optimal dynamic pricing of inventories with stochastic demand over finite horizons in many industries managers face the problem of selling a given stock of items by a deadline we investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm s objective is to maximize expected revenues examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry which markets space such as seats on airline flights cabins on vacation cruises and rooms in hotels that become worthless if not sold by a specific time we formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp price as a function of the stock level and the length of the horizon for a particular exponential family of demand functions we find the optimal pricing policy in closed form for general demand functions we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity finally we extend our results to the case where demand is compound poisson only a finite number of prices is allowed the demand rate is time varying holding costs are incurred and cash flows are discounted the initial stock is a decision variable and reordering overbooking and random cancellations are allowed

on the structure of lost sales inventory models we provide a new approach to the structural analysis of the standard lost sales inventory system this approach is we think easier to work with than the original one we also derive new bounds on the optimal policy then we show that more variable demand leads to higher cost finally we extend the analysis to several important variations of the basic model

joint management of capacity and inventory in make to stock production systems with multi class demand we evaluate the benefits of coordinating capacity and inventory decisions in a make to stock production environment we consider a firm that faces multi class demand and has additional capacity options that are temporary and randomly available we formulate the model as a markov decision process mdp and prove that a solution to the optimal joint control problem exists for several special cases we characterize the structure of the optimal policy for the general case however we show that the optimal policy is state dependent and in many instances non monotone and difficult to implement therefore we consider three pragmatic heuristic policies and assess their performance we show that the majority of the savings originate from the ability to dynamically adjust capacity and that a simple heuristic that can adjust production capacity based on workload fluctuation but uses a static production rationing policy can result in significant savings

production planning and pricing policy in a make to stock system with uncertain demand subject to machine breakdowns abstract we consider a make to stock system served by an unreliable machine that produces one type of product which is sold to customers at one of two possible prices depending on the inventory level at the time when a customer arrives i e the decision point the system manager must determine the production level and selling price at each decision point we first show that the optimal production and pricing policy is a threshold control which is characterized by three threshold parameters under both the long run discounted profit and long run average profit criteria we then establish the structural relationships among the three threshold parameters that production is off when inventory is above the threshold and that the optimal selling price should be low when inventory is above the threshold under the scenario where the machine is down or up finally we provide some numerical examples to illustrate the analytical results and gain additional insights

finite lifetimes and the effects of budget deficits on national saving abstract even though realistic deficit policies shift sizable tax burdens to future generations the assumption of an infinite horizon is a good approximation for analyzing a deficit s short run saving effect on individuals who are neither liquidity constrained nor myopic recent u s experience casts significant doubt on these assumptions however and appears difficult to reconcile with the ricardian equivalence proposition that the timing of taxes does not affect national saving recent deficits have coincided with reduced national saving and a substantial increase in the share of gnp devoted to consumption

optimal dynamic scheduling policy for a make to stock production system this paper considers the dynamic scheduling problem of a single server make to stock queue with two products for the case of poisson demands and exponential production times we show that it is optimal to produce the product with the larger b index when it is backordered if the production times are identically distributed the optimal policy can further be characterized by monotone switching curves we also prove that a base stock policy coupled with a switching curve is optimal for some initial inventory levels a simple linear switching rule for determining production priority is proposed and compared with other heuristic policies in a computational experiment

social security public education and the growth inequality relationship abstract we study how the relationship between economic growth and inequality depends upon the levels of funding of two of the largest government programs public education and social security we do this in the context of an overlapping generations economy with heterogeneous agents where the government collects a tax on labor income to finance these programs we show that in our model an increase in government spending on social security reduces income inequality and can have a non monotonic effect on growth when the initial level of social security funding is low as is the case in most poor economies then its increase will enhance growth when its funding level is high as is typical for developed countries we show that its further increase can slow down growth while reducing income inequality these results obtain regardless of whether the increase in social security funding is financed by a tax increase or by cutting the public education budget we also find that the effects of increasing the level of public education expenditures or the overall size of the government budget holding the budget composition fixed are characterized by similar non monotonic growth inequality relationships

dynamic capacity management with substitution we examine a multiperiod capacity allocation model with upgrading there are multiple product types corresponding to multiple classes of demand and the firm purchases capacity of each product before the first period within each period after demand arrives products are allocated to customers customers who arrive to find that their product has been depleted can be upgraded by at most one level we show that the optimal allocation policy is a simple two step algorithm first use any available capacity to satisfy same class demand and then upgrade customers until capacity reaches a protection limit so that in the second step the higher level capacity is rationed we show that these results hold both when all capacity is salvaged at the end of the last demand period as well as when capacity can be replenished in the latter case an order up to policy is optimal for replenishment although finding the optimal protection limits is computationally intensive we describe bounds for the optimal protection limits that take little effort to compute and can be used to effectively solve large problems using these heuristics we examine numerically the relative value of strictly optimal capacity and dynamic rationing the value of perfect demand information and the impact of demand and economic parameters on the value of optimal substitution

stock rationing under service level constraints in a vertically integrated distribution system this paper addresses a rationing problem in a two level vertically integrated distribution system composed of one manufacturer and several retail points the motivating case developed in the vending machine sector and modeled as a newsvendor like problem is representative of many real settings where short term changes in demand can be substantial while capacity modification is not a viable option the paper provides an analytical discussion of the problem from two different standpoints a pure profit maximization perspective and a minimum service level perspective both subject to a product availability constraint that affects the service level the company can provide and the related expected profit by analyzing the lagrangean formulation of the problem we devise efficient computational procedures based on dichotomy search to find the optimal allotments to retailers maximizing the expected profit and ensuring a minimum service level then we extend the analysis to the evaluation of the highest service level that can be provided under a product availability constraint we identify conditions such that the proposed search procedures succeed in finding the optimal solutions as well as bounds for the search domains the proposed approach is legitimated under several demand distribution functions subject to a few commonly adopted restrictions that encompass many of the usually adopted continuous distributions finally the paper presents a three step decision making framework using the proposed procedures summarizing the decision paths the manufacturer might follow in order to optimize the allocation decision

