a comparison among various partial backlogging inventory lot size models for deteriorating items on the basis of maximum profit abstract during the past few years there are many researches that deal with different inventory shortage models for deteriorating items and then use minimizing cost as objective to find the optimal replenishment policy over a finite planning horizon in contrast to the other articles we here use maximizing profit as the objective to find the optimal replenishment policy we consider the case of partial backlogging for deteriorating items with four different inventory models not only the opportunity cost due to lost sale but also the purchase cost is taken into account we then make an appropriate comparison among these four alternatives finally some numerical examples are provided

optimal lot size model for deteriorating items with demand rate dependent on displayed stock level dsl and partial backordering in this paper we consider the problem of determining the lot size of a single deteriorating item with the demand rate dependent on displayed stock level selling price of an item and frequency of advertisement in the popular electronic and print media also through the sales representatives shortages if any are allowed and partially backlogged with a variable rate which depends on the duration of waiting time upto the arrival of next lot here the transportation cost for replenishing the goods is considered explicitly and the storage capacity of the showroom shop is assumed to be limited finite according to the relative size of the stock level dependency demand parameters and the storage capacity of the showroom shop different scenarios with sub scenarios have been mentioned and solved with the help of grg generalised reduced gradient method and the computational procedure the convexity analysis is done by showing the average profit function in each case as pseudo concave to illustrate the results and its significant features a numerical example is given finally to study the effect of changes of demand parameters deterioration backlogging parameters and mark up rate on the maximum initial stock level shortage level frequency of advertisement per cycle along with the maximum average profit are presented numerically

optimal pricing and lot sizing under conditions of perishability finite production and partial backordering and lost sale abstract perishable products constitute a sizable component of inventories common questions in a production and selling situation involving a perishable or a non perishable product are what should be the price and what should be the size of the replenishment when demand for the product is price sensitive pricing and lot sizing decisions are interdependent similarly when a product is highly perishable the demand may need to be backlogged to avoid costs due to deterioration i e perishability and backlogging are complementary conditions in this paper we consider the pricing and lot sizing problem for a perishable good under finite production exponential decay and partial backordering and lost sale the backlogging phenomenon in the literature is often modeled using backordering and lost sale costs these cost parameters however are not easy to estimate in practice in this paper we use a new approach to model backlogging of demand in this approach customers are viewed to be impatient the backlogging option gets used only when it is economic to do so we extend the analysis presented for a perishable product to the case in which the product is non perishable

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

purchasing power parity in the long run a cointegration approach this paper utilizes cointegration analysis to examine purchasing power parity relationships over a long time horizon the results indicate that the exchange rate is cointegrated strongly with the wholesale price index ratio and somewhat weakly with the consumer price index ratio the cointegrating coefficient between the exchange rate and the price ratio is close to one when cointegration is confirmed the hypothesis that the real exchange rate follows a random walk is rejected in most cases finally a new test for common trends finds no such common trends in exchange rates or price ratios copyright 1990 by ohio state university press

deviations from purchasing power parity in the long run this paper demonstrates that deviations from purchasing power parity reveal a remarkable and possibly startling consistency with martingale behavior during both fixed and flexible rate periods for a wide variety of countries and in both monthly and annual data since this pattern appears to be much more general than one would expect on the basis of models founded on international commodity arbitrage the paper proposes an alternative explanation which instead relies on financial arbitrage in bonds as the underlying mechanism this paper will demonstrate that deviations from purchasing power parity ppp reveal a remarkable and possibly startling consistency with martingale behavior during both fixed and flexible exchange rate periods for a wide variety of countries and in both monthly and annual data this pattern appears to be much more general than one would expect on the basis of models founded on international commodity arbitrage the paper therefore proposes an alternative explanation which does not presuppose free trade in goods but which instead relies on financial arbitrage in bonds as the underlying mechanism the major implication of the theory and the results is that ppp is as likely to be violated in the long as in the short run as an empirical matter deviations from ppp can be observed for most currencies at any instant see kravis et al 21 stockman 37 and genberg 15 among others these deviations are typically both cumulative and persistent the real exchange rate can remain on either side of parity for lengthy but variable time intervals of a year or more as a consequence the current consensus shared

