analysis of an inventory system with exponential partial backordering abstract in this paper we study an inventory model with partial backlogging where unsatisfied demand is partially backlogged according to an exponential function in this model the total cost is the sum of the order cost the holding cost the backorder cost which includes a fixed cost and a cost proportional to the length of time for which the backorder exists and the cost of lost sales a general approach for finding the optimal policy is developed numerical examples are used to illustrate how the approach works

model and heuristic algorithm of the joint replenishment problem with complete backordering and correlated demand abstract in practice demands for items are often correlated with each other because of cross selling effects traditional inventory models hold the assumption that demands are independent which may lead to the risk of misestimating the inventory cost of associated items this paper addresses a multi item inventory system where demands for some minor items are correlated with that for a major item because of the cross selling demand for minor items may either be raised by the sales of the major item or be pulled down by the unsatisfied demands for the major item thus a joint inventory policy considering correlations across items should be pursued considering general integer policy we propose a joint replenishment problem jrp model with complete backordering and correlated demand through the use of derivatives the model is transformed to minimize a cost function with respect to multiples of the major item s order cycle given that the optimal solution should offer a trade off between the ordering cost and the inventory holding cost of each item we develop a heuristic algorithm by adjusting the replenishment frequencies of minor items to solve the model the heuristic is tested by simulated numerical examples and shows satisfactory results

information rational expectations and macroeconomic modelling book reivewed in this article thomas j sargent 1987 dynamic macroeconomic theory m hashem pesaran 1987 the limits to rational expectations

theoretical analysis regarding a zero lower bound on nominal interest rates this paper explores several issues concerning a possible zero lower bound zlb including its theoretical rationale the magnitude of effects of low sustained inflation on real interest rates the validity of analyzing monetary policy in models with no monetary variables and the dynamic stabilizing properties of taylor rules in a zlb context the most important argument however is that if the short nominal rate is immobilized at zero there nevertheless exists a route for monetary stabilization policy to be effective via the foreign exchange market its quantitative importance is examined in a calibrated optimizing open economy model

an economic order quantity model with partial backordering and all units discount abstract the classic economic order quantity model assumes that the unit purchasing cost is not based on the order quantity in practice a supplier may offer purchasers an all units discount we develop a model and solution procedure for the eoq with all unit discounts and partial backordering at a constant rate we show and illustrate with a numerical example how that model can be used to find the solution for the eoq with discount and full backordering a multi factor experiment is used to gain insights into the improvement in performance of the proposed procedure relative to using the basic eoq or the eoq with full backordering and to identify the model parameters that have the greatest impact on the model s performance

optimal lot size for a production inventory system with partial backlogging and mixture of dispatching policies abstract in this paper we study a production inventory model for a single product where shortages are partially backlogged both the backorder cost and the lost sale cost depend on a fixed cost and a cost proportional to the shortage time we assume a mixture between the dispatching policies known as lifo last in first out and fifo first in first out in the discipline of service to fill the backlogged demand by using a sequential optimization procedure we determine in a closed form the optimal production policies and the optimal profit for all the possible cases obtained from the developed model we show how this new model generalizes several inventory models proposed in the literature finally numerical results are presented to analyze the sensitivity of the optimal policies with respect to changes in some parameters of the system

on monetary theory in this lecture i shall take up three topics the demand for money the implication of missing markets for the theory of asset pricing and lastly equilibrium with asymmetric information with special focus on the credit market all of these topics have been the subject of much recent work and my debt to that work will be obvious my manner of proceeding is somewhat abstract this is largely due to the circumstances of my intellectual past i simply find it easier and more likely to avoid mistakes however i shall attempt to bring out the main elements of my story without going through all of the algebra the main points derive from a single theme which in one way or another has interested me for a long time an economy which uses an intrinsically worthless means of exchange must be what radner called a sequence economy that is in contrast to an arrow debreu economy it must have trading at every date thus at the centre of monetary theory we require an economy which either makes it too costly or impossible to engage in all desirable arrow debreu trades in i97i and i973 this led me to study economies in which transaction costs were an essential element some of the results particularly on the constrained pareto inefficiency of such economies have recently re emerged in a different context and i shall discuss them later but there are other explanations for the absence of desired trading possibilities which turn on moral hazard and on adverse selection my discussion of these elements of an eventually satisfactory theory is the least satisfactory i have not found it possible either to formulate sharp propositions or to agree that those which have recently been proposed are satisfactory at the very end of this lecture i shall take a very brief look at one particular macro economic implication of my analysis much of what goes under the title of classical macro economics i find profoundly unsatisfactory i find it so not because of any keynesian pieties nor i hope because of political preferences it is the crudeness and incompleteness of the theoretical foundation which

