized only if the true estimates of both players are not far part we also discuss the effect of different risk profiles on the nature of the bargaining solution in three extensions of the model we consider the following variants of the basic problem first we analyze the effect of early versus late negotiation on the bargaining solution then we study the case of endogenous supply reliability and finally for the case of repeated interactions we discuss the impact of updating delivery estimates on the order quantity and negotiated prices of future orders

technical note optimal inventory policy in the presence of a long term supplier and a spot market we consider a stochastic inventory control problem in which a buyer makes procurement decisions while facing periodic random demand and two supply sources namely a long term contract supplier and a spot market the contract between the buyer and the supplier partially shields the latter from the vicissitudes of the spot market in that the price paid by the buyer to the supplier is only partially linked to the spot price at the moment after fulfilling the minimum order commitment with the supplier the buyer has the full freedom to source from both the supplier and the market procurement from the spot market also incurs a fixed setup cost we show that an optimal policy consists of three different policy forms with the realization of each depending on the buyer s inventory level and the prevalent spot price certain conditions are identified under which monotone trends exist between policy parameters and the current spot price

sub supply chain coordination in a three layer chain under demand uncertainty and random yield in production abstract one of the major objectives of modern supply chain management is to deal with the growing decentralization among the involved entities and hence minimizing the double marginalization effect inside the chain especially when the end customers demand is not deterministic to address this a three layer supply chain with one raw material supplier one manufacturer and one retailer is developed and studied in this paper effects of both supply chain coordination as well as sub supply chain coordination are examined optimal order and production quantities are obtained for the centralized system which depicts the scenario under coordination optimal order quantities and expected profits of the individual channel actors are maximized locally in the decentralized system under commonly used price only contract semi integrated models are also studied under price only contract the optimal strategies under different power structures are compared and the effects of the channel parameters on the optimal strategies are also examined numerical example is given to illustrate the developed model

selecting a portfolio of suppliers under demand and supply risks we analyze a planning model for a firm or public organization that needs to cover uncertain demand for a given item by procuring supplies from multiple sources each source faces a random yield factor with a general probability distribution the model considers a single demand season all supplies need to be ordered before the start of the season the planning problem amounts to selecting which of the given set of suppliers to retain and how much to order from each so as to minimize total procurement costs while ensuring that the uncertain demand is met with a given probability the total procurement costs consist of variable costs that are proportional to the total quantity delivered by the suppliers and a fixed cost for each participating supplier incurred irrespective of his supply level each potential supplier is characterized by a given fixed cost and a given distribution of his random yield factor the yield factors at different suppliers are assumed to be independent of the season s demand which is described by a general probability distribution determining the optimal set of suppliers the aggregate order and its allocation among the suppliers on the basis of the exact shortfall probability is prohibitively difficult we have therefore developed two approximations for the shortfall probability although both approximations are shown to be highly accurate the first based on a large deviations technique ldt has the advantage of resulting in a rigorous upper bound for the required total order and associated costs the second approximation is based on a central limit theorem clt and is shown to be asymptotically accurate whereas the order quantities determined by this method are asymptotically optimal as the number of suppliers grows most importantly this clt based approximation permits many important qualitative insights

letter to the editor comments on on optimal inventory policies when ordering prices are random by kamal golabi comments on on optimal inventory policies when ordering prices are random by kamal golabi golabi k 1985 optimal inventory policies when ordering prices are random opns res 33 575 588

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

technical note linear inflation rules for the random yield problem analysis and computations in this paper we propose a simple heuristic approach for the inventory control problem with stochastic demand and multiplicative random yield our heuristic tries to find the best candidate within a class of policies that are referred to in the literature as the linear inflation rule lir policies our approach is computationally fast easy to implement and intuitive to understand moreover we find that in a significant number of instances our heuristic performs better than several other well known heuristics that are available in the literature

a newsvendor approach to compliance and production under cap and trade emissions regulation abstract since the 1990s governmental agencies have increasingly turned to market based cap and trade programs to control the emission of pollutants firms subject to cap and trade regulation are typically required to acquire emissions allowances via open auction markets the cost to acquire allowances may impose a substantial financial burden on a firm while emissions reduction efforts may eliminate some firm s need to acquire additional allowances there are still numerous firms that need to purchase additional allowances on the open market this study presents a new forward buying heuristic designed for those firms that need to purchase emissions allowances via auctions which reduces the impact of emissions allowance acquisitions on the firms financial performance the heuristic designated as the newsvendor production planning with emissions allowance forward buying nppafb method applies a forward buying algorithm to determine the number of periods for which to forward buy allowances the current production order up to level and the current and future emissions allowance requirements which serves as the order up to level for allowance purchases additionally nppafb also authorizes unused emissions allowances to be sold when market conditions are favorable compared against three existing production planning and allowance procurement strategies a simulation exercise finds that the nppafb method significantly reduces a firm s emissions allowance expenditures these results indicate that heuristic can be readily adopted by any firm that is required to procure emissions allowances via open markets in an effort to improve the firm s profitability

analysis of an inventory system under backorder correlated deterministic demand and geometric supply process abstract in this article we propose a single item periodic review model that investigates the effects of changes in the demand process that occur after stockout realizations we investigate a system where the demands in successive periods are deterministic but affected by the backorder realizations in order to capture the effects of changes in the demand process we use a geometric type supply availability we analytically derive the necessary components for obtaining profit related performance measures and provide computational analysis

concepts for safety stock determination under stochastic demand and different types of random production yield abstract we consider a manufacturer s stochastic production inventory problem under periodic review and present methods for safety stock determination to cope with uncertainties that are caused by stochastic demand and different types of yield randomness following well proven inventory control concepts for this problem type we focus on a critical stock policy with a linear order release rule a central parameter of this type of policy is given by the safety stock value when non zero manufacturing lead times are taken into account in the random yield context it turns out that safety stocks have to be determined that vary from period to period we present a simple approach for calculating these dynamic safety stocks for different yield models additionally we suggest approaches for determining appropriate static safety stocks that are easier to apply in practice in a simulation study we investigate the performance of the proposed safety stock variants

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

theoretical models of sales promotions contributions limitations and a future research agenda our objective in this paper is to review theoretical models of sales promotions we highlight the key contributions of these models discuss their limitations and outline an agenda for future research managerial questions examined in these models include some very fundamental issues such as why firms resort to the use of sales promotions in mature markets and why the use of sales promotions has increased dramatically during the last two decades also included in this review are models that address firm level strategic issues such as the allocation of dollars between advertising and sales promotions and the relative emphasis on trade promotions vis a vis consumer promotions we also review theoretical models that explain how consumers respond to price promotions and what type of sales promotion tools may be superior to others in a particular market the review concludes with a possible agenda for future research

rationalizability learning and equilibrium in games with strategic complementarities we study a rich class of noncooperative games that includes models of oligopoly competition macroeconomic coordination failures arms races bank runs technology adoption and diffusion r d competition pretrial bargaining coordination in teams and many others for all these games the sets of pure strategy nash equilibria correlated equilibria and rationalizable strategies have identical bounds also for a class of models of dynamic adaptive choice behavior that encompasses both best response dynamics and bayesian learning the players choices lie eventually within the same bounds these bounds are shown to vary monotonically with certain exogenous parameters we study the class of noncooperative supermodular games introduced by topkis 1979 and further analyzed by vives 1985 1989 who also pointed out the importance of these games in industrial economics supermodular games are games in which each player s strategy set is partially ordered the marginal returns to increasing one s strategy rise with increases in the competitors strategies so that the game exhibits strategic complementarity 2 and if a player s strategies are multidimensional marginal returns to any one com ponent of the player s strategy rise with increases in the other components this class turns out to encompass many of the most important economic applications of noncooperative game theory in macroeconomics diamond s 1982 search model and bryant s 1983 1984 rational expectations models can be represented as supermodular games in each of these models more activity by some members of the economy raises the returns to increased levels of activity by others in oligopoly theory some models of bertrand oligopoly with differentiated products qualify as supermodu lar games in these games when a firm s competitors raise their prices the marginal profitability of the firm s own price increase rises a similar structure is present in games of new technology adoption such as those of dybvig and spatt 1983 farrell and saloner 1986 and katz and shapiro 1986 when more users hook into a communication system or more manufacturers adopt an interface standard the marginal return to others of doing the same often rises similarly in some specifications of the bank runs model introduced by diamond and dybvig 1983 when more depositors withdraw their funds from a bank it is more worthwhile for other depositors to do the same in the warrant exercise