two warehouse partial backlogging inventory models for deteriorating items under inflation abstract in many real life situations the practical experiences reveal that some but not all customers will wait for backlogged items during a shortage period such as for fashionable commodities or high tech products with short product life cycle the longer the waiting time is the smaller the backlogging rate would be according to such phenomenon taking the backlogging rate into account is necessary thus i here extend the models introduced in yang 2004 two warehouse inventory models for deteriorating items with shortages under inflation european journal of operational research 157 2 344 356 to incorporate partial backlogging and then compare the two two warehouse inventory models based on the minimum cost approach the study shows that the optimal solution not only exists but also is unique and model 2 is still less expensive to operate than model 1 if the factors of partial backlogging and inflationary effect are considered finally some numerical examples for illustration are provided and sensitivity analysis on some parameters is made

deterministic inventory model for deteriorating items with capacity constraint and time proportional backlogging rate in this paper a deterministic inventory model for deteriorating items with two warehouses is developed a rented warehouse is used when the ordering quantity exceeds the limited capacity of the owned warehouse and it is assumed that deterioration rates of items in the two warehouses may be different in addition we allow for shortages in the owned warehouse and assume that the backlogging demand rate is dependent on the duration of the stockout we obtain the condition when to rent the warehouse and provide simple solution procedures for finding the maximum total profit per unit time further we use a numerical example to illustrate the model and conclude the paper with suggestions for possible future research

a note on eoq models for deteriorating items under stock dependent selling rate abstract in 1995 padmanabhan and vrat presented inventory models for deteriorating items with stock dependent selling rate and derived the profit functions without backlogging and with complete backlogging first this paper develops the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions of the profit per unit time functions without backlogging and with complete backlogging second this paper explains that it is appropriate to use the newton raphson method to find the optimal solutions of the profit functions per unit time in both situations modelled

partial backlogging inventory lot size models for deteriorating items with fluctuating demand under inflation abstract in this paper the traditional inventory lot size model is extended to allow not only for general partial backlogging rate but also for inflation the assumptions of equal cycle length and constant shortage length imposed in the model developed by moon et al moon i giri b c ko b 2005 economic order quantity models for ameliorating deteriorating items under inflation and time discounting european journal of operational research 162 3 773 785 are also relaxed for any given number of replenishment cycles the existence of a unique optimal replenishment schedule is proved and further the convexity of the total cost function of the inventory system in the number of replenishments is established the theoretical results here amend those in yang et al yang h l teng j t chern m s 2001 deterministic inventory lot size models under inflation with shortages and deterioration for fluctuating demand naval research logistics 48 2 144 158 and provide the solution to those two counterexamples by skouri and papachristos skouri k papachristos s 2002 note on deterministic inventory lot size models under inflation with shortages and deterioration for fluctuating demand by yang et al naval research logistics 49 5 527 529 finally we propose an algorithm to find the solution and obtain some managerial results by using sensitivity analyses

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

an inventory model with partial backordering and unit backorder cost linearly increasing with the waiting time as the implementation of jit practice becomes increasingly popular each echelon in a supply chain tends to carry fewer inventories and thus the whole supply chain is made more vulnerable to lost sales and or backorders the purpose of this paper is to recast the inventory model to be more relevant to current situations where the penalty cost for a shortage occurrence at a downstream stage in a supply chain is continually transmitted to the upstream stages the supplier in this case at the upstream of the supply chain is responsible for all the downstream shortages due to the chain reaction of its backlog the current paper proposes a model in which the backorder cost per unit time is a linearly increasing function of shortage time and it claims that the optimal policy for the supplier is setting the optimal shortage time per inventory cycle to minimize its total relevant cost in a jit environment

lag length selection and tests of granger causality between money and income one of the most widely accepred relationships in macroeconomics is the positive relationship between the rate of growth of the money supply and the rate of growth of income a diversity of opinion arises however with the attempt to identify a causal relationship between these variables while friedman and schwartz 1963 initiated the empirical investigation of money income causality sims 1972 made the most significant contribution to this literature with a practical application of the criterion developed by granger 1969 for identifying a causal relationship since the appearance of sims s approach and an alternative one advanced by sargent 1976 many researchers have applied these techniques to the investigation of the causal relationship between money and income l with two exceptions hsiao 1981 and mcmillin and fackler 1984 these researchers have arbitrarily chosen the lengths of their distributed lags the purpose of this paper is to test for granger causality between money and income this paper differs from previous work in that considerably more attention is focused on the effect of the lag specification on the test results in particular we investigate the extent to which rules of thumb arbitrary lag specifications and