deteriorating inventory model with quantity discount pricing and partial backordering inventory models with quantity discount pricing and partial backordering although common in practice have received very little attention from researchers the objective of this study is to develop a deterministic inventory model with quantity discount pricing and partial backordering when the product in stock deteriorates with time most retailers make pricing decisions of their products at certain times of the year and these decisions affect demand in this study the demand rate is assumed to decrease as price for the product increases unlike traditional inventory models that seek to minimize cost the objective of this study is to maximize profit the findings of this study are particularly relevant to retailers of deteriorating products in a competitive environment a numerical example is given to illustrate the theory

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

deterministic eoq with partial backordering and correlated demand caused by cross selling abstract there has been much work regarding the deterministic eoq with partial backordering the majority of these studies assume no correlation in sales so independent demands across items is applied in the models however it is generally recognized that cross selling effects between items often appear in real contexts thus incorporating such effects in the inventory model in the form of correlated demands makes it of more practical relevance in this paper the authors address a two item inventory system where the demand of a minor item is correlated to that of a major item because of cross selling we firstly present a two item eoq model with identical order cycles where the unmet demand of the major item can be partially backordered with lost sales whereas the demand of the minor item must be met without stockouts this model is further extended to fit a more practical case where the order cycle of the major item is an integer multiple of that of the minor item the optimal solutions of the two models as well as the inventory decision procedures are also developed comparative analysis on these two eoq models has been drawn in the computational study which presents some insights into the parameter effect on the optimal inventory policy

the deterministic eoq with partial backordering a new approach previous authors have shown that if demand that cannot be filled from stock is partially backordered then using the full backordering model or assuming that all stockouts will result in lost sales can lead to substantial increases in cost relative to using a model that specifically recognizes the percentage of the stockouts that will be backordered the models that these authors developed resulted in procedures or equations that are relatively difficult to use in this paper we take a different approach to modeling the deterministic eoq with partial backordering that results in equations that are more like the comparable equations for the basic eoq and its full backordering extension

an economic order quantity model with a known price increase and partial backordering abstract a constant unit purchase cost is one of the main assumptions in the classic economic order quantity model in practice suppliers sometimes face a known price increase in this paper we develop eoq models with a known price increase and partial backordering under two different assumptions about when the increase will occur we prove the concavity of the extra profit functions for both scenarios if a special order is placed just before the price increases a solution method is proposed and numerical examples are presented

the production inventory problem of a product with time varying demand production and deterioration rates abstract in this paper we consider the production inventory problem in which the demand production and deterioration rates of a product are assumed to vary with time shortages of a cycle are allowed to be backlogged partially two models are developed for the problem by employing different modeling approaches over an infinite planning horizon solution procedures are derived for determining the optimal replenishment policies a procedure to find the near optimal operating policy of the problem over a finite time horizon is also suggested

an economic order quantity model with partial backordering and a special sale price abstract a constant unit purchase cost is one of the main assumptions in the classic economic order quantity model in practice suppliers sometimes offer special sale prices to stimulate sales or decrease inventories of certain items in this paper we develop an eoq model with a special sale price and partial backordering we prove the convexity of the cost reduction function if a special order is placed at the special sale price a solution method is proposed and numerical examples are presented