aggregate and distributional effects of fair social security abstract in an overlapping generations economy with production endogenous labor supply a bequest motive and uncertain lifetime we show that a fair fully funded social security program reduces the aggregate levels of output employment capital and savings we determine the necessary and sufficient conditions for this social security program to increase the inequality of the income distribution the conclusions apply to the entire non stationary competitive equilibrium path taken by the economy following the introduction of social security

a note on the rationing policies of multiple demand classes with lost sales abstract we study inventory rationing in a system with multiple demand classes and lost sales it is assumed to have at most one outstanding order resulting in two periods in an order cycle separated by the time of order release we review the most related work by melchiors 2001 2003 ph d thesis university of aarhus int j prod econ 81 82 11 461 468 and find that the existing approximated and optimal policies are not easy to obtain due to computational complexity also as the rationing issue before order release is not well addressed in literature in this paper we prove the static rationing being optimal furthermore in such a system with two distinct periods the optimal rationing policy is a combination of a dynamic policy during the replenishment lead time and a static policy before order release in order to make the rationing policies to be readily used in practice we introduce two approximated methods for calculating the rationing levels in two periods respectively the results in particular the combination of static and dynamic rationing outperform the existing approximations in literature in addition the computation is obviously simplified due to the efficient algorithm of dynamic rationing and the explicit expressions of static rationing

distributional effects of public education in an economy with public pensions we study how the allocation of government expenditures between two major outlays education and pay as you go social security affects human capital distribution in an economy with heterogeneous agents we consider an overlapping generations economy where the government maintains both programs and allocates tax revenues to finance them in our model human capital is one of the factors of production it is itself produced as a combined result of public inputs and private inputs parents decisions to invest time and material resources in education of their children are motivated by altruism heterogeneous in its strength across the population which leads to heterogeneity of incomes we investigate the effect of an increase in public funding for education on the human capital distribution we show that in this framework contrary to some earlier results increased spending on public education may lead to higher inequality our results depend crucially on the interaction of education funding with the social security budget and on the elasticity of substitution in the learning technology

integrated capacity and inventory management with capacity acquisition lead times we model a make to stock production system that utilizes permanent and contingent capacity to meet non stationary stochastic demand where a constant lead time is associated with the acquisition of contingent capacity we determine the structure of the optimal solution concerning both the operational decisions of integrated inventory and flexible capacity management and the tactical decision of determining the optimal permanent capacity level furthermore we show that the inventory either before or after production the pipeline contingent capacity the contingent capacity to be ordered and the permanent capacity are economic substitutes we also show that the stochastic demand variable and the optimal contingent capacity acquisition decisions are economic complements finally we perform numerical experiments to evaluate the value of utilizing contingent capacity and to study the effects of capacity acquisition lead time providing useful managerial insights

a dynamic rationing policy for continuous review inventory systems stock rationing is an inventory policy that allows differential treatment of customer classes without using separate inventories in this paper we propose a dynamic rationing policy for continuous review inventory systems which utilizes the information on the status of the outstanding replenishment orders for both backordering and lost sales environments we conduct simulation studies to compare the performance of the dynamic policy with the static critical level and the common stock policies and quantify the gain obtained we propose two new bounds on the optimum dynamic rationing policy that enables us to tell how much of the potential gain the proposed dynamic policy realizes we discuss the conditions under which stock rationing both dynamic and static is beneficial and assess the value of the dynamic policy

is the budget deficit too large yes specifically we find that recent spending and taxing policies of the government if continued violate the government s intertemporal budget constraint as a result government spending must be reduced and or tax revenues must be increased these conclusions are based on tests of whether government spending and revenue are cointegrated in addition to examining real spending and revenue we also normalize these variables by real gnp and population for a growing economy these normalized measures are perhaps more pertinent we also test and find support for the hypothesis that deficits have become a problem only in recent years

pay as you go social security and the distribution of altruistic transfers this paper studies the impact of an unfunded social security system on the distribution of altruistic transfers in a framework where savings are due to both life cycle and random altruistic motivations we show that the effect of social security on the distribution of these transfers depends crucially on the strength of the bequest motive in explaining savings behaviour we measure this strength by the expected weight that individuals attach to the utility of future generations on the one hand if the bequest motive is strong then an increase in the social security tax raises the bequests left by altruistic parents on the other hand when the importance of altruism in motivating savings is sufficiently low the increase in the social security tax could result in a reduction of the bequests left by altruistic parents under some conditions on the attitude of individuals toward risk and on the relative returns associated with private saving and social security some implications concerning the transitional effects of introducing an unfunded social security scheme are also discussed

a make to stock system with multiple customer classes and batch ordering this paper examines the impact of customer order sizes on a make to stock system with multiple demand classes we first characterize the manufacturer s optimal production and rationing policies when the demand is nonunitary and lost if unsatisfied we also investigate the optimal policies of a backorder system with two demand classes and fixed order sizes through a numerical study we show the effects of batch orders on the manufacturer s inventory cost as well as on the benefit of optimal stock rationing it is shown that batch ordering may reduce the manufacturer s overall cost if carefully introduced in a first come first served fcfs system with the same effective demand rates the customers order sizes also have a strong impact on the benefit of optimal stock rationing

centralized admission and production control in a two stage supply chain with single component and customized products abstract this paper considers a two stage supply chain that a make to stock facility produces a single component in anticipation of future demand and a make to order facility produces customized products using components with the option of to accept or reject each customer order we address the problem of centralizing the admission and production control that maximizes the supply chain s profit subject to the system costs using a markov decision process model we characterize the structure of the optimal admission control and production policy and establish the monotonic impact of system parameters on the optimal policy two heuristics are presented and their performance is numerically compared to the optimal policy under different operating conditions of the system