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

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

real exchange rates in the short medium and long run abstract this paper uses long horizon autocorrelations and variance ratio statistics to test for long term mean reversion in real exchange rates unlike most previous tests of this hypothesis the tests do reject a random walk for monthly data in the post bretton woods era however the statistics indicate that positively correlated innovations rather than mean reversion are the source of the rejection tests using annual data for the twentieth century also reject the random walk in this case however the rejection can be attributed to mean reversion and confirms that ppp is a long term phenomenon

an inventory model with generalized type demand deterioration and backorder rates abstract this study is motivated by the paper of skouri et al skouri konstantaras papachristos ganas european journal of operational research 192 1 2009 79 92 we extend their inventory model from ramp type demand rate and weibull deterioration rate to arbitrary demand rate and arbitrary deterioration rate in the consideration of partial backorder we demonstrate that the optimal solution is actually independent of demand that is for a finite time horizon any attempt at tackling targeted inventory models under ramp type or any other types of the demand becomes redundant our analytical approach dramatically simplifies the solution procedure

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

inflation and the optimal inventory replenishment schedule within a finite planning horizon abstract the subject of this paper is the problem of finding the optimal replenishment schedule for an inventory subject to time dependent demand and deterioration within a finite time planning horizon it is shown that taking inflation into account has a profound effect on the solution of the problem for instance there is a critical number of replenishment periods in excess of which the optimal schedule is characterized by the inclusion of token orders at the end of the planning horizon this and other conclusions obtained via a careful mathematical analysis of the problem rectify those of earlier studies

an inventory model under inflation for deteriorating items with stock dependent consumption rate and partial backlogging shortages abstract in this paper we extend teng j t chang h j dye c y hung c h 2002 an optimal replenishment policy for deteriorating items with time varying demand and partial backlogging operations research letters 30 6 387 393 and hou k l 2006 an inventory model for deteriorating items with stock dependent consumption rate and shortages under inflation and time discounting european journal of operational research 168 2 463 474 by considering an inventory lot size model under inflation for deteriorating items with stock dependent consumption rate when shortages are partial backlogging the proposed model allows for 1 partial backlogging 2 time varying replenishment cycles and 3 time varying shortage intervals consequently the proposed model is in a general framework that includes numerous previous models as special cases we then prove that the optimal replenishment schedule exists uniquely and provide a good estimate for finding the optimal replenishment number furthermore we briefly discuss some special cases of the proposed model related to previous models finally numerical examples to illustrate the solution process and some managerial implications are provided

real and nominal exchange rates in the long run an empirical investigation abstract this paper reports on econometric tests of the hypothesis that purchasing power parity holds as a long run relationship using data on eight industrialized countries during the flexible exchange rate period the empirical work proceeds by i testing whether nominal exchange rates and relative price levels are co integrated and ii conducting impulse response analysis of long run exchange rate and relative price level changes to explain the data keynesian models suggest that shocks during the estimation period were due principally to exogenous shifts in aggregate demand while equilibrium models suggest that monetary factors have been relatively more important

an eoq model for perishable items under stock dependent selling rate and time dependent partial backlogging in the present paper we extend padmanabhan and vrat s model by proposing a time proportional backlogging rate to make the theory more applicable in practice the existence and uniqueness of the solutions of the relevant systems are examined subsequently a numerical example is presented to illustrate the application of developed model

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

inventory models with ramp type demand rate partial backlogging and weibull deterioration rate in this paper an inventory model with general ramp type demand rate time dependent weibull deterioration rate and partial backlogging of unsatisfied demand is considered the model is studied under the following different replenishment policies a starting with no shortages and b starting with shortages the model is fairly general as the demand rate up to the time point of its stabilization is a general function of time the backlogging rate is any non increasing function of the waiting time up to the next replenishment the optimal replenishment policy for the model is derived for both the above mentioned policies

optimal stopping and restarting production times for an eoq model with deteriorating items and time dependent partial backlogging abstract yan and cheng j operational res soc 49 1998 1288 1295 presented a general production inventory model with production rate product demand rate and deterioration rate all considered as functions of the time their model allows for shortages and partial backlogging of the unsatisfied demand at a constant rate in this paper we extend the results of yan and cheng to cover the case where the backlogging rate is a time dependent function and we propose an algorithm for the solution of this problem we also propose some conditions which we believe to be necessary for the validity for some of yan s and cheng s statements the paper closes with numerical examples which cover each one of the cases considered in the paper

note on inventory model with a mixture of back orders and lost sales abstract competitiveness is an important means of determining whether a company will prosper business organizations compete with one another in a variety of ways among these competitive methods are time and cost factors the purpose of this paper is to examine the inventory models presented by padmanabhan and vrat international journal of systems sciences 21 1990 1721 with a mixture of back orders and lost sales we develop the criterion for the optimal solution for the total cost function if the criterion is not satisfied this model will degenerate into one cycle inventory model with a finite inventory period this implies an extension of shortage period as long as possible to produce lower cost however we know that time is another important factor in company competitiveness customers will not indefinitely wait for back orders a tradeoff will be made between the two most important factors time and cost the minimum total cost is evaluated under the diversity cycle time and illustrations are applied to explain the calculation process this work provides a reference for decision makers

