a comparison of average and discounted cost models for the dynamic lot size inventory problem abstract it is a common practice in the inventory literature to use average cost models as approximations to the theoretically correct discounted cost models an average cost model minimizes the average undiscounted cost per period while a discounted cost model minimizes the total discounted cost over the problem horizon this paper attempts to answer an important question how good are the results the total discounted costs for the average cost models compared to those for the discounted cost models this question has been conclusively answered for the simplest inventory model where the demand rate and other parameters are assumed to remain constant in time this paper addresses this issue for the first time for the case where demand rates are allowed to be nonstationary in time a discounted cost model has been developed in the paper to carry out this comparison it is shown that a simple dynamic programming algorithm can be used to find optimal order policies for the discounted cost model the effect of the varying interest rates and other parameters on the relative performance of the average cost model has been studied by developing an insightful analysis and also by doing a computational study the results show that while the average cost model can cost as much as about 26 more than the discounted cost model in extreme cases this increase is not significant for the parameter values in the range of the common interest

efficiency and equilibria in complementary teams abstract this paper considers a team or partnership where the partners effort levels enter as strict complements in the production function the existence of a linear budget balancing sharing mechanism is demonstrated which implements the team s efficient outcome as a nash equilibrium this result is in contrast to a result derived in holmstrom 1982

real rigidities and the non neutrality of money rigidities in real prices are not sufficient to create rigidities in nominal prices and real effects of nominal shocks and by themselves small frictions in nominal adjustment such as costs of changing prices create only small non neutralities but this paper shows that substantial nominal rigidity can arise from a combination of real rigidities and small nominal frictions the paper shows the connection between real and nominal rigidity given the presence of nominal frictions both in general and for two specific sources of real rigidity one arising from goods market imperfections and the other from labour market imperfections

single period multiproduct inventory models with substitution we study a single period multiproduct inventory problem with substitution and proportional costs and revenues we consider n products and n demand classes with full downward substitution i e excess demand for class i can be satisfied using product j for i j we first discuss a two stage profit maximization formulation for the multiproduct substitution problem we show that a greedy allocation policy is optimal we use this to write the expected profits and its first partials explicitly this in turn enables us to prove additional properties of the profit function and several interesting properties of the optimal solution in a limited computational study using two products we illustrate the benefits of solving for the optimal quantities when substitution is considered at the ordering stage over similar computations without considering substitution while ordering specifically we show that the benefits are higher with high demand variability low substitution cost low profit margins or low price to cost ratio high salvage values and similarity of products in terms of prices and costs

on the optimality of joint ordering policies in a multi product dynamic lot size model with individual and joint set up costs abstract this paper considers a deterministic dynamic multi product lot size model with individual and joint set up costs the computational effort required by dynamic programming algorithms for finding simultaneously optimal multi product ordering policies particularly increases exponentially with the number of products it is possible to crack up this exponential dependence of computational requirements on the number of products if joint ordering of several products is optimal it is the aim of the present paper to give conditions for the optimality of joint ordering policies particular attention is given to the usefulness of joint ordering results in simplifying computations

new keynesianism and aggregate economic activity this paper addresses various attempts by so called new keynesians writing mainly in the 1980s and 1990s to strengthen the analytical basis in particular the microeconomic foundations of these assertions what exactly have then the new keynesians accomplished and how should their contributions be valued in the relation to other recent contributions to macroeconomics this abstract was borrowed from another version of this item

strong planning and forecast horizons for a model with simultaneous price and production decisions abstract in this paper we have solved a general inventory model with simultaneous price and production decisions both linear and non linear strictly convex production cost cases are treated upper and lower bounds are imposed on state as well as control variables the problem is solved by using the lagrangian form of the maximum principle strong planning and strong forecast horizons are obtained these arise when the state variable reaches its upper or lower bound the existence of these horizons permits the decomposition of the whole problem into a set of smaller problems which can be solved separately and their solutions put together to form a complete solution to the problem finally we derive a forward branch and bound algorithm to solve the problem the algorithm is illustrated with a simple example

a dynamic marketing operations interface model of new product updates abstract two critical success factors for nearly any firm are the introduction of new products and the integration of the marketing and operations functions within the business enterprise the series of products being considered are associated with sequential non disruptive innovations in technology but disruptive in fashion the study presents a model that integrates and builds upon the popular dynamic bass model for new product diffusion in marketing and the wagner and whitin dynamic lot sizing model a seminal model in operations management the end result is a model that simultaneously determines the optimal timing for the introduction of new product generations pricing production timing and produced quantities this model is then used to examine the impact of variations in marketing and operations parameters on both optimal profit and optimal product lifecycle length the study finds that larger profit and a faster pace of new product introductions are generally associated with faster diffusion lower price elasticity larger market potential lower new product introduction cost and more costly consumer products

implicit contracts life cycle labor supply and intertemporal substitution the implicit contract model is a serious alternative to the spot market interpretation of the labor market however its usefulness has been limited because the wage is unobserved and hence it has not been possible to estimate an intertemporal frisch supply elasticity for the model using microdata in this article we show that one can estimate this elasticity from microdata within the context of the implicit contract model under relatively weak assumptions based on consumer theory we implement our approach on two micro data sets and for both obtain a reasonably precise elasticity estimate of approximately 1 0

optimal inventory policies when ordering prices are random we consider a single item inventory model with deterministic demands at the beginning of each period a random ordering price is received according to a known distribution function a decision must be made as to how much if any of the item to order in each period so as to minimize total expected costs while satisfying all demands we show that in each period a sequence of critical price levels determines the optimal ordering strategy so that it is optimal to satisfy the demands of the next n periods if and only if the random price falls between the nth and the n 1st levels we derive recursive expressions that describe the critical price numbers and demonstrate the relationship of these expressions to minimal expected cost we study finite horizon as well as infinite horizon models and show that the critical number strategy is also average cost optimal

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

parametric analysis of setup cost in the economic lot sizing model without speculative motives in this paper we consider the important special case of the economic lot sizing problem in which there are no speculative motives to hold inventory we analyze the effects of varying all setup costs by the same amount this is equivalent to studying the set of optimal production periods when the number of such periods changes we show that this optimal set changes in a very structured way this fact is interesting in itself and can be used to develop faster algorithms for such problems as the computation of the stability region and the determination of all efficient solutions of a lot sizing problem furthermore we generalize two related convexity results which have appeared in the literature

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

an eoq model for deteriorating items with a linear trend in demand and shortages in all cycles abstract we consider here the inventory replenishment problem over a finite time horizon for a deteriorating item with a linear trend in demand equal replenishment cycles and shortage in every cycle the reorder number the interval between two successive reorders and the shortage intervals are all determined in an optimal manner so as to minimize the average system cost the advantage of allowing shortage in all cycles is illustrated with a numerical example

a comparison of simple heuristics for multi product dynamic demand lot sizing with limited warehouse capacity abstract the paper analyzes the problem of the replenishment of multiple products to satisfy dynamic demands when the warehouse capacity or the available inventory budget is limited in this context the timing of replenishment lot sizes has to be staggered to account for the capacity conflict and to provide an effective space sharing in addition to the solution of the trade off between setup and inventory holding costs we analyze three simple heuristics first we review a forward algorithm that successively builds lots by extending replenishments according to a cost based priority rule the second heuristic solves the lot sizing problems independently for each product in a first step and then resolves capacity violations by a smoothing mechanism further this paper adapts a heuristic for single item uncapacitated lot sizing that successively improves an initial lot for lot schedule by combining replenishments according to a cost savings based priority rule to the multi item capacitated problem the performance of the three simple methods is compared in an extensive numerical study and benchmarked against the solution of a mixed integer programming approach the results show the different ability of the approaches to simultaneously account for the individual lot sizing problems and the lot staggering problem across multiple products especially the savings approach appears to provide better results for a broad range of problems especially for large tightly capacitated problems with high demand variability

a network approach to modeling the multi echelon spare part inventory system with backorders and interval valued demand a multi echelon inventory system implies the existence of a hierarchy of stocking locations and the dependence and interaction between them we consider a multi echelon spare part inventory management problem with outsourcing and backordering the problem is characterized by deterministic repair time cost and supply and demand that lie within prescribed intervals and that vary over time the objective is to minimize the total inventory and transportation costs we develop a network model for problem analysis and present a network flow algorithm for solving the problem we prove that the wagner whitin property known for the lot sizing problem can be extended to the spare part inventory management problem under study

the economic lot sizing problem with perishable items and consumption order preference abstract we consider the economic lot sizing problem with perishable items els pi where each item has a deterministic expiration date although all items in stock are equivalent regardless of procurement or expiration date we allow for an allocation mechanism that defines an order in which the items are allocated to the consumers in particular we consider the following allocation mechanisms first expiration first out fefo last expiration first out lefo first in first out fifo and last in first out lifo we show that the els pi can be solved in polynomial time under all four allocation mechanisms in case of no procurement capacities this result still holds in case of time invariant procurement capacities under the fifo and lefo allocation mechanisms but the problem becomes np hard under the fefo and lifo allocation mechanisms

the single item uncapacitated lot sizing problem with time dependent batch sizes np hard and polynomial cases abstract this paper considers the uncapacitated lot sizing problem with batch delivery focusing on the general case of time dependent batch sizes we study the complexity of the problem depending on the other cost parameters namely the setup cost the fixed cost per batch the unit procurement cost and the unit holding cost we establish that if any one of the cost parameters is allowed to be time dependent the problem is np hard on the contrary if all the cost parameters are stationary and assuming no unit holding cost we show that the problem is polynomially solvable in time o t 3 where t denotes the number of periods of the horizon we also show that in the case of divisible batch sizes the problem with time varying setup costs a stationary fixed cost per batch and no unit procurement nor holding cost can be solved in time o t 3 log t

the single item lot sizing problem with immediate lost sales abstract we introduce a profit maximization version of the well known wagner whitin model for the deterministic uncapacitated single item lot sizing problem with lost sales demand cannot be backlogged but it does not have to be satisfied either costs and selling prices are assumed to be time variant differentiating our model from previous models with lost sales production quantities and levels of lost sales in different periods represent a twofold decision problem we first transform the total profit function into a special total cost function we then prove several properties of an optimal solution a forward recursive dynamic programming algorithm is developed to solve the problem optimally in o t 2 time where t denotes the number of periods in the problem horizon the proposed algorithm can solve problems of sizes up to 400 periods in less than a second on a 500 mhz pentium iii processor

real wages in the business cycle and the theory of income distribution an unresolved conflict between theory and facts in mainstream macroeconomics the focus of this article is the recurring tension between mainstream macroeconomics and observed facts in connection with the difficult task of providing explanations of the business cycle consistent both with the traditional theory of income distribution and with the empirical evidence concerning the co movements of real wages and employment over the cycle the attempts to reconcile facts and theory have led to the continuous introduction of specific and arguably ad hoc hypotheses in contrast with the search for greater theoretical rigour claimed by the various streams of macroeconomic modelling subsequent to the neo classical synthesis in addition the specific assumptions introduced in the models or their implications are in turn often contradicted or at best not confirmed by subsequent empirical research it is suggested in the conclusions that the difficulty of keeping together in a simple and consistent framework theory and facts reflects the flawed theoretical foundations of mainstream theory

in search of a stylised fact do real wages exhibit a consistent pattern of cyclical variability the paper surveys the studies on the cyclical behaviour of real wages published from the twenties onwards the traditional simple neoclassical model of the labour market suggests that real wages tend to move countercyclically however from a theoretical viewpoint there are few reasons to expect this behaviour once the simple model is extended to account for imperfect competition uncertainty lagged responses or contracting between firms and workers empirical studies give different answers to the problem the contributions reviewed in the paper are arranged roughly in a chronological order the interwar period the postwar pre econometric studies the econometric work using aggregate data the evidence produced on the basis of longitudinal data the analyses of the shock responsiveness of real wages and finally the most recent papers attempting a reconciliation of the somewhat conflicting evidence derived from aggregate and panel data

the intertemporal substitution model of labour market fluctuations an empirical analysis the paper uses two approaches to study whether aggregate fluctuations in employment and unemployment may be explained within a market clearing framework as intertemporal substitution in labour supply first log linear equations for labour supply and unemployment are estimated using a forecasting model to measure wage and price expectations second a utility function is used to derive and estimate an equation for labour supply as a function of the current real wage and consumption the influence of expected future real wages and interest rates is captured by the consumption variable the empirical results do not support the intertemporal substitution model

production strategies for a stochastic lot sizing problem with constant capacity abstract this paper presents a single item capacitated stochastic lot sizing problem motibated by a dutch company operating in a make to order environment due to a highly fluctuating and unpredictable demand it is not possible to keep any finished goods inventory in response to a customer s order a fixed delivery date is quoted by the company the objective is to determine in each period of the planning horizon the optimal size of production lots so that delivery dates are met as closely as possible at the expense of minimal average costs these include set up costs holding costs for orders that are finished before their promised delivery date and penalty costs for orders that are not satisfied on time and are therefore backordered given that the optimal production policy is likely to be too complex in this situation attention is focused on the development of heuristic procedures in this paper two heuristics are proposed the first one is an extension of a simple production strategy derived by dellaert 5 for the uncapacitated version of the problem the second heuristic is based on the well known silver meal algorithm for the case of deterministic time varying demand experimental results suggest that the first heuristic gives low average costs especially when the demand variability is low and there are large differences in the cost parameters the silver meal approach is usually outperformed by the first heuristic in situations where the available production capacity is tight and the demand variability is low

efficient and nearly efficient partnerships this paper shows in two ways that the degree to which free riding diminishes the performance of deterministic partnerships may be less than has been generally thought first a necessary and sufficient condition is provided for a partnership to sustain full efficiency it implies that many non trivial partnerships sustain efficiency such as generic ones with finite action spaces and neoclassical ones with leontief technologies second approximate efficiency is shown to be achievable in a large class of partnerships including ones with smooth and monotonic production and disutility functions approximate efficiency is achieved by mixed strategy equilibria one partner takes with small probability an inefficient action the degree to which efficiency is approximated is restricted only by the amount of liability the partners can bear nonetheless their equilibrium payments are not arbitrarily large

labour force participation timing and persistence this paper examines the relative importance of timing and persistence elements in explaining cyclical fluctuations in labour supply data from the natural experiment provided by world war ii and cross sectional data on american local labour markets as well as aggregate time series data are used in the empirical work we find little evidence that timing effects play an important role in labour market dynamics the evidence suggests that views emphasizing persistence are more accurate and that previous employment tends to raise the probability of subsequent employment much of the development of applied economic theory within the past 25 years has emphasized the importance of viewing economic decisions in a life cycle context consumption decisions are today frequently viewed as being determined by wealth or permanent income the human capital revolution has brought life cycle considerations to the forefront of modern labour economics while the life cycle dynamics of labour force participation decisions have important implications for macroeconomic theory and policy they have received relatively little empirical attention with the notable exceptions of lucas and rapping 1969 and hall 1980 none of the large body of work on cyclical fluctuations in employment has explicitly relied on a dynamic model of labour supply this paper uses several types of data to examine two elements of participation dynamics the first is the aspect of timing which is implicit in the work of lucas and rapping and in mincer s 1966 early discussion of hidden unemployment the timing argument which is presented most explicitly in ghez and becker 1975 holds that leisure is easily substitutable across periods hence relatively small transitory movements in the perceived real wage or real rate of return can have large effects on the path of labour supply as individuals time their participation to coincide with periods of high transitory wages on the other hand permanent changes because they do not affect the timing decision are expected to have a much smaller effect on participation it is this view of labour supply which underlies new classical macroeconomic models the dependence is made explicit in lucas 1975 who claims that what we do know indicates that leisure in one period is an excellent substitute for leisure in other nearby periods the ability of classical macroeconomic models to explain fluctuations in employment depends on the presence of strong intertemporal substitution effects unless

inflation and unemployment the world economy today is vastly different from the 1930s when seymour harris the chairman of this meeting infected me with his boundless enthusiasm for economics and his steadfast confidence in its capacity for good works economics is very different too both the science and its subject have changed and for the better since world war ii but there are some notable constants unemployment and inflation still preoccupy and perplex economists statesmen journalists housewives and everyone else the connection between them is the principal domestic economic burden of presidents and prime ministers and the major area of controversy and ignorance in macroeconomics i have chosen to review economic thought on this topic on this occasion partly because of its inevitable timeliness partly because of a personal interest reaching back to my first published work in 1941

market structure and cyclical fluctuations in u s manufacturing the relevance of imperfect competition for models of economic fluctuations has received increased attention from researchers in both macroeconomics and industrial organization the authors outline a new methodology for estimating industry markups of price over marginal cost and the influence of market structure on cyclical movements in total factor productivity measures of industry concentration import competition and unionization are important for explaining markups in some industry groups much of the estimated markup of price over marginal cost is accounted for by noncapital fixed costs finally the authors show that their estimated margins fluctuate substantially over the cycle in particular markups are countercyclical especially in concentrated durable goods industries copyright 1988 by mit press

multi product lot sizing with a transportation capacity reservation contract abstract although transportation costs can form more than 50 of the total logistics costs of a product they are often neglected in lot sizing research and modelling nonetheless the body of research that does take transportation costs into account is gradually growing the bulk of this type of research however assumes that freight rates decrease as shipping weights and or volumes increase inspired by the situation with a large european manufacturing company we study a multi product lot sizing model where in any period any portion of a reserved transportation capacity can be used in exchange for a guaranteed price if the capacity is insufficient then the shipper needs to contract additional transportation capacity on the spot market where the prevailing price is higher accordingly the freight rates are piece wise linearly increasing in our model we prove that the problem of determining transportation lot sizes so as to meet warehouse demand with no backlogging allowed and to minimize total costs that is the sum of inventory carrying ordering and transportation costs is np hard in the strong sense furthermore we present a lagrangean relaxation algorithm to compute lower and upper bounds of which comprehensive computational experiments show the compelling performance in terms of quality and speed

note performance bounds for lot sizing heuristics this paper deals with the classical dynamic lot size problem without backlogging and capacity limitation we derive worst case performance bounds for a class of lot sizing heuristics when the considered methods are applied a decision whether to have a set up or not in a certain period is taken without regarding the future demand it is shown that 2 is a lower bound for the worst case performance ratio for such heuristics the results illustrate circumstances under which the approximate techniques fail

simulation based sequencing and lot size optimisation for a production and inventory system with multiple items abstract we investigate the following decision problem a manufacturing unit has to meet a random demand for n items at the same time only one item can be manufactured manufacturing times are random whereas set up times are known positive constants but different for different items finished production is stored in a warehouse with finite capacity the availability of raw material is always guaranteed demand that cannot be satisfied by items in the warehouse will be backordered in a queue with given capacity demand that meets a full backorder queue is lost we assume cost for manufacturing items for production switches for holding items in the warehouse for waiting and lost demand for sold items a given reward is earned the problem now is to define such a manufacturing policy i e a sequencing rule and a lot size rule which maximises the expected profit per time unit since that problem is too complex for an analytical solution we restrict our search for an optimal policy to simple structured policies which can be described by a few parameters to find optimal parameter values we use simulation optimisation where a simulator for the system is combined with a genetic algorithm as an optimiser the paper is finished with some numerical examples to show the applicability of the proposed approach

adapting the newsvendor model for infinite horizon inventory systems abstract we address inventory decisions in the context of the reorder point order quantity policy in infinite horizon stochastic lead time demand inventory systems in which the parameters may be non stationary we develop a heuristic policy based on the simple economic order quantity eoq model and the one period newsvendor model using illustrative numerical examples we demonstrate that our simple and easy to understand heuristic policy performs nearly as well as the optimal policy derived from complicated mathematical procedures our heuristic policy is simple easy to implement and flexible in that it can be easily adapted to situations when the parameters of the inventory system may change analytical modeling under non stationary parameters would be extremely complex and the derivation of closed form optimal policies is mathematically intractable in most cases in such cases practitioners will find our heuristic policy an attractive option

the single product lot sizing problem with constant parameters and backlogging exact results a new solution and all parameter stability regions we consider the single product lot sizing problem over a finite planning horizon demand at each period is constant and excess demand is completely backlogged holding and backlogging costs are proportional to the amount of inventory stocked or backlogged while ordering cost is fixed independent of the quantity ordered the optimal policy targets to minimize the total relevant costs over the planning horizon the key results of this paper are 1 an explicit formula for the optimal total cost as a function of the model parameters and the number of cycles of the policy 2 a new polynomial time algorithm which determines the overall optimal policy and 3 stability regions for any solution considering simultaneous variations on all cost and demand parameters the proposed algorithm is easy to implement and therefore is suitable for practical use

the relative effects of employed and unemployed job search a lthough many early models of job search assumed that job seekers were unemployed economists have come to recognize the importance of on the job search mattila 1974 for example found that roughly 60 of quitters experienced no unemployment between jobs implying that the majority of voluntary job changers engaged in on the job search the choice of search mode i e employed vs unemployed search has been modelled in the theoretical search literature barron and mccafferty 1977 burdett 1978 however there have been no attempts to estimate empirically the determinants of this choice 2 some researchers have however examined the resulting wages associated with these two types of search and found a greater wage return to employed than to unemployed search mattila 1969 black 1980 however because voluntarily unemployed search involves forgoing income burdett 1978 while employed search does not abstracting from voluntary reductions in hours incomemaximizing job seekers would never quit to search unless the expected net return to unemployed search exceeded that for employed search thus the previously mentioned empirical findings at first glance might appear to contradict the assumption of income maximization by job seekers because some workers do quit into unemployment 3 in this paper it is argued that previous attempts to compare the returns of employed and unemployed job search suffer from a selectivity problem specifically searchers who accept offers without experiencing any unemployment are likely to have unobservable variables such as informal job contacts and ability which will raise the relative return to employed search compared to that of voluntarily unemployed job seekers 4 providing an explanation for higher wages for on the job searchers than for unemployed searchers this paper estimates the relative wage effects of employed and unemployed search and the determinants of the choice of search mode i e employed vs unemployed search unlike earlier work mattila 1969 black 1980 the previously mentioned selectivity problems are accounted for this is the first attempt to estimate the determinants of choice of search mode 5 without adjusting for selectivity bias as regards employed vs unemployed search it is found that employed search is associated with greater expected wage offers than unemployed search controlling for measurable personal characteristics however accounting for selectivity the expected wage offer given unemployed search is greater than that given employed search finally the greater is the difference between the expected offer given unemployed and that given employed search the more likely one is to choose unemployed search these findings suggest that quitting to search unemployed may be a wealth maximizing decision received for publication november 5 1980 revision accepted for publication august 17 1981 university of illinois at urbana champaign and arizona state university respectively professor low is partially supported by a faculty grant from the graduate college at arizona state university the authors thank francine blau wallace hendricks and two anonymous referees for comments and suggestions i for a summary of this literature see lippman and mccall 1976 2 barron and mccafferty 1977 do estimate an aggregate time series model of the log of the proportion of quits entering unemployment as a function of the vacancy rate proxied by the help wanted advertising index however such a model ignores search that does not lead to quits and does not include variables beyond the vacancy rate that influence an individual s choice of search mode i it is also possible that the forgone earnings due to unemployed search could in principle be less than the possible savings in direct search costs due to unemployed search relative to employed search see burdett 1978 in this case a lower wage return to unemployed search could imply that quitting was based on income considerations further individuals may have quit for nonwage reasons 4 black 1980 found that other things equal those who planned to seek new employment but did not quit had significantly lower wage growth than those who did not plan to search and did not quit this finding strongly suggests the likelihood of a selectivity bias black 1980 p 227 black s 1976 1980 data the michigan panel study of income dynamics psid for his work on employed search did not allow him to distinguish employed and unemployed search

approximation algorithms for deterministic continuous review inventory lot sizing problems with time varying demand this work deals with the continuous time lot sizing inventory problem when demand and costs are time dependent we adapt a cost balancing technique developed for the periodic review version of our problem to the continuousreview framework we prove that the solution obtained costs at most twice the cost of an optimal solution we study the numerical complexity of the algorithm and generalize the policy to several important extensions while preserving its performance guarantee of two finally we propose a modified version of our algorithm for the lot sizing model with some restricted settings that improves the worst case bound

job search by employed and unemployed youth analysis of data from the new youth cohort of the national longitudinal survey yields evidence that young unemployed job seekers chose higher levels of search effort as measured by number of methods used and time spent per method and lower reservation wages relative to offered wages than did comparable employed job seekers in 1981 these differences in search choices at least partly explain differences in search outcomes between the two groups unemployed searchers apparently were more likely than employed searchers to gain new employment and the wages they obtained were slightly lower the author argues that the greater search effort by unemployed job seekers is due to the higher costs of search they bear because of foregone earnings

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

the relation between price and marginal cost in u s industry an examination of data on output and labor input reveals that some u s industries have marginal cost well below price the conclusion rests on the finding that cyclical variations in labor input are small compared with variations in output in booms firms produce substantially more output and sell it for a price that exceeds the costs of the added inputs the paper documents the disparity between price and marginal cost where marginal cost is estimated from annual variations in cost it considers a variety of explanations of the findings that are consistent with competition but none is found to be completely plausible

ending inventory valuation in multiperiod production scheduling when making lot sizing decisions managers often use a model horizon t that is much smaller than any reasonable estimate of the firm s future horizon this is done because forecast accuracy deteriorates rapidly for longer horizons while computational burden increases however what is optimal over the short horizon may be suboptimal over the long run resulting in errors known as end effects a common end effect in lot sizing models is to set end of horizon inventory to zero this policy can result in excessive setup costs or stock outs in the long run we present a method to mitigate end effects in lot sizing by including a valuation term vit for end of horizon inventory it in the objective function of the short horizon model we develop this concept within the classical eoq modeling framework and then apply it to the dynamic lot sizing problem dlsp if demand in each period of the dlsp equals the long run average demand rate then our procedure induces an optimal ordering policy over the short horizon that coincides with the long run optimal ordering policy we test our procedure empirically against the wagner whitin algorithm and the silver meal heuristic under several demand patterns within a rolling horizon framework with few exceptions our approach significantly outperforms the other approaches tested for modest to long model horizons we discuss applicability to more general lot sizing problems

intertemporal substitution in labor supply evidence from micro data the sensitivity of the supply of labor to intertemporal variation in the wage is an important issue in macroeconomics the analysis of social security and pensions and the study of life cycle patterns of work this paper explores two approaches to the measurement of intertemporal substitution that have appeared in the literature the first approach is to use consumption to control for wealth and unobserved expectations about future wages in the labor supply equation the second approach is to estimate a first difference equation for hours in which labor supply from the previous period serves as a control for wealth and wage expectations the results indicate that intertemporal substitution elasticity for married men is positive but small

testing intertemporal substitution implicit contracts and hours restriction models of the labor market using micro data we present new tests of three theories of the labor market intertemporal substitution hours restrictions and implicit contracts the intertemporal substitution test we implement is an exclusion test robust to many specification errors and we consistently reject this model we model hours restrictions as part of an endogenous switching model we compare the implicit probit equation to an unrestricted probit equation for unemployment and reject the hours restriction model for the implicit contracts model we estimate non separable within period labor supply and consumption equations we test a cross equation restriction of the model and cannot reject the implicit contracts model jel e30 j22 j60

production inventory games a new class of totally balanced combinatorial optimization games in this paper we introduce a new class of cooperative games that arise from production inventory problems several agents have to cover their demand over a finite time horizon and shortages are allowed each agent has its own unit production inventory holding and backlogging cost cooperation among agents is given by sharing production processes and warehouse facilities agents in a coalition produce with the cheapest production cost and store with the cheapest inventory cost we prove that the resulting cooperative game is totally balanced and the owen set reduces to a singleton the owen point based on this type of allocation we find a population monotonic allocation scheme for this class of games finally we point out the relationship of the owen point with other well known allocation rules such as the nucleolus and the shapley value

analytical evaluation of heuristics performance for the single level lot sizing problem for products with constant demand abstract in this paper we examine the performance of several commonly used heuristics for the single level lot sizing problem for products with stationary demand and cost parameters a particular combination of demand and cost combination introduced by blackburn and millen called the lot sizing index lsi is shown to be an excellent predictor of heuristics performance for any finite horizon problem the importance of the lsi as a performance predictor is established through an analysis of the heuristics objective function and the optimal cost function

the new keynesian synthesis the new keynesians made more rapid progress in understanding the microeconomics of unemployment than in understanding the microeconomics of nominal price rigidity but the past five years have seen important breakthroughs in this second area this paper will describe these breakthroughs discuss our current understanding of nominal rigidity and assess the work that remains to be done

operations research in inventory management a review and critique the objectives of inventory management including the relevant related costs are examined in this paper a brief review of standard problems that have been effectively solved is presented however we point out that a serious gap exists between theory and practice in many organizations suggestions are made for bridging this gap finally a list is provided of a number of research problems whose implementable solution would have a major beneficial impact on the practice of inventory management

predicting competitive response to a major policy change combining game theoretic and empirical analyses this research uses procter gamble s value pricing initiative as a context for testing whether actual competitor and retailer response to a major policy change can be predicted using a game theoretic model we first estimate demand functions for p g and competitor brands from the period before value pricing was initiated we then formulate a dynamic manufacturer retailer stackelberg model that includes p g a national brand competitor and a retailer the model takes p g s move as given and prescribes the price and promotion response of the competitors and the retailer we substitute the estimated demand parameters into the model to obtain prescriptions for each competitor and the retailer and see whether these prescriptions are related to the actual response we find that the dynamic game theoretic model calibrated with empirical estimates of demand parameters has significant predictive power we also test the predictive power of two benchmark models the first is based on the reaction function approach of leeflang and wittink leeflang peter s h wittink dick r 1992 diagnosing competitive reactions using aggregated scanner data internat j res marketing9 39 57 and the second is a simplification of our dynamic model where the retailer is not strategic the dynamic game theoretic model performs better than either benchmark

requirements planning with pricing and order selection flexibility past requirements planning research has typically assumed that the firms demands are determined prior to production planning in contrast we explore a single stage planning model that implicitly decides through pricing decisions the demand levels the firm should satisfy in order to maximize contribution to profit we briefly discuss solution methods and properties for these problems when production capacities are unlimited the key result of this work is a polynomial time solution approach to the problem under time invariant finite production capacities and piecewise linear and concave revenue functions in price

on the present state of the capital controversy the post war capital controversy seems to have had two distinguishable stages thanks to the unambiguous phenomena of reswitching and reverse capital deepening the first stage was conclusive in discarding from pure theory the traditional versions of neoclassical theory that relied on the notion of capital as a single quantity subsequently however when the implications of those phenomena took centre stage in the controversy together with the reformulations of the theory which intended to do away with the quantity of capital several misunderstandings prevented i shall contend decisive progress in the analysis and we entered an inconclusive phase of the discussion

intertemporal substitution and constraints on labor supply evidence from panel data intertemporal substitution and constraints on labor supply evidence from panel data i introduction through much of the 1970s and 1980s macroeconomic stabilization analysis has been dominated by equilibrium models in which fluctuations in employment result from intertemporal substitution workers voluntarily vary their labor supply over time in response to movements in wages and interest rates a number of recent empirical tests of intertemporal substitution models for example altonji 1982 mankiw et al 1985 ham 1986 strongly reject the intertemporal substitution approach these results have led some economists to reject equilibrium macro models in favor of keynesian models in which workers face quantity constraints on labor supply in keynesian models employment fluctuations result from changes in the severity of constraints that is changes in involuntary unemployment rather than intertemporal substitution on the other hand many economists remain unconvinced by recent rejections of intertemporal substitution models because the results are consistent with many possible explanations for tractability empirical studies always impose restrictive assumptions such as separability of utility over time and between goods or such as the existence of a representative consumer data also suffer from numerous problems such as aggregation bias measurement error and the use of average rather than marginal wage rates consequently even the authors of the studies seem hesitant to draw firm conclusions they often simply conclude that workers behavior is explained either by quantity constraints or by a more complicated intertemporal substitution model than the one they have tested 1 this paper attempts to determine which of these explanations is correct are changes in employment a sophisticated form of intertemporal substitution or are they involuntary the crucial data come from questions in the panel study of income dynamics about whether workers experience unemployment or are unable to work as many hours as they want following ham 1982 1986 this information is used to classify workers as quantity constrained in their labor supply or unconstrained i then test a simple intertemporal substitution model for each group of workers if the tests suffer from overly restrictive utility functions or data problems then the model should be rejected for both samples on the other hand if some workers truly face quantity constraints then the model should perform better for the sample of unconstrained workers 2 the tests yield two main results first the model indeed performs worse for the constrained workers for this group the data reject the model s overidentifying restrictions and the parameter estimates contradict the model in contrast the results for the unconstrained workers are weakly consistent with the model as keynesian theories suggest quantity constraints alter workers behavior second the estimates of the intertemporal labor supply elasticity for prime age men are close to zero even for unconstrained workers even if workers are free to vary their hours they apparently choose to respond little to movements in wages the paper addresses two other issues first do constraints on borrowing influence labor supply in the intertemporal substitution model workers borrow and lend to smooth consumption while varying hours of work as this suggests the model performs best for workers who not only face no labor supply constraints but who also own substantial assets and thus are unlikely to face liquidity constraints finally the paper proposes a new approach to identifying intertemporal labor supply equations previous micro studies do not adequately address the problem that wages are correlated with unobservable characteristics that affect tastes for work i propose two identifying restrictions 1 changes in tastes are uncorrelated with levels of time in variant variables and 2 changes in tastes have no aggregate component

dynamic lot sizing models with pricing for new products while previous dynamic lot sizing dls models mainly consider mature products this study analyzes production planning decisions for new products the demand dynamics caused by new product diffusion complicate production decisions for new products we integrate dls and discrete bass models to provide optimal decisions for pricing and production planning problems moreover we study the joint influence of product diffusion and pricing parameters on the dls decisions this leads to the following insights first coordinated production pricing and dynamic pricing improve profitability second the optimal pricing strategy is affected by market conditions the penetration pricing strategy outperforms the skimming pricing strategy when consumers are less sensitive to relative price changes than to the introductory price when the product diffuses slowly or when the consumer initiative level is low otherwise the latter outperforms the former finally pricing strategies and product diffusion patterns reshape the cost structure of a firm coordinated decisions and dynamic pricing strategy substantially reduce the cost revenue ratio whereas an increase in the consumer initiative level or product diffusion speed can improve cost efficiency

dynamic lot sizing with batch ordering and truckload discounts this paper studies two important variants of the dynamic economic lot sizing problem that are applicable to a wide range of real world situations in the first model production in each time period is restricted to a multiple of a constant batch size where backlogging is allowed and all cost parameters are time varying several properties of the optimal solution are discussed based on these properties an efficient dynamic programming algorithm is developed the efficiency of the dynamic program is further improved through the use of monge matrices using the results developed for the first model an o n3log n algorithm is developed to solve the second model which has a general form of product acquisition cost structure including a fixed charge for each acquisition a variable unit production cost and a freight cost with a truckload discount this algorithm can also be used to solve a more general problem with concave cost functions

production allocation with dual provisioning abstract consider a manufacturer that has existing in house capacity to produce certain products however due to recent growth in demand the existing capacity is insufficient to meet the total requirements over a finite planning horizon as a short term solution the manufacturer has decided to order part of the total requirements from an external supplier this paper presents a model that focuses on the issue of allocating a production quantity among the in house facility and an external supplier we construct a product allocation problem that determines an optimal allocation so that the total relevant cost in house production cost ordering cost etc is minimized in addition we analyze the complexity of the problem and develop two different lagrangian heuristics for generating near optimal allocations

a master production scheduling procedure for stochastic demand and rolling planning horizons abstract the problem of interest is a one product uncapacitated master production schedule mps in which decisions are made under rolling planning horizons demand is stochastic and time varying and effectiveness is measured by inventory holding production setup and backorder costs typically in both the research literature and the business practice the stochastic nature of the problem is modeled in an ad hoc fashion the stochastic mps problem is usually solved by adding safety stock to production quantities obtained from a deterministic lot sizing algorithm here the stochastic nature of the problem is explicitly considered as an optimal algorithm for solving the static probabilistic dynamic lot sizing problem is adapted to rolling planning horizons the resulting algorithm is found to dominate traditional approaches over a wide variety of experimental factors reducing total costs by an average of 16 over traditional methods

lot sizing for products with finite demand horizon and periodic review inventory policy abstract this paper analyzes and develops an efficient algorithm for solving a simple generalization of the classical economic order quantity eoq model where the demand horizon is finite and a periodic review inventory policy is followed such problems could arise in production shops where the product under consideration is going to be discontinued and or replaced by some other product after a certain known number of periods such problems could also arise as subproblems in large prodution inventory problems were demand rate is constant in some periods and varying in others

an inverse economic lot sizing approach to eliciting supplier cost parameters recent literature on supply chain coordination offers a wide range of game theoretic and optimization approaches that ensure efficient planning in the supply chain but assume that the involved parties have complete information about each other however in reality complete information is rarely available and those models alone do not present any incentive for the parties to reveal their private information e g the cost parameters that they use when solving their planning problems this paper proposes an inverse lot sizing model for eliciting the cost parameters of a supplier from historic demand vs optimal delivery lot size pairs gathered during repeated earlier encounters it is assumed that the supplier solves a single item multi period uncapacitated lot sizing problem with backlogs to optimality to calculate its lot sizes and the buyer is aware of this fact the inverse lot sizing problem is reformulated to an inverse shortest path problem which is in turn solved as a linear program this model is used to compute the ratios of the supplier s cost parameters i e the setup the holding and the backlog cost parameters consistent with all the historic samples the elicited cost parameters can be used as input for various game theoretic or bilevel optimization models for supply chain coordination computational experiments on randomly generated problem instances indicate that the approach is very efficient in predicting future supplier actions from the historic records 2013 elsevier b v all rights reserved

dynamic lot sizing when demand timing is uncertain we characterize optimal solutions for the dynamic lot sizing problem when demand quantities are known but their timing is uncertain the characterization states that for some possible history of demands following a period of production there is a period with zero inventory before another period with production using this characterization we outline a dynamic program for the solution of these problems some results from sample problems illustrate the variety of optimal solutions that can occur

note a note on the dynamic lot size model with uncertainty in demand and supply processes in this paper we give some extensions of a result of nevison and burstein nevison c h m burstein 1984 the dynamic lot size model with stochastic lead times management sci 30 100 109 who discuss a dynamic lot sizing model with stochastic lead times they consider a situation in which the lead time distribution is unaltered by the amount which is ordered but is otherwise arbitrary and characterize the optimal solution in terms of points at which there is zero inventory here we give a more precise characterization and show that these results can be extended to a situation in which the demands are also stochastic and in which there is uncertainty relating to quantity as well as to the timing of demands and order arrivals the method of proof that we use is different from that used by nevison and burstein

effects of discounting and demand rate variability on the eoq the economic order quantity eoq formula is probably the most well known formula in inventory theory it determines the optimal value of the ordering quantity by minimizing the average cost in an ordering cycle it is based on the assumptions that there is a fixed lead time and a constant demand rate these assumptions are usually not fulfilled in practice especially when dealing with slow moving items demand seems to fluctuate furthermore since the time between two successive orderings is often large for slow moving items discounted costs instead of average costs should be minimized in this paper we determine the optimal ordering quantity if demand is modelled by a poisson process and the expected discounted costs are minimized we also analyze the case where demand is uniform and or the average cost criterion is used we give graphical presentations of the optimal ordering quantities besides easily determining the optimal values these allow us to show what the effects of changing the objective function and of changing the demand distribution are we derive a simple discounted cost ordering quantity formula denoted by eoq d for slow moving items we show that for items with a small demand rate and high fixed ordering costs the eoq d is much closer to the optimal discounted cost ordering quantity than the traditional eoq formula c 1998 elsevier science b v all rights reserved

an approach to evaluate the impact of interaction between demand forecasting method and stock control policy on the inventory system performances abstract usually in stock control studies demand data are considered as an input to the model without explicitly considering that they are the results of a demand forecasting system stock control system is examined independently of the demand forecasting system and it is assumed that demand data or forecast errors have been properly modelled however the interactions that may exist between demand forecasting methods and stock control systems in terms of their effects on global system performances are not considered in the paper an approach for evaluating these interactions based on a comparative simulation test of global system costs using historical data is presented the approach is explained through a real case the replenishment from different suppliers of a central depot of tinned food which supplies more than 700 items to warehouses at the lower echelon results of the simulation study show that traditional measures of forecast errors cannot be taken as sole indicators for the choice among different demand forecasting methods these methods on the contrary have to be evaluated on the basis of total costs and service level of the global inventory control system

real wages and the business cycle the objectives of this review are threefold 1 to characterize the empirical literature on the cyclical behavior of real wages 2 to identify the sources of the differences in results across studies and 3 to enumerate key factors that determine the cyclicality of real wages given a host of measurement and methodological issues drawing firm conclusions is difficult but several generalizations can be made the estimated cyclicality of real wages depends crucially on the time period of analysis and the choice of whether to examine the production or the consumption wage composition effects play an important but complicated role as well

pricing and manufacturing decisions when demand is a function of prices in multiple periods in most deterministic manufacturing decision models demand is either known or induced by pricing decisions in the period that the demand is experienced however in more realistic market scenarios consumers make purchase decisions with respect to price not only in the current period but also in past and future periods we model a joint manufacturing pricing decision problem accounting for that portion of demand realized in each period that is induced by the interaction of pricing decisions in the current period and in previous periods we formulate a mathematical programming model and develop solution techniques we identify structural properties of our models and develop closed form solutions and effective heuristics for various special cases of our models finally we conduct extensive computational experiments to quantify the effectiveness of our heuristics and to develop managerial insights

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

efficiency and equilibria in complementary teams a comment abstract we argue that visile s 1994 claim that the moral hazard in the teams problem depends on the assumption that the inputs are perfect substitutes is incorrect discontinuities in the marginal product curves not complementarity of the inputs allows the moral hazard problem to be avoided in vislie s perfect complements example

robust economic order quantity models abstract in this paper we study the classical economic order quantity eoq model under significant in particular the problem under consideration is the economic order quantity model with the input data of the demand rate the order cost and the holding cost rate being uncertain a robustness approach based on scenario characterization of the input data is adopted to describe the uncertainties the aim of the approach is to find an inventory policy that performs well under all realizable input data scenarios an efficient linear time algorithm is devised to find the robust decisions analytical results are obtained for the case where input data are defined in continuous intervals comparisons on performances between the robust decisions and the stochastic optimization decisions are conducted the results demonstrate the advantages of robustness approach

computing core allocations in cooperative games with an application to cooperative procurement abstract cooperative game theory defines several concepts for distributing outcome shares in a cooperative game with transferable utilities one of the most famous solution concepts is the core which defines a set of outcome allocations that are stable such that no coalition has an incentive to leave the grand coalition in this paper we propose a general procedure to compute a core element or to detect that no core allocation exists which is based on mathematical programming techniques the procedure proposed in this paper can be applied to a wide class of cooperative games where the characteristic function is given by the optimum objective function value of a complex optimization problem for cooperative procurement which is an example from the field of supply chain management where some literature on the core concept already exists we prove the applicability and provide computational results to demonstrate that games with 150 players can be handled

retrospectives real and money wage rates abstract in the general theory john maynard keynes held money and real wage rates move in opposite directions in expansion prices increase faster because of increasing costs and a rise in the proportion of product going to profits neoclassical economists held similarly money illusion of workers supported their common view the author s 1938 article rather showed a procyclical pattern significant to macroeconomic models of the economy contemporary literature with new elements of compensation and new measures of wages supports a slightly procyclical relationship increased output and employment in expansion do not require lower real wages

the reverse wagner whitin model with variable manufacturing and remanufacturing cost abstract in this paper the reverse wagner whitin model is extended to the case with additional variable manufacturing and remanufacturing cost this model can be regarded as a combination of the classical wagner whitin model and a pure reverse wagner whitin model with given returns of used products the combined model is more appropriate to practice if the alternate application of remanufacturing and manufacturing processes is analysed for the case of time constant cost and demand data we prove the optimality of a policy starting with remanufacturing before switching to manufacturing and give an estimation for the optimal switching point finally it is investigated how the disposal of excess inventory would change the solution

retail replenishment models with display space elastic demand we study a single store multi product inventory problem in which product sales are a composite function of shelf space since sales tend to deplete the amount of product on display the effective shelf space assigned to the product diminishes with time unless replenishment occurs we consider the problem of optimal replenishment times under these conditions we assume a linear dependence of sales rate to effective shelf space in all our analysis we present exact and approximate solutions for the single product and multi product cases for the single product case we study the effect of space elasticity cross elasticity and empty space elasticity on the optimal replenishment period for the multi product case we present a computationally attractive method using matrix exponentials and develop error bounds for this method

infinite horizon production planning in time varying systems with convex production and inventory costs we consider the planning of production over the infinite horizon in a system with time varying convex production and inventory holding costs this production lot size problem is frequently faced in industry where a forecast of future demand must be made and production is to be scheduled based on the forecast because forecasts of the future are costly and difficult to validate a firm would like to minimize the number of periods into the future it needs to forecast in order to make an optimal production decision today in this paper we first prove that under very general conditions finite horizon versions of the problem exist that lead to an optimal production level at any decision epoch in particular we show it suffices for the first period infinite horizon production decision to solve for a horizon that exceeds the longest time interval over which it can prove profitable to carry inventory we then develop a closed form expression for computing such a horizon and provide a simple finite algorithm to recursively compute an infinite horizon optimal production schedule

the profit maximizing capacitated lot size pclsp problem this paper extends the results for capacitated lot sizing research to include pricing based on a few examples the new version appears to by much easier to solve computationally the paper by including price can modify demand as well as production schedule due to model assumptions form of demand a feasible solution can be found easily unlike clsp