on the limitations of government borrowing a framework for empiricaltesting this paper seeks to distinguish empirically between two views on the limitations of government borrowing according to one view nothing precludes the government from running a permanent budget deficit paying interest due on the growing debt load simply by issuing new debt an alternative perspective holds that creditors would be unwilling to purchase government debt unless the government made a credible commitment to balance its budget in present value terms we show that distinguishing between these possibilities is mathematically equivalent to testing whether a continuing currency inflation might be fueled by speculation alone or is instead driven solely by economic fundamentals empirical tests which have been developed for this economic question lead us to conclude that postwar u s deficits are largely consistent with the proposition that the government budget must be balanced in present value terms this abstract was borrowed from another version of this item

managing an assemble to order system with after sales market for components abstract in this paper we consider an assemble to order manufacturing system producing a single end product assembled from n components and serving an after sales market for individual components components are produced in a make to stock fashion one unit at a time on independent production facilities production times are exponentially distributed with finite production rates the components are stocked ahead of demand and therefore incur a holding cost rate per unit demand for the end product as well as for the individual components occurs continuously over time according to independent poisson streams in order to characterize the optimal production and inventory rationing policies we formulate such a problem using a markov decision process framework in particular we show that the optimal component production policy is a state dependent base stock policy we also show that the optimal component inventory rationing policy is a rationing policy with state dependent rationing levels recognizing that such a policy is generally not only difficult to obtain numerically but also is difficult to implement in practice we propose three heuristic policies that are easier to implement in practice we show that two of these heuristics are highly efficient compared to the optimal policy in particular we show that one of the two heuristics strikes a balance between high efficiency and computational effort and thus can be used as an effective substitute of the optimal policy

dynamic pricing through discounts for optimizing multiple class demand fulfillment in a multiple customer class model of demand fulfillment for a single item we consider the use of dynamic price discounts to encourage backlogging of demand for customer classes denied immediate service customers are assumed to arrive over several stages in a period and customer classes are distinguished by their contractual price and sensitivity to discounts through dynamic programming we determine the optimal discounts to offer assuming a linear model for the sensitivity of customers to such inducements we show that customers are served in class order and allocation of inventory to demand is determined by considering the current number of customers backlogged as well as the current inventory position through comparison to a naive supplier allocating inventory first come first served with no discounting we show that profits are primarily influenced by the allocation of capacity and the use of price discounts primarily benefits the second class customers overall fill rate heuristics for implementation of the solution in real time settings are given

a stock rationing policy in a s s controlled stochastic production system with 2 phase coxian processing times and lost sales abstract this paper analyzes a s s controlled stochastic production system with multi class demands and lost sales demands in each class are assumed to arrive according to a poisson process and the time required to process an item is assumed to follow a 2 phase coxian distribution for each class a stock rationing level is set when customers arrive if the inventory level is lower than the predetermined rationing level the demands are lost for future demands with higher priorities a behavior of the production system is modeled as a continuous time markov chain and an efficient algorithm to calculate the steady state probability distribution of the system is proposed the average operating cost under the stock rationing policy is compared with the one without stock rationing numerical experiment shows that the proposed stock rationing policy reduces the average operating cost significantly depending on the system parameters

long run limits on the us federal debt abstract this letter distinguishes three nested long run constraints on the u s federal debt tests and rejects the strongest of the three and illustrates how hazardous it is to base inference regarding unit roots on misspecified test regressions

admission and inventory control of a single component make to order production system with replenishment setup cost and lead time abstract we consider the admission control and inventory management problems of a single component make to order production system components are purchased from suppliers in batches of fixed size subject to stochastic lead times and setup costs a control policy specifies when a batch of components is purchased and whether the demand for each mto production is accepted upon arrival we formulate the problem as a markov decision process mdp model and characterize the structure of optimal admission control and inventory replenishment policies we show that a state dependent base stock policy is optimal for the inventory replenishment although the mdp value function is not necessarily convex we also show that the optimal admission control can be identified as a lattice dependent policy a sensitivity analysis is conducted to show how the optimal policy changes as a function of the system parameters to effectively coordinate admission and inventory control decisions we propose simple implementable and yet effective heuristic policies our extensive numerical results suggest that the proposed heuristics can greatly help firms to effectively coordinate their admission and inventory control activities

integrated production and allocation policies with one direct shipping option we consider a single period inventory problem in which a supplier faces stochastic demands and customer specific waiting costs from multiple customers the objective is to develop integrated production allocation and distribution policies so that the total production and customer waiting costs are minimized we present an optimal policy for the two customer problem and derive a heuristic for a general problem based on the structural results of the two customer case we show numerically that the heuristic performs very well with error bounds of less than 2 on average while typical approximations may lead to significant sub optimality

revenue management approach to stochastic capacity allocation problem abstract to formulate stochastic capacity allocation problems in a manufacturing system the concept and techniques of revenue management is applied in this research it is assumed the production capacity is stochastic and hence its exact size cannot be forecasted in advance at the time of planning there are two classes of frequent and occasional customers demanding this capacity the price rate as well as the penalty for order cancellation caused by overbooking is different for each class the model is developed mathematically and we propose an analytical solution method the properties of the optimal solution as well as the behavior of objective function are also analyzed the objective function is not concave in general however we prove it is a unimodal function and by taking advantage of this property the optimal solution is determined

reduce shortage with self reservation policy for a manufacturer paying both fixed and variable stockout expenditure this study considers a single item make to stock system with continuous time production and inventory controls to meet bulk demand with an exponential inter arrival time a key issue in this system is the non convex shortage cost consisting of fixed and variable expenditures when the demand is not fully satisfied we propose a self reservation policy by building a markov decision process to minimize the overall cost we find that the optimal production control is still a base stock policy but the structure of the optimal self reservation policy is very complicated however if the effective outstanding variable shortage cost is sufficiently large the optimal self reservation policy has an easy form of reserve all or nothing our numerical examples indicate the optimal policy may reduce the total average cost by 47 on average

capacity rationing decision procedures with order profit as a continuous random variable abstract when expected demand is more than available capacity a make to order manufacturer should take the more profitable orders and reject the less profitable orders in order to better allocate its limited capacity and maximize its profit however various orders will arrive at different times in the future so the manufacturer cannot look at all the order inquiries at the same time and choose the most profitable ones when an order inquiry arrives the manufacturer must promptly determine without knowing exactly what the future orders might be whether to accept the order or to reject the order thus reserving the capacity for future more profitable orders this study focuses on such an order selection decision problem under the following assumptions 1 the arrival of future customer orders is a poisson process 2 the capacity requirement of a future customer order is a continuous random variable and 3 the profit per unit capacity used by an order is also a continuous random variable under the stochastic problem assumptions this study investigates two decision procedures that determine whether to accept or to reject an order inquiry based on the available information including 1 current available manufacturing capacity 2 capacity requirement by the order and 3 the profit per unit capacity of the order one procedure is called static probability capacity rationing decision procedure spcr the other one is called dynamic stochastic capacity rationing decision procedure dscr simulation experiments are conducted to validate the proposed procedures an optimal solution method that uses 0 1 knapsack problem formulation to obtain the decisions with perfect information is used to measure the effectiveness of the proposed procedures the results show that the approach utilizing dscr outperforms other approaches by providing the highest profit and is also very robust under various problem conditions

multi class dynamic inventory rationing with stochastic demands and backordering dynamic inventory rationing is considered for systems with multiple demand classes stationary stochastic demands and backordering in the literature dynamic programming has been often applied to address this type of problems however due to the curse of dimensionality computation is a critical challenge for dynamic programming in this paper an innovative two step approach is proposed based on an idea similar to the certainty equivalence principle first the deterministic inventory rationing problem is studied where the future demands are set to be the expectation of the stochastic demand processes the important properties obtained from solving the problem with the kkt conditions are then used to develop effective dynamic rationing policies for stochastic demands which gives closed form expressions for dynamic rationing thresholds these expressions are easy to calculate and are applicable to any number of demand classes numerical results show that the expressions are close to and provide a lower bound for the optimal dynamic thresholds they also shed light on important managerial insights for example the relation between different parameters and the rationing thresholds

uncertainty and optimal social security systems this paper examines the annuity aspect of social security within the framework of an overlapping generations model the duration of life is assumed to be uncertain under a fully funded system demand for social security is determined by each generation so as to maximize expected lifetime utility taking into account the welfare of future generations under a pay as you go system with intergenerational transfers demand for retirement benefits by the working population takes into account taxes paid by descendants it is shown that the two modes of finance are equivalent in terms of all real aggregates effects of changes in expected lifetime and in the birth rate are analyzed starting at the optimal level a compulsory balanced increase in social security taxes and benefits is shown to increase short run savings

welfare and comparative statics implications of fair social security a steady state analysis abstract this paper examines the steady state welfare and comparative statics implications of fair social security in an overlapping generations model with uncertain lifetime the model is designed to capture the effects of lifetime uncertainty extending over the individual s entire lifespan the effects of intentional and unintentional bequests and the effects of the earning profile he shows that the welfare effects depend on the size of the benefits and the structure of the social security tax in particular even fair social security may have negative welfare implications if the underlying tax structure is ill designed some comparative statics implications are analyzed

design and evaluation of a dynamic capacity apportionment procedure abstract deploying a decision theory based approach we develop a heuristic for short term constrained capacity allocation to multiple product classes in make to order manufacturing attempting to maximize profit by discriminating between product classes efficacy of the heuristic is evaluated by comparing its performance to a base case and an upper bound under a wide variety of operational conditions such as variations in profit attractiveness capacity tightness customer order size structure customer order rate structure and demand coefficient of variation considering three different scenarios of time variant order rate of products the results indicate that the heuristic is effective in obtaining increased profit when capacity is very tight and products are well differentiated on average it yields an increase of 9 38 in total profit with a concomitant decrease of 0 85 in capacity utilization the results of this study serve to highlight the value of proactively seeking to differentiate products particularly when demand exceeds capacity

technical note optimal control of an assembly system with multiple stages and multiple demand classes we consider an assembly system with multiple stages multiple items and multiple customer classes the system consists of m production facilities each producing a different item items are produced in variable batch sizes one batch at a time with exponentially distributed batch production times demand from each class takes place continuously over time according to a compound poisson process at each decision epoch we must determine whether or not to produce an item and should demand from a particular class arise whether or not to satisfy it from existing inventory if any is available we formulate the problem as a markov decision process and use it to characterize the structure of the optimal policy in contrast to systems with exogenous and deterministic production lead times we show that the optimal production policy for each item is a state dependent base stock policy with the base stock level nonincreasing in the inventory level of items that are downstream and nondecreasing in the inventory level of all other items for inventory allocation we show that the optimal policy is a multilevel state dependent rationing policy with the rationing level for each demand class nonincreasing in the inventory level of all nonend items we also show how the optimal control problem can be reformulated in terms of echelon inventory and how the essential features of the optimal policy can be reinterpreted in terms of echelon inventory

managing an available to promise assembly system with dynamic short term pseudo order forecast we study an order promising problem in a multiclass available to promise atp assembly system in the presence of pseudo orders a pseudo order refers to a tentative customer order whose attributes such as the likelihood of an actual order order quantity and confirmation timing can change dynamically over time a unit demand from any class is assembled from one manufactured unit and one inventory unit where the manufactured unit takes one unit of capacity and needs a single period to produce an accepted order must be filled before a positive delivery lead time the underlying order acceptance decisions involve trade offs between committing resources production capacity and component inventory to low reward firm orders and reserving resources for high reward orders we develop a markov chain model that captures the key characteristics of pseudo orders including demand lumpiness nonstationarity and volatility we then formulate a stochastic dynamic program for the atp assembly system that embeds the markov chain model as a short term forecast for pseudo orders we show that the optimal order acceptance policy is characterized by class prioritization resource imbalance based rationing and capacity inventory demand matching in particular the rationing level for each class is determined by a critical value that depends on the resource imbalance level defined as the net difference between the production capacity and component inventory levels extensive numerical tests underscore the importance of the key properties of the optimal policy and provide operational and managerial insights on the value of the short term demand forecast and the robustness of the optimal policy this paper was accepted by martin lariviere operations management

stock rationing in an m ek 1 make to stock queue this paper considers the stock rationing problem of a single item make to stock production system with several demand classes and lost sales when demand is poisson and processing time has an erlang distribution we show that a single state variable called work storage level can be employed to completely capture the information regarding inventory level and the status of current production the optimal rationing policy can be characterized by a sequence of monotone critical work storage levels for each demand class there exists a work storage level at or below which it is optimal to start rejecting the demand of this class in anticipation of future arrival of higher priority demands the optimal production policy can also be characterized by a critical work storage level our numerical examples indicate that a critical stock level policy which ignores information on the status of current production performs very well

education social security and growth abstract we study the role of government s allocation of tax revenues between two outlays public investment in education a transfer to the young generation and social security benefits to the older generation in an overlapping generations economy with pay as you go social security and altruistically motivated transfers from parents to children we analyze how the allocation of the tax revenues between the two outlays affects growth and welfare in competitive equilibria a we obtain comparative dynamics results for nonstationary equilibria subject to a change in the allocation profile b for stationary equilibria we show that for a given allocation profile of the tax revenues educational subsidies can either increase the growth rate or decrease it depending on the parameters of the model preferences production function and the tax rate c if government seeks to allocate funds in a way that maximizes the growth rate we demonstrate that under some plausible conditions it is not optimal to maintain pay as you go social security however if parents preferences combine strong concern for their retirement with significant degree of altruism towards their children then pay as you go social security system does enhance growth and welfare

restricted time remembering policies for the inventory rationing problem abstract we analyse an s q inventory model with unit poisson demand several demand classes and lost sales when dealing with different demand classes the usual approach is to control the inventory by critical levels at which stock is reserved for demand of higher priority we focus on time remembering policies where the critical levels are allowed to depend on the time since the actual outstanding order if any was issued in particular we introduce a new class of policies called restricted time remembering rtr policies we divide the lead time in m intervals of time and restrict the critical levels of the rtr policy to be constant over each interval of time this policy is much easier to implement than the optimal rationing policy where the critical levels can change continuously over time and in a numerical study we show that the performance of the rtr policy is close to that of the optimal policy even when the number of intervals is 2 or 3

optimal production and rationing policy of two stage tandem production system abstract the rationing literature has been so far oblivious to the fact that sellable items may not only be finished products but also intermediate products to manufacture subsequent sellable products we address this gap by considering an inventory rationing problem in a two product tandem make to stock production inventory system bulk demand arrives to a partial batch production system with exponentially distributed production time for each batch the management has to decide whether to run or stop production and whether the various classes of demand for both products intermediate product ip and finished product or end product ep have to be satisfied from available inventory or not in which case demand is lost in order to maximize the firm s expected profit we present the corresponding dynamic programming formulation and characterize the optimal policy the resulting policy depends on dynamic switching curves which define a thresholds to continue or discontinue production and b thresholds to satisfy or turn down incoming orders we identify the key value drivers and compare various heuristic policies through extensive numerical analyses

optimal policies for inventory systems with priority demand classes we consider a periodic review inventory system with two priority demand classes one deterministic and the other stochastic the deterministic demand must be met immediately in each period however the units of stochastic demand that are not satisfied during the period when demand occurs are treated as lost sales at each decision epoch one has to decide not only whether an order should be placed and how much to order but also how much demand to fill from the stochastic source the firm has the option to ration inventory to the stochastic source i e not satisfy all customer demand even though there is inventory in the system we first characterize the structure of the optimal policy we show that in general the optimal order quantity and rationing policy are state dependent and do not have a simple structure we then propose a simple policy called s k s policy wheres ands ordering policy determine when and how much to order whilek rationing policy specifies how much of the stochastic demand to satisfy we report the results of a numerical study which shows that this simple policy works extremely well and is very easy to compute

integrating resource and production decisions in a simple multi stage assembly system we consider a simple multi stage assembly system with stationary stochastic demand for a single final product that is made to stock the assembly tasks are performed by human resources this workforce consists of two parts regular workforce with a long term contract and temporary workforce that are contracted based on the actual demand contracting resources early is always cheaper than contracting later when we separate resource and production decisions we can first determine order up to levels and production decisions in a standard way and afterwards find the best mix of regular and temporary workforce next to this decoupled approach we present an integrated approach where these decisions influence each other in a set of examples we show that the integrated approach can be very beneficial

the role of inventory in delivery time competition the paper operationalizes the notion of shortage cost by considering the behavior of customers and competing firms and examines the role of inventory in response time competition we start with a single firm production control model in which customers are characterized by their preferences of price quality and delivery time the optimal production inventory policy and the optimal choice between make to order and make to stock operations are determined in simple newsboy like formulas the basic model is then extended to an n firm market game in which firms compete for orders from the aspect of early delivery one could think of this setting as an oligopoly racing market the analysis shows that competition can breed a demand for produce to stock just as other economic phenomena such as economies of scale uncertainty or seasonality can induce make to stock and that delivery time competition increases the buyer s welfare while decreasing the producer s welfare

a threshold inventory rationing policy for service differentiated demand classes motivated by a study of the logistics systems used to manage consumable service parts for the u s military we consider a static threshold based rationing policy that is useful when pooling inventory across two demand classes characterized by different arrival rates and shortage stockout and delay costs the scheme operates as a q r policy with the following feature demands from both classes are filled on a first come first serve basis as long as on hand inventory lies above a threshold levelk once on hand inventory falls below this level low priority i e low shortage cost demand is backordered while high priority demand continues to be filled we analyze this static policy first under the assumption that backorders are filled according to a special threshold clearing mechanism structural results for the key performance measures are established to enable an efficient solution algorithm for computing stock control and rationing parameters i e q r andk numerical results confirm that the solution under this special threshold clearing mechanism closely approximates that of the priority clearing policy we next highlight conditions where our policy offers significant savings over traditional round up and separate stock policies encountered in the military and elsewhere finally we develop a lower bound on the cost of the optimal rationing policy numerical results show that the performance gap between our static threshold policy and the optimal policy is small in environments typical of the military and high technology industries