a reexamination of the uncovered interest rate parity hypothesis abstract it is now widely known that the uncovered interest rate parity uip hypothesis which states that forward exchange rates are unbiased predictors of future spot exchange rates is generally rejected by empirical evidence we show in this paper by means of a cox et al 1985 model extended to a two country economy that a careful examination of the no arbitrage principle leads to a different formulation for this hypothesis roughly speaking this new formulation states that the expected future spot exchange rate is equal to the forward exchange rate multiplied by a term premium whose closed form expression can be derived moreover this multiplicative term premium reduces to 1 i e the standard uip hypothesis holds if and only if conditional variances are deterministic in short we show that rejection of the standard uip hypothesis is not surprising as long as arch effects have been evidenced in exchange rate data as a by product we provide a parametric and tractable specification for the so called risk premium i e the component of the expected exchange rate in excess of the forward exchange rate

a deteriorating inventory model with time varying demand and shortage dependent partial backlogging abstract recently chu et al p chu k l yang s k liang t niu note on inventory model with a mixture of back orders and lost sales european journal of operational research 159 2004 470 475 presented the necessary condition of the existence and uniqueness of the optimal solution of padmanabhan and vrat g padmanabhan p vrat inventory model with a mixture of back orders and lost sales international journal of systems science 21 1990 1721 1726 however they included neither the purchase cost nor the cost of lost sales into the total cost in this paper we complement the shortcoming of their model by adding not only the cost of lost sales but also the non constant purchase cost and then extend their model from a constant demand function to any log concave demand function we also provide a simple solution procedure to find the optimal replenishment schedule further we use a couple of numerical examples to illustrate the results and conclude with suggestions for future research

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 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

a generalization of sensitivity of the inventory model with partial backorders abstract in this paper we use the elementary techniques of differential calculus to investigate the sensitivity analysis of montgomery et al s montgomery d c bazaraa m s keswani a k 1973 inventory models with a mixture of backorders and lost sales naval research logistics quarterly 20 225 263 inventory model with a mixture of backorders and lost sales and generalize chu and chung s chu p chung k j 2004 the sensitivity of the inventory model with partial backorders european journal of operational research 152 289 295 sensitivity analysis we provide three numerical examples to demonstrate our findings and remark the interpretation of the global minimum of the average annual cost at which the complete backordering occurs

autoregressive modelling and money income causality detection abstract a step wise procedure based on granger s concept of causality and abaike s final prediction error criterion is suggested as a practical means to identify the order of lags of each variable in a multivariate autoregressive process the model seems useful because it can serve as a reduced form formulation to avoid imposing often spurious or false restrictions of the model it also provides a reasonably powerful test of causality the idea is applied to u s postwar money and income data it is found that between m1 and gnp a bivariate feedback model fits the data best between m2 and gnp a one way causal model from money to income performs better diagnostic checks applied to our model seem to indicate the adequacy of our approach

optimal price and order size under partial backordering incorporating shortage backorder and lost sale costs abstract in this paper we consider the pricing and lot sizing problem for a product subject to general rate of deterioration and partial backordering we use impatience functions to model backlogging of demand we show that even when lost sale and backorder costs are present the problem is well posed in the reduced space we provide an iterative procedure for solving the overall problem we describe structural properties of the solution for the new model and comment on the recent work incorporating backorder cost we illustrate the solution procedure for the new model with examples

determining optimal selling price and lot size with a varying rate of deterioration and exponential partial backlogging in this paper a deterministic inventory model for deteriorating items with price dependent demand is developed the demand and deterioration rates are continuous and differentiable function of price and time respectively in addition we allow for shortages and the unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time under these assumptions for any given selling price we first develop the criterion for the optimal solution for the replenishment schedule and prove that the optimal replenishment policy not only exists but also is unique if the criterion is not satisfied the inventory system should not be operated next we show that the total profit per unit time is a concave function of price when the replenishment schedule is given we then provide a simple algorithm to find the optimal selling price and replenishment schedule for the proposed model finally we use numerical examples to illustrate the algorithm

retailer s optimal pricing and lot sizing policies for deteriorating items with partial backlogging pricing is a major strategy for a retailer to obtain its maximum profit therefore in this paper we establish an economic order quantity model for a retailer to determine its optimal selling price replenishment number and replenishment schedule with partial backