does a procurement service provider generate value for the buyer through information about supply risks we consider a supply chain with one buyer and two suppliers who are subject to disruptions and whose likelihoods of disruption are their private information in such a setting does the buyer benefit from engaging the services of a better informed procurement service provider psp compared to procuring directly from the suppliers intuition might suggest that hiring a psp is always the right choice because the psp s knowledge of the supply base improves supplier selection and management on the other hand earlier studies prove that using a psp purely for its superior knowledge about supply costs is always worse for a buyer than contracting with the suppliers directly our answer to this research question is more nuanced contrary to the findings of earlier studies we find that the buyer may benefit from using a psp we identify quantify and explain all of the benefits and the costs of using a psp and describe conditions under which the benefits exceed the costs the benefits of using a psp are deriv

optimality of myopic ordering policies for inventory model with stochastic supply this paper addresses a discrete time inventory model where the maximum amount of supply from which instantaneous replenishment orders can be made is a random variable optimal ordering policies are characterized as critical number policies with monotone increasing optimal critical values a sufficient condition is then presented for myopic ordering policies to be optimal

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

continuous review inventory models where random lead time depends on lot size and reserved capacity the processing time of large orders is in many industries longer than that of small orders this renders supply lead times in such settings to be increasing in the order size yet that pattern is not re ected in existing inventory control models especially those allowing for random lead times this work aims at rectifying the situation our setting is an order quantity reorder point model with backordering where the shortage penalty is incurred per unit per unit time the processing time of each unit is random the processing time of a lot is correlated with its size for the case where lead time is proportional to the lot size we obtain a closed form solution that is unlike the classical q r model where lead time is independent of lot size no iterations are required here we also analyze a case where the processing time exhibits economies of scale in the lot size finally we consider a situation where a customer can secure shorter processing times by reserving capacity at the supplier s manufacturing facility 2000 elsevier science b v all rights reserved

a periodic review production planning model with uncertain capacity and uncertain demand optimality of extended myopic policies increasing product complexity manufacturing environment complexity and an increased emphasis on product quality are all factors leading to uncertainties in production processes these uncertainties are in the form of unplanned machine maintenance varying production yields and rework among others in planning for production an adequate model must incorporate these uncertainties into the representation of the production process this paper treats the aggregate planning problem for a single product with random demand and random capacity in the single period problem random capacity does not affect the optimal policy but results in a unimodal nonconvex cost function in the multiple period and infinite horizon settings order up to policies that are dependent on the distribution of capacity are shown to be optimal in spite of a nonconvex cost in the infinite horizon setting an intuitive description of the situation leads to the notion of a class of extended myopic policies requiring the consideration o

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

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

existence of coordinating transshipment prices in a two location inventory model we consider a two location production inventory model where each location makes production decisions and is subject to uncertain capacity each location optimizes its own profits transshipment at a cost is allowed from one location to another we focus on the question of whether one can globally set a pair of coordinating transshipment prices i e payments that each party has to make to the other for the transshipped goods that induce the local decision makers to make inventory and transshipment decisions that are globally optimal a recent paper suggests for a special case of our model that there always exists a unique pair of coordinating transshipment prices we demonstrate through a counterexample that this statement is not correct and derive sufficient and necessary conditions under which it would hold we show that in some conditions coordinating prices may exist for only a narrow range of problem parameters and explore conditions when this can happen finally we study the effects of demand and capacity variability on the magnitude of coordinating transshipment prices

capacitated multi item inventory systems with random and seasonally fluctuating demands implications for postponement strategies we address multi item inventory systems with random and seasonally fluctuating and possibly correlated demands the items are produced in two stages each with its own lead time in the first stage a common intermediate product is manufactured the production volumes in the first stage are bounded by given capacity limits we develop an accurate lower bound and close to optimal heuristic strategies of simple structure the gap between them evaluated in an extensive numerical study is on average only 0 45 we use the model to investigate the benefits of various delayed product differentiation postponement strategies as well as other strategic questions including i the benefits of flexible versus dedicated production facilities ii the trade off between capacity and inventory investments and iii the trade off between capacity investments and service levels

ad revenue optimization in live broadcasting in live broadcasting the break lengths available for commercials are not always fixed and known in advance e g strategic and injury time outs are of variable duration in live sports transmissions broadcasters actively manage their advertising revenue by jointly optimizing sales and scheduling policies we characterize the optimal dynamic schedule in a simplified setting that incorporates stochastic break durations and advertisement lengths of 15 and 30 seconds the optimal policy is a greedy look ahead rule that accounts for the remaining number of breaks in this setting there is no value to perfect information at the scheduling stage and hence knowing the duration of all breaks would not change the schedule we present heuristics to help solve scheduling problems of even greater complexity the performance of these heuristics under various scenarios is tested by running simulations calibrated using industry data the simple greedy heuristic is shown to perform well except when revenues are con