the effect of commonality on safety stock in a simple inventory model we examine the effects of component commonality on optimal safety stock levels in a two product two level inventory model the criterion is to minimize system safety stock subject to a service level constraint although our model is specialized its analysis provides insights not available in other multilevel inventory models

component rationing for available to promise scheduling in configure to order systems abstract we address the problem of rationing common components among multiple products in a configure to order system with order configuration uncertainty the objective of this problem is to maximize expected revenue by implementing a threshold rationing policy under this policy a product is available to promise if fulfilling the order for the product will not cause the inventory of any one of its required components to fall below the component s threshold level for that product the problem is modeled as a two stage stochastic integer program and solved using the sample average approximation approach a heuristic is developed to generate good feasible solutions and lower bound estimates using industry data we examine the benefit of component rationing as compared to a first come first served policy and show that this benefit is correlated to the average revenue per product and the variability in the revenue across products whose components are constrained

current and anticipated deficits interest rates and economic activity abstract there is a widespread feeling that current deficits in europe and the u s may hurt rather than help the recovery this paper examines some of the issues involved through a sequence of three models the first model focuses on sustainability and characterizes its determinants it suggests that the issue of sustainability may indeed be relevant in some countries the second model focuses on the effects of fiscal policy on real interest rates and in particular on the relative importance of the level of deficits and the level of debt in determining interest rates the third model focuses on the effects of fiscal policy on the speed of the recovery it shows how a sharply increasing fiscal expansion might be initially contractionary rather than expansionary

uncertain lifetimes and the welfare enhancing properties of annuity markets and social security this paper explores the implications of social security programs and annuity markets through which agents who are characterized by different distributions of length of lifetime share deathrelated risks when annuity markets operate a non discriminatory social security program affects only the intragenerational allocation of resources in the absence of private information regarding individual survival probabilities such a program will lead to a non optimal intragenerational allocation of resources however the presence of adverse selection considerations gives rise to a pareto improving role for a mandatory non discriminatory social security program

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 rationing in a make to stock production system with several demand classes and lost sales this paper considers the stock rationing problem of a single item make to stock production system with several demand classes and lost sales for the case of poisson demands and exponential production times we show that the optimal policy can be characterized by a sequence of monotone stock rationing levels for each demand class there exists a stock rationing level at or below which it is optimal to start rejecting the demand of this class in anticipation of future arrival of higher priority demands a simple queueing model is analyzed to compute the operating cost of a rationing policy in a numerical study we compare the optimal rationing policy with a first come first served policy to investigate the benefit of stock rationing under different operating conditions of the system

a single product inventory model for multiple demand classes we consider a single product inventory system that serves multiple demand classes which differ in their shortage costs or service level requirements we assume a critical level control policy and a backorder clearing mechanism in which we treat a backorder for a lower priority class equivalent to a reserve stock shortfall for the higher priority class we show the equivalence between this inventory system and a serial inventory system based on this equivalence we develop a model for cost evaluation and optimization under the assumptions of poisson demand deterministic replenishment lead time and a continuous review q r policy with rationing we propose a computationally efficient heuristic and develop a bound on its performance we provide a numerical experiment to show the effectiveness of the heuristic and the value from a rationing policy finally we describe how to extend the model to permit service times and how to extend the model to a multi echelon setting

dynamic inventory rationing for systems with multiple demand classes and general demand processes we consider the dynamic rationing problem for inventory systems with multiple demand classes and general demand processes we assume that backorders are allowed our aim is to find the threshold values for this dynamic rationing policy for single period systems dynamic critical level policy is developed and the detailed cost approximation subject to this policy is derived for multiperiod systems a dynamic rationing policy with periodic review is proposed the numerical study shows that our dynamic critical level policies are close to being optimal for various parameter settings

a brownian approximation of a production inventory system with a manufacturer that subcontracts this paper considers a production inventory problem where a manufacturer fulfills stochastic stationary demand for a single product from a finished goods inventory the inventory can be replenished by two production resources in house production and a subcontractor which both have finite capacity we construct a brownian approximation of the optimal control problem assuming that the manufacturer uses a dual base stock policy to control replenishment from the two sources and that her objective is to minimize average cost a closed form expression is obtained for one optimal base stock policy and an analytical expression is derived from which the other optimal base stock can be computed numerically we show conditions under which the objective is convex in capacity and the unique globally optimal capacity can be computed numerically we thus provide a tractable approximation to the two source problem which is generally intractable we demonstrate the accuracy of this approximation for an m m 1 model we also draw managerial insight from the brownian optimal base stock results into how the optimal base stock policies control the inventory distribution and under what conditions the contingent source is used to build inventory or to resolve backorders

a note on the aggregate effects of social security abstract in an overlapping generations economy of karni and zilcha 1989 a fully funded social security program is shown to reduce the aggregate levels of output consumption employment and capital when the social security and the existing private annuities are equally unfair actuarially

inventory policies for systems with stochastic and deterministic demand we consider a periodic review inventory system with demand arriving simultaneously from a deterministic source and a random source the deterministic demand has to be satisfied immediately and the stochastic demand can be backordered assuming that the stochastic demand is never backlogged if there is stock in the system we prove that a modified s s policy is optimal under general conditions if there is a setup cost if there is a smoothing cost instead of the setup cost we observe that the problem corresponds to a standard model with one source of demand

production and inventory control of a single product assemble to order system with multiple customer classes we consider the optimal production and inventory control of an assemble to order system with m components one end product and n customer classes a control policy specifies when to produce each component and whenever an order is placed whether or not to satisfy it from on hand inventory we formulate the problem as a markov decision process and characterize the structure of an optimal policy we show that a base stock production policy is optimal but the base stock level for each component is dynamic and depends on the inventory level of all other components more specifically it is nondecreasing we show that the optimal inventory allocation for each component is a rationing policy with different rationing levels for different demand classes the rationing levels for each component are dynamic and also nondecreasing in the inventory level of all other components we compare the performance of the optimal policy to heuristic policies including the commonly used base stock policy with fixed base stock levels and find them to perform surprisingly well especially for systems with lost sales

pay as you go or funded social security a general equilibrium comparison abstract this paper demonstrates that the analysis of fiscal sustainability of social security must include the education funding dimension of public policy which affects the productivity of future workers this fact is true under both social security regimes pay as you go payg and fully funded ff we consider an olg economy where the government in addition to running social security also funds education via a dedicated tax the education tax rates are chosen in each period by a majoritarian rule we demonstrate contrary to conjectures in the literature that the ff social security system produces political support for a relatively higher compared to payg education funding and hence generates higher rates of human capital accumulation physical capital accumulation and economic growth furthermore it also results in a comparatively lower degree of income inequality

reservation and allocation policies for influenza vaccines abstract this research investigates the impact of alternative allocation mechanisms that can be employed in the context of vaccine inventory rationing available vaccine inventory can be allocated to arrivals from high priority target groups such as healthcare professionals and low priority non target groups demand classes using partitioned allocation pa standard nesting sn and theft nesting tn in any one of the mechanisms a part of the available inventory is reserved for the exclusive use of the high priority demand class they differ however in how the unreserved portion of the inventory is utilized under pa demand from the high low priority class consumes only the reserved unreserved quantity under sn demand from the high priority class first consumes the reserved quantity once and if this quantity is exhausted high priority demand competes with low priority demand for the remaining inventory under tn the sequence of allocation is reversed both demand classes first compete for the unreserved inventory once this portion of inventory is exhausted high priority demand is fulfilled from the reserved inventory and low priority demand is rejected we develop service level probability of fulfilling the entire demand and fill rate fraction of demand fulfilled expressions for all three allocation mechanisms based on these expressions numerical analyses are conducted to illustrate which allocation mechanism a health planner should choose depending on the availability of vaccines and how the health planner should set the reserved quantity for the high priority class we observe that 1 there exist certain conditions under which one of the allocation mechanisms outperforms the others and 2 this effect is determined by the decision maker s choice of the performance measure

precautionary saving and accidental bequests this paper presents a simple general equilibrium model of precautionary saving and accidental bequests this model is used to analyze the implications of individual lifetime uncertainty for aggregate consumption and capital accumulation a precautionary demand for saving arises because an individual consumer does not know in advance the date at which he will die and he wants to avoid low levels of consumption in the event that he lives longer than expected an implication of this precautionary saving is that when death does occur the consumer is generally holding some wealth which is then passed on to his heirs in the form of an accidental bequest even if all consumers have the same ex ante mortality probabilities there will be some intracohort variation in the date of death consequently there will be a nondegenerate distribution of bequests left by consumers in a cohort this nondegenerate distribution of bequests left by one generation induces variation in the distributions of wealth consumption and bequests of subsequent generations the importance of bequests in aggregate saving has been established by laurence kotlikoff and lawrence summers 1981 who reported that 80 percent of u s household wealth is inherited wealth one interpretation of this finding is that the simple life cycle model without bequest motives is an inadequate description of saving behavior in the united states but the model i present demonstrates that accidental bequests by selfish consumers can account for a potentially sizeable fraction of aggregate wealth although some part of bequests especially by the wealthy undoubtedly results from an explicit bequest motive accidental bequests also play a role in the intergenerational transfer of wealth as well as in the intragenerational variation in wealth in order to focus on the role of accidental bequests i purposely exclude a bequest motive from the specification of the utility function the effects of lifetime uncertainty on individual consumption behavior were first examined formally in a seminal paper by menachem yaari 1965 yaari s model provided the basic framework for virtually all subsequent work on uncertain lifetimes including well known papers by nils hakansson 1969 stanley fischer 1973 robert barro and james friedman 1977 david levhari and leonard mirman 1977 and kotlikoff and avia spivak 1981 however all of these papers focused on the consumption decision of an individual and ignored the effect of accidental bequests on the behavior of the recipients of these accidental bequests 2 as will be shown at various points in this paper changes in the economic environment can have effects on aggregate behavior which differ sharply from the effects on individual behavior because of the endogenous adjustment of bequests the effects of department of economics harvard university cambridge ma 02138 this paper is a revised version of bequests and social security with uncertain lifetimes nber working paper no 1372 june 1984 i thank olivier blanchard john burbidge christopher cavanagh robert clower stanley fischer benjamin friedman elhanan helpman mervyn king nobuhiro kiyotaki laurence kotlikoff robert mcdonald james pesando julio rotemberg lawrence summers lars svensson mark watson and jeffrey wolcowitz for valuable conversations and correspondence i also thank the participants in seminars at boston university columbia university cornell university federal reserve board harvard university university of iowa mit university of minnesota university of montreal national bureau of economic research north carolina state university the wharton school and yale university and two anonymous referees for their helpful comments i also thank the national science foundation for financial support 1 in the presence of perfect annuity and life insurance markets there may or may not be bequests depending on the presence or absence of a bequest motive but there would be no accidental bequests 2 kotlikoff and spivak focus on the role of the family in providing an incomplete annuities market but stop short of a full scale overlapping generations model in which the distribution of bequests is determined endogenously

persistent deficits and the market value of government debt summary this paper investigates whether postwar canadian public financial policy satisfies a borrowing constraint direct tests of the present value relation suggested by this constraint shed light on the sustainability of current policy we examine monthly data on canadian federal government finances using tests for cointegration the finding is that the joint behaviour of real debt and real surpluses is inconsistent with intertemporal budget balance for the government one interpretation of this finding is that the government is systematically paying real returns to bondholders by issuing further debt alternatively bondholders may expect the government to finance future interest payments from a source other than primary surpluses e g the sale of physical assets much empirical macroeconomics is concerned with the effects of public financial policies numerous studies have examined whether such policies affect interest rates inflation or national income and its components these examinations raise the question of the efficacy of government budget deficits they generally assume that a borrowing constraint holds in the public finances some positive theories of public debt creation also make this assumption examples include barro s 1979 history of us federal deficits and sargent s 1986 rationalizations of recent us budgetary policy lucas and stokey s 1983 discussion of optimal taxation also involves this assumption hansen roberds and sargent 1987 outline the testable implications of present value budget balance and hamilton and flavin 1986 investigate the feasibility of recurring deficits by directly testing the us federal government s borrowing constraint such tests seem natural given both the recent boom is testing more complicated first order difference equations in macroeconomics and the widespread discussion of current deficits this paper tests the present value borrowing constraint using recently constructed data on the market value of outstanding canadian federal government debt we use monthly rather than annual as in hamilton and flavin data and conduct tests of univariate integration and of bivariate cointegration to investigate the joint time series properties of debt and deficits one finding is that real debt and real surpluses are integrated processes evidence of their cointegration is mixed and point estimates of the cointegrating vector suggest that the expected real rate of return on debt is negative moreover the surplus measured to include interest payments as government spending is nonstationary these findings are inconsistent

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

dynamic inventory rationing with mixed backorders and lost sales abstract customers may react differently when stockouts occur in this paper we investigate the rationing policy for an inventory system with a mixture of demand classes of backorder type and lost sales type since the penalty cost of backorders varies with time the priorities of demand classes also alter with time this totally changes the problem structure compared with the classic rationing models a dynamic rationing policy is studied in this paper by considering the dynamics of demand priorities a markov decision model is developed to obtain the optimal dynamic rationing levels for multiple demand classes the results indicate that between the priority switching points rationing levels often exhibit different patterns for lost sales demand classes the rationing levels always decrease as the remaining time approaches to zero for backorder demand classes the rationing levels increase in some parts due to declining of the priorities the rationing levels of all demand classes finally decline to zero to reduce the inventory holding cost the application of dynamic rationing is further extended from a single period model to a multi period s t model where unit cost has to be included the optimal ordering policy is proved to be a myopic base stock policy and the dynamic rationing policy in the single period model can still be applied with modified time independent penalty costs for lost sales classes to overcome the computational complexity a heuristic dynamic rationing policy is introduced due to its good outcome implementing such a heuristic dynamic rationing policy can be a practical solution for inventory system with mixed backorders and lost sales in order to enhance the system performance

component commonality with service level requirements this paper extends recent results of baker et al baker k r m j magazine h l w nuttle 1986 the effect of commonality on safety stocks in a simple inventory model management sci 32 982 988 in understanding the impact of component commonality on stocking levels under service level constraints a model is formulated for an arbitrary number of products with general joint demand distribution the results obtained are not all intuitive while utilizing commonality is beneficial nothing general can be said about the resulting change in the components stock levels when the cost structure is of a particular simple form though some interesting general patterns do emerge we also discuss the case of using a service level measure where rationing of common components might be required and characterize the implied rationing rule

inventory sharing and rationing in decentralized dealer networks an increasing number of manufacturers have started to pursue a strategy that promotes inventory sharing among the dealers in their distribution network in this paper we analyze a decentralized dealer network in which each independent dealer is given the flexibility to share his inventory we model inventory sharing as a multiple demand classes problem in which each dealer faces his own customer demand with high priority and inventory sharing requests from other dealers with low priority assuming that each dealer uses a base stock and threshold rationing policy for his inventory stocking and inventory sharing decisions we explicitly model the interactions between the dealers through inventory sharing and obtain aclosed form cost function for each dealer based on the steady state distribution of the inventory levels at the two dealers we then provide a detailed supermodularity analysis of the inventory sharing and inventory rationing game in which each dealer has a two dimensional strategy set stocking level and rationing level we show that the full sharing game in which dealers precommit to sharing all of their on hand inventory and the fixed sharing level game in which dealers precommit to sharing a portion of their on hand inventory are supermodular and thus a pure strategy nash equilibrium is guaranteed to exist for the rationing game in which dealers precommit to their stocking levels we show that there exists a dominant strategy equilibrium on the dealers sharing rationing levels finally a comprehensive computational study is conducted to highlight the impact of the manufacturer s incentives subsidies and or transshipment fees on the dealers sharing behavior

using imperfect advance demand information in ordering and rationing decisions in this paper we consider an inventory problem with two demand classes having different priorities the appropriate policy of rationing the available stock i e reserving some stock for meeting prospective future demand of preferred customers at the expense of deliberately losing some of the currently materialized demand of lower demand class es relies on the estimation of the future demand utilizing current signals on future demand which we refer to as imperfect advance demand information adi decreases uncertainty on future demand and may help to make better decisions on when to start rejecting lower class demand we develop a model that incorporates imperfect adi with inventory ordering replenishment decision and rationing available stock in a two period setting we show some structural properties solve the rationing problem and propose solution methods based on monte carlo simulation for the ordering problem we conduct numerical tests to measure the impact of system parameters on the expected value of imperfect adi and provide useful managerial insights

dynamic inventory rationing strategies for inventory systems with two demand classes poisson demand and backordering we study inventory systems with two demand classes critical and non critical poisson demand and backordering we analyze dynamic rationing strategies where the number of items reserved for critical demand depends on the remaining time until the next order arrives different from results in the literature we do not discretize demand but derive a set of formulae that determine the optimal rationing level for any possible value of the remaining time moreover we show that the cost parameters can be captured in a single relevant dimension which allows us to present the optimal rationing levels in charts and lookup tables that are easy to implement numerical examples illustrate that the optimal dynamic rationing strategy outperforms all static strategies with fixed rationing levels

influence of dependency between demands and returns in a reverse logistics system we consider two reverse logistics systems where returned products are as good as new for the first system the product return flow is independent of the demand flow we prove that the optimal policy is of base stock type and we establish monotonicity results for the optimal base stock levels with respect to the system parameters arrival rate production rate return rate production cost lost sale cost return cost and holding cost we also provide an efficient algorithm to compute the optimal base stock level for the second system demands and returns are strongly correlated a satisfied demand induces a product return after a stochastic return lead time with a certain probability when the return lead time is null we extend the results obtained for the first system when the return lead time is positive the optimal control problem is more complex and we do not prove that the optimal policy is of base stock type however we provide a framework to analyse base stock policies finally we carry out a numerical study on many scenarios to investigate the impact of ignoring dependency between demands and returns we observe that ignoring this dependency yields to non negligible cost increase