an inventory control model with stochastic review interval and special sale offer abstract periodic review inventory models are widely used in practice especially for inventory systems in which many different items are purchased from the same supplier however most of periodic review models have assumed a fixed length of the review periods in practice it is possible that the review periods are of a random stochastic length this paper presents an inventory control model in the case of random review intervals and special sale offer from the supplier the replenishment interval is assumed to obey from two different distributions namely exponential and uniform distributions also shortages are allowed in the term of partial backordering for this model its convexity condition is discussed and closed form solutions are proposed

how many parts to make at once reprinted from factory the magazine of management volume 10 number 2 february 1913 pp 135 136 152 interest on capital tied up in wages material and overhead sets a maximum limit to the quantity of parts which can be profitably manufactured at one time set up costs on the job fix the minimum experience has shown one manager a way to determine the economical size of lots

a century of evolution from harris s basic lot size model survey and research agenda abstract determining the economic lot size has always represented one of the most important issues in production planning this problem has long attracted the attention of researchers and several models have been developed to meet requirements at minimum cost in this paper we explore and discuss the evolution of these models during one hundred years of history starting from the basic model developed by harris in 1913 up to today following harris s work a number of researchers have devised extensions that incorporate additional considerations the evolution of eoq theory strongly reflects the development of industrial systems over the past century here we outline all the research areas faced in the past by conducting a holistic analysis of 219 selected journal papers and trying to give a comprehensive view of past work on the eoq problem finally a new research agenda is proposed and discussed

pareto optima and competitive equilibria with adverse selection and moral hazard this paper explores the extent to which standard general equilibrium analysis of pareto optima and of competitive equilibria can be applied to environments with moral hazard and adverse selection problems allowing for lotteries contracts with random components we first establish that an adverse selection insurance economy a moral hazard insurance economy a signaling economy and a private information labor market economy are all special cases of a simple general structure we then show that techniques for characterizing pareto optimal contracts as solutions to concave programming problems are useful and nice and appear to be broadly applicable allowing for lotteries we show how to characterize the optimal allocations for the adverse selection insurance and labor market economies we then show that standard existence and optimality theorems for competitive equilibria apply in the linear space containing lotteries if agents with characteristics which are distinct and privately observed at the time of initial trading enter the economy wide resource constraints in a homogeneous way other kinds of diversity are not critical for economies with moral hazard which satisfy the homogeneity condition competitive contract markets single out a subset of the optima and thus can be consistent with apparent unemployment and with a random allocation of labor supplied though all households are averse to risk the adverse selection insurance and signaling economies however do not satisfy the homogeneity condition and are difficult to decentralize efficiently with a price system

an eoq model for perishable product with special sale and shortage abstract in this paper for the first time an inventory control model to determine the optimal order and shortage quantities of a perishable item when the supplier offers a special sale is developed four possible cases based on decision that the purchaser might make about the first replenishment policy using regular economic order quantity model at reduced price or regular price if he did not take the special order and coincidence of special period length with positive or negative inventory level of the last regular period length during the special period are investigated moreover several useful theorems are suggested through which one can find closed form solution directly when there are integer operators involved in an objective function at the end in order to illustrate the proposed theorems and the solution method some numerical examples are solved and a sensitivity analysis is reported too

an integrated production inventory model with imperfect production processes and weibull distribution deterioration under inflation abstract this study develops an integrated production and inventory model from the perspectives of both the manufacturer and the retailer the model assumes a varying rate of deterioration partial backordering inflation imperfect production processes and multiple deliveries the elapsed time until the production process shift is assumed to be arbitrarily distributed the discounted cash flow and classical optimization technique are used to derive the optimal solution a numerical example including the sensitivity analysis is given to validate the results of the production inventory model the integrated decision results in lower optimal joint cost compared with an independent decision by the manufacturer and the retailer

the deterministic eoq and epq with partial backordering at a rate that is linearly dependent on the time to delivery abstract our original models for the eoq and epq with partial backordering assumed that the backordering rate is a constant in this paper we extend those models to allow to increase linearly as the time until delivery decreases we show how those previous models can be adapted to find the optimal decision variable values for this new assumption and develop for each model type a condition that the initial value of must meet for partial backordering to be optimal