optimal production and inventory policy for multiple products under resource constraints we show that a modified base stock policy is optimal for multiproduct infinite horizon production inventory systems where demand for the products is random and the products share a finite resource every period we characterize the optimal policy for the case of homogeneous products because of the difficulty in computing the optimal base stock levels for the heterogeneous case we propose a heuristic that is simple enough for practical applications we present numerical results that suggest that the heuristic yields near optimal solutions

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

inventory control with markovian capacity and the option of order rejection we consider a stochastic inventory control problem with markovian capacity and the option of order rejection we show its optimal policy to be the combination of a capacity dependent modified base stock production policy and a capacity dependent critical point order acceptance policy when capacity is stochastically monotone we show that the policy parameters change over the current capacity level in an intuitive way all these results can be extended to the infinite horizon case with or without cost discounting our computational study substantiates the benefits from both exploiting the markovian behavior of the capacity and rejecting orders when necessary

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

a non stationary periodic review production inventory model with uncertain production capacity and uncertain demand abstract in this paper we consider a nonstationary periodic review dynamic production inventory model with uncertain production capacity and uncertain demand the maximum production capacity varies stochastically it is known that order up to or base stock critical number policies are optimal for both finite horizon problems and infinite horizon problems we obtain upper and lower bounds of the optimal order up to levels and show that for an infinite horizon problem the upper and the lower bounds of the optimal order up to levels for the finite horizon counterparts converge as the planning horizons considered get longer furthermore under mild conditions the differences between the upper and the lower bounds converge exponentially to zero

the risk averse newsvendor problem with random capacity abstract we study the effect of capacity uncertainty on the inventory decisions of a risk averse newsvendor we consider two well known risk criteria namely value at risk var included as a constraint and conditional value at risk cvar for the risk neutral newsvendor we find that the optimal order quantity is not affected by the capacity uncertainty however this result does not hold for the risk averse newsvendor problem specifically we find that capacity uncertainty decreases the order quantity under the cvar criterion under the var constraint capacity uncertainty leads to an order decrease for low confidence levels but to an order increase for high confidence levels this implies that the risk criterion should be carefully selected as it has an important effect on inventory decisions this is shown for the newsvendor problem but is also likely to hold for other inventory control problems that future research can address

a capacitated production inventory model with periodic demand for a single product single stage capacitated production inventory model with stochastic periodic cyclic demand we find the optimal policy and characterize some of its properties we study the finite horizon the discounted infinite horizon and the infinite horizon average cases a simulation based optimization method is provided to compute the optimal parameters based on a numerical study several insights into the model are also provided

double marginalization and coordination in the supply chain with uncertain supply abstract this paper explores a generalized supply chain model subject to supply uncertainty after the supplier chooses the production input level decentralized systems under wholesale price contracts are investigated with double marginalization effects shown to lead to supply insufficiencies in the cases of both deterministic and random demands we then design coordination contracts for each case and find that an accept all type of contract is required to coordinate the supply chain with random demand which is a much more complicated situation than that with deterministic demand examples are provided to illustrate the application of our findings to specific industrial domains moreover our coordination mechanisms are shown to be applicable to the multi supplier situation which fills the research gap on assembly system coordination with random yield and random demand under a voluntary compliance regime

benefits of leadtime information and of its combination with demand forecast information abstract this paper studies both the benefits of leadtime information and the interrelationships among demand forecast information leadtime uncertainty and leadtime information for improving inventory control performance to this end it explicitly incorporates both leadtime information and demand forecast information into an inventory model although they have conventionally been dealt with individually in the literature specifically it considers a periodic review inventory model with uncertain leadtimes in which both leadtime information and demand forecast information are available the leadtime information is modeled as the information of the arrival of outstanding orders and the demand forecast information as the martingale model of forecast evolution mmfe the paper analyzes the way to use both leadtime information and demand forecast information for inventory control operations specifically under certain conditions the optimality of the state dependent base stock policy is shown and an effective heuristic policy is developed it also derives some managerial insights for exploiting both leadtime information and demand forecast information in the case where leadtimes are uncertain for instance while leadtime information itself significantly improves inventory control performance it also enhances the benefits of demand forecast information specifically the benefits of demand forecast information may significantly decrease as leadtime uncertainty increases however the decrease of the benefits of demand forecast information may be alleviated with leadtime information