dynamic replenishment production and pricing decisions in the face of supply disruption and random price sensitive demand abstract we study a joint decision problem for replenishment production pricing strategies in the face of both supply and demand uncertainties the supply of the raw material suffers from a potential supply disruption while the demand for the finished goods is price sensitive and random we assume that the raw material is storable and unfilled demands are fully backordered we characterize the optimal policies for raw material replenishment finished goods production and pricing we find that the optimal replenishment policy is an order up to type for a given finished goods stock level while it is a threshold type for a given raw material stock level for either a given finished goods stock level or a given raw material stock level the optimal production policy is a threshold type and the optimal pricing policy is a modified list price type respectively

exact and heuristic linear inflation policies for an inventory model with random yield and arbitrary lead times abstract we investigate a periodic review inventory system for a single item with stochastic demand and random yield since the optimal policy for such a system is complicated we study the class of stationary linear inflation policies where orders are only placed if the inventory position is below a critical stock level and where the order quantity is controlled by a yield inflation factor we consider two different models for the uncertain supply namely binomial and stochastically proportional yield and we allow positive and constant lead times as well as asymmetric demand and yield distributions in this paper we propose two novel approaches to derive optimal and near optimal numerical values for the critical stock level minimizing the average holding and backorder cost for a given inflation factor first we present a markov chain approach which is exact in case of negligible lead time second we provide a steady state analysis to derive approximate closed form expressions for the optimal critical stock level we conduct an extensive numerical study to test the performance of our approaches the numerical experiments reveal an excellent performance of both approaches since our derived formulas are easily implementable and highly accurate they are very valuable for practical application

periodic review inventory systems with fixed order cost and uniform random yield abstract we consider periodic review stochastic inventory control problems with both fixed order cost and uniform random yield our objective is to characterize some structural properties of the optimal policies so that efficient approaches can then be established towards finding an optimal policy in particular we provide a lower and upper bound structure for the optimal policy at the beginning of any period such that it is optimal not to order anything if the initial stock level is above the upper bound and it is optimal to order a positive quantity if the initial stock level is below the lower bound where the optimal quantity can be found efficiently for any initial stock level in between the upper and lower bounds in each period a partial characterization of the optimal policy is provided furthermore we show that the optimal order quantity is monotonically decreasing in the initial stock level in any period and this will help the search for the optimal order quantity at any initial stock level in addition we illustrate a few interesting phenomena about the behavior of an optimal policy these phenomena show that the structure of the optimal policy for this problem is in general significantly different from that for the traditional periodic review inventory control problems with certain yield and fixed order cost

inventory management with random supply and imperfect information a hidden markov model in most of the papers on inventory models operating in a random environment the state of the environment in each period is assumed to be fully observed with perfect information however this assumption is not realistic in most real life situations and we provide a remedy in this paper by assuming that the environment is only partially observed with imperfect information we accomplish this by analyzing two formulations of single item models with periodic review and random supply in a random environment in the first one supply is random due to random capacity of production and random availability of transportation we show that state dependent base stock policy is optimal if the capacity and all costs are observed while demand and availability are unobserved in the second model we consider a model with random availability only with fixed ordering cost we show that state dependent s s policy is optimal if the availability process is observable