planning for shortages net present value analysis for a deteriorating item with partial backlogging abstract this paper develops inventory models to help answer strategic questions concerning whether planning for shortages offers financial benefits a production inventory system producing a deteriorating product in batches at a finite production rate with partial backordering is considered customers pay a deposit when placing a backorder backordered items receive a discount on the sales price as lost sales may lead to customers not returning the demand rate may depend on the fraction of lost sales we develop a cash flow based profit maximising net present value npv model without the inventory cost parameters commonly used in this context unit holding cost unit backorder cost unit deterioration cost and unit lost sales cost the model finds the optimal inventory policy just like npv models that discount the traditional parameters but has the advantage of not needing to estimate the value of the traditional parameters it is shown that in models based on discounting the traditional parameters the parameters are not exogenously determinable but are non trivial functions of non financial endogenous system parameters such as the production rate annual demand rate and backorder rate extensive numerical experiments illustrate how cash flow npv models provide insights into the value of planning for shortages and strategic choices about the design of the production inventory system it also provides insight into the classical problem of how to interpret unit backorder cost and unit lost sales cost the study indicates that these insights cannot be reliably obtained from npv models based on discounting unit backorder costs and unit lost sales costs

an extension of partial backordering eoq with correlated demand caused by cross selling considering multiple minor items abstract zhang et al 2011 proposed the partial backordering eoq with correlated demand caused by cross selling where a portion of the sales of a minor item is associated with those of a major item in this paper we extend their model to make it more applicable to dealing with the inventory replenishment problem for multiple associated items we formulate the model as a mixed integer nonlinear programming minlp problem and develop a global optimum search procedure with the fill rate given we further employ a one dimensional search on the fill rate to obtain the minimum total inventory cost within a predetermined precision which enjoys polynomial computational complexity

optimal monetary policy with missing markets in real business cycle models with spot markets agents respond optimally to fluctuations by varying their labor supply while this is individually optimal the employment volatility that results is efficient the inefficiency is due to the lack of forward markets for labor and the consequent inability of the young to insure against future shocks a real business cycle model is constructed in which an active monetary policy accommodating past price shocks to prevent the expectation of price reversion pareto dominates a stable moeny stock by stabilizing employment over the cycle stable employment approximates the outcome with complete insurance markets the young would like to sell a fixed volume of labor forward allowing less risk averse agents to bear the volatility in the spot labor market these results undermine the use of the full information competitive equilibrium as a benchmark for policy analysis in spot market models copyright 1989 by the london school of economics and political science

optimal pricing and lot sizing under conditions of perishability and partial backordering we formulate a generalized model of dynamic pricing and lot sizing by a reseller who sells a perishable good we assume that when it is economic to backlog demand the reseller can plan for periods of shortage during which demand can be partially backordered when the good is highly perishable the reseller may need to backlog demand in order to market the good at a reasonable price we present a simple solution procedure for solving the optimization problem the procedure entails solving first a single nonlinear equation and then if required two nonlinear equations

a survey of deterministic models for the eoq and epq with partial backordering models for the basic deterministic eoq or epq problem with partial backordering or backlogging make all the assumptions of the classic eoq or epq model with full backordering except that only a fraction of the demand during the stockout period is backordered in this survey we review deterministic models that have been developed over the past 40 years that address the basic models and extensions that add other considerations such as pricing perishable or deteriorating inventory time varying or stock dependent demand quantity discounts or multiple warehouses

generalized eoq formula using a new parameter coefficient of backorder attractiveness abstract this paper introduces and examines a generalized eoq formula based on the model with linear and fixed backordering costs the new square root formula is a combination of two well known classical models the basic eoq model without stockouts and the eoq model with backorders and linear backordering costs helping to combine the two is a new parameter a fractional coefficient capturing the attractiveness of backorders the coefficient is explained and discussed the paper concludes with a brief discussion of generalizations in eoq models including epq