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

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

analysis of an inventory system under supply uncertainty in this paper we analyze a periodic review single item inventory model under supply uncertainty the objective is to minimize expected holding and backorder costs over a finite planning horizon under the supply constraints the uncertainty in supply is modeled using a three point probability mass function the supply is either completely available partially available or the supply is unavailable machine breakdowns shortages in the capacity of the supplier strikes etc are possible causes of uncertainty in supply we demonstrate various properties of the expected cost function and show the optimality of order up to type policies using a stochastic dynamic programming formulation under the assumption of a bernoulli type supply process in which the supply is either completely available or unavailable and when the demand is deterministic and dynamic we provide a newsboy like formula which explicitly characterizes the optimal order up to levels an algorithm is given that computes the optimal inventory levels over the planning horizon extensions and computational analysis are presented for the case where the partial supply availability has positive probability of occurrence

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

ordering and production decisions with supply quality and demand uncertainty in this paper we solve a production planning problem that has a direct bearing on the cost to a facility of vendor quality and reliability this solution is also an important first step in solving the multi plant coordination problem we consider a manufacturing facility with one critical raw material and one or more products whose demand needs to be met it is assumed that demand for finished goods and the arrival process for raw material are stochastic we calculate simultaneously the optimal production level and the raw material order quantity which minimize the total expected cost subject to capacity and release level constraints the results obtained by our model the integrated model show that the production level should be no larger than the production level obtained by solving the traditional nonintegrated models and that major savings are obtained by solving the integrated model we are also able to characterize and evaluate the cost of reliable supplies of raw material in addition we solve the above problem in the presence of capacity constraints a procedure which allocates capacity to different products is presented

optimum pricing of mutual guarantees for credit the main finding of this paper is that under financial market impediments and asymmetric information a mutually guaranteed and correctly schemed and priced insurance credit contract should have an abnormal actuarial profit such a contract improves welfare by simultaneously eliminating underinvestment ui and overinvestment oi and by reducing the probability of the insurer s ruin this solution is relevant for mutual credit insurance agencies and international or governmental agencies interested in increasing the value creation of small and medium enterprises that suffer from limited access to equity and debt markets

some ideas regarding reserving supplier capacity and selecting replenishment quantities in a project context abstract in this paper we consider the context of a major project whose execution takes several periods specifically we are interested in the procurement policy for a resource material commodity or engineered item that is used throughout the project two types of uncertainty are considered namely i uncertainty in the requirements period by period and ii uncertainty in the capacity period by period of the supplier providing the resource there is the possibility of paying a premium to reserve dedicated capacity that can vary from period to period hence the first group of decision variables are the capacities to reserve period by period there is typically a long lead time involved so that all the capacities must be reserved prior to the first replenishment decision the second class of decision variables encompasses the procurement quantities period of period these decisions can be made as the project progresses we present some general approaches to dealing with this complex problem as well as some important insights

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

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

supply and demand functions in inventory models the central issue in supply chain management is to match supply with demand and the heart of a planning model is the modeling of supply and demand functions to allow for analytical tractability the existing literature often assumes almost surely linear supply and demand functions which greatly limits the applicability of the models the goal of this paper is to provide a unified approach to analyze general random supply and demand functions by transforming the problem into one defined on a higher dimension we show that many of the seemingly highly nonlinear supply and demand functions in the almost sure sense are linear in the stochastic sense with this new notion of linearity called stochastic linearity in midpoint our ability to analyze supply chain problems is much enhanced we are able to prove the concavity of the profit function in the transformed supply and demand decisions for a general class of supply and demand functions that include but are not restricted to the ones studied in the

a production inventory system with markovian capacity and outsourcing option we study the optimal production inventory outsourcing policy for a firm with markovian in house production capacity that faces independent stochastic demand and has the option to outsource we find very simple optimal policy forms under fairly reasonable assumptions in addition when the capacity markov process is stochastically monotone the policy parameters decrease in the firm s current capacity level under additional assumptions all these results extend to the infinite horizon and undiscounted cost cases we analyze comparative statics and the necessity of some technical conditions and discuss when the outsourcing option is more valuable

inventory models with random yield in a random environment abstract we consider a single item inventory model which is observed periodically in a randomly changing environment all model parameters are specified by the state of the environment which is assumed to be a time homogeneous markov chain yield is random due to the random capacity of the vendor i e a given order is fully received if the order quantity is less than this capacity otherwise the quantity received is equal to the available capacity the problem is analyzed in single multiple and infinite periods and it is shown that in all cases the optimal policy is the well known base stock policy where the optimal order up to level depends on the state of the environment the results are compared with the solutions of the certain yield model when there is infinite capacity we show that the order up to levels are equal in the single period case however in multiple and infinite periods we order the same or more if the yield is random

joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity abstract in this paper we study a joint optimization problem of replenishment and pricing for a periodic review inventory system with random supply capacity when making replenishment and pricing decisions at the beginning of each period the firm only knows the supplier s available capacity in the current period but does not know what will be the available capacity in future periods the salient feature of our model is that the random supply capacities for different periods are dependent several stochastic dependency structures are considered for the supply capacity sequence including the one lag and the multi lag dependency we show that the optimal inventory control policy is of the modified base stock type and the base stock level is decreasing in the available capacity of the current period and that the optimal pricing policy is a list price coined with markdown and markup this paper generalizes the work of federgruen and zipkin federgruen a zipkin p 1986a an inventory model with limited production capacity and uncertain demands i the average cost criterion mathematics of operations research 11 193 207 federgruen a zipkin p 1986b an inventory model with limited production capacity and uncertain demands ii the discounted cost criterion mathematics of operations research 11 208 215 in which the supply capacity and selling price are assumed to be fixed constants and the work of federgruen and heching federgruen a heching a 1999 combining pricing and inventory control under uncertainty operations research 47 454 475 on joint optimization of replenishment and pricing with unlimited supply capacity

computing equilibrium prices for a capital asset pricing model with heterogeneous beliefs and margin requirement constraints abstract the mean variance capital asset pricing model capm is a useful mathematical tool for studying a variety of financial problems in contrast to existing work in the literature which has primarily focused on deriving analytical solutions under restrictive assumptions we propose a numerical algorithm for efficiently computing the set of equilibrium prices of a capm model with heterogeneous investors and arbitrary margin requirements we present the mathematical formulation of the capm model derive structural properties of the portfolio selection and excess demand functions and establish the asymptotic convergence of the proposed algorithm under mild conditions to illustrate the utility of the algorithm we perform sensitivity analysis on a simple example to study the impact of marginal requirements and interest rates on the resulting equilibrium prices numerical studies are also carried out to compare the performance of the algorithm with that of two other popular methods namely the fixed point method and the brand and bound algorithm

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

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

coordinating inventory control and pricing strategies under batch ordering in this paper we investigate joint pricing and inventory control problems in a finite horizon single product periodic review setting with certain uncertain supply capacities the demands in different periods are random variables whose distributions depend on the posted price exhibiting the additive form the order quantity in each period is required to be of integral multiples of a given specific batch size denoted by q inventory replenishment incurs a linear ordering cost referred to as the cost rate function the sum of holding and backorder costs can either be convex or quasi convex the objective is to determine a joint ordering and pricing decision that can maximize the total expected profit over the planning horizon we first consider the case in which the cost rate function is convex and show that the modifiedr q list price policy is optimal for the system with certain and limited capacities a special case of which is the r q list price policy when capacities become unlimited as supply capacities become random the optimal policy follows a new structure wherein the optimal order up to level and posted price must be coordinated to make the optimal safety stock level follow the r q policy we further consider the case of a quasi convex cost rate function which may arise when a service level constraint is used as a surrogate for the shortage cost we demonstrate that the r q list price policy is optimal for the system without supply capacity constraints in addition extensions to several other models are discussed the enabling technique is based on the notion of q jump convexity and its variants

interrelating operational and financial performance measurements in inventory control financial supply chain management and working capital management are increasingly receiving attention as important avenues to increase profitability in supply chains by actively managing payment terms and working capital requirements managers can influence financial performance and achieve significant cost savings however measures to improve financial performance implicitly restrict and influence operational performance in our research we elaborate on the benefits of equally considering both operational and financial aspects in decision making for the physical and financial supply chain we develop a mathematical model that determines the optimal purchasing order quantity under working capital restrictions and payment delays we analyze the trade offs between the most commonly used financial and operational measurements such as service level return on investment profit margin and inventory level our results demonstrate the significance of payment delays increases decreases in the upstream downstream payment delays favor the system s operations by decreasing operational costs moreover increases in the working capital employed in the system decrease the total operational cost increase the total financial cost and lower the return on working capital investment c 2009 elsevier b v all rights reserved

optimal policies for inventory systems with finite capacity and partially observed markov modulated demand and supply processes we analyze a single item periodic review inventory system with random yield and finite capacity operating in a random environment the primary objective is to extend the model of gallego and hu 2004 to the more general case when the environment is only partially observable although our analysis is specific to inventory systems it can also be applied to production systems by replacing the fixed capacity supplier with a fixed capacity producer using sufficient statistics we consider single period multiple period and infinite period problems to show that a state dependent modified inflated base stock policy is optimal moreover we show that the multiple period cost converges to the infinite period cost as the length of the planning horizon increases

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

periodic review production models with variable capacity random yield and uncertain demand we investigate a production planning problem in a periodic review environment with variable production capacity random yields and uncertain demand the implications of random yields and variable capacity for lot sizing previously have been explored separately but not jointly many production environments are likely to be subject to both types of uncertainties to minimize the total discounted expected costs production holding and shortage costs we formulate the problem as a stochastic dynamic program for the finite horizon problem we prove that the objective function is quasi convex and that the structure of the optimal policy is characterized by a single critical point for the initial stock level at each period that is if the initial stock is greater than this critical point the optimal planned production is zero otherwise it is greater than zero expressions for solving the critical point and the optimal planned production are obtained we further show that the solution for the finite horizon problem converges to that of the infinite horizon problem

production and inventory control for a make to stock calibrate to order system with dedicated and shared resources consider a firm that produces multiple products on dedicated production lines stage 1 which are further customized calibrated on a shared resource stage 2 common to all products the dedicated production lines and the shared resource for calibration face capacity uncertainties the firm holds inventory of products that are not yet calibrated and carries out calibration when an order is received we analyze a multiperiod inventory model for two products and derive the optimal production policy at stage 1 as well as the optimal allocation of the shared resource to demands at stage 2 for the shared resource because of its capacity uncertainty not only the total planned production quantities matter but also the sequence in which the products are processed we characterize the optimal allocation of the shared resource and show that the optimal policy keeps the ending inventories of products as close to a so called target path as possible for the dedicated production lines because of their capacit

continuous review inventory control when capacity is variable abstract many complex production inventory systems are characterized by uncertain capacities due to unexpected breakdowns unplanned repairs etc we analyze the effects of variable capacity on optimal lot sizing in continuous review environments two models are considered the basic eoq model and the order quantity reorder point model with backlogging for both cases we obtain the optimality conditions for generally distributed variable capacity we then show that the optimal order quantities for both models and the optimal reorder point for the second one are greater than those without variable capacity when the variable capacity distribution is exponential we develop effective procedures for finding the optimal solutions

integrating dynamic pricing and replenishment decisions under supply capacity uncertainty this paper examines an integrated decision making process regarding pricing for uncertain demand and sourcing from uncertain supply which are often studied separately in the literature our analysis of the integrated system suggests that the base stock list price policy fails to achieve optimality even under deterministic demand instead the optimal policy is characterized by two critical values a reorder point and a target safety stock under this policy a positive order is issued if and only if the inventory level is below the reorder point when this happens the optimal order and price are coordinated to achieve a constant target safety stock which aims at hedging the demand uncertainty we further investigate the profit improvement obtained from deploying dynamic pricing as opposed to static pricing our results indicate that either supply limit or supply uncertainty may induce a significant benefit from dynamic pricing and the compound effect of supply limit and uncertainty can be much more pronounced than the individual effects whether or not the supply capacity is limited has a major implication on the value of dynamic pricing under unlimited supply dynamic pricing is more valuable when procurement cost is high or when demand is more sensitive to price with limited supply however the capacity restriction tends to be relaxed reducing the value of dynamic pricing

a note on coordination in decentralized assembly systems with uncertain component yields abstract gurnani and gerchak h gurnani y gerchak coordination in decentralized assembly systems with uncertain component yields european journal of operational research 176 2007 1559 1576 study coordination of a decentralized assembly system in which the demand of the assembler is deterministic and the component yields are random they present incentive alignment control mechanisms under which system coordination is achieved in this note we extend gurnani and gerchak s model to the case of positive salvage value and n asymmetric suppliers and show that the shortage penalty contract which can coordinate gurnani and gerchak s model no longer coordinates the extended model furthermore we present a new kind of contract surplus subsidy contract to coordinate the extended model and prove that the profit of the supply chain under coordination can be arbitrarily divided between the component suppliers and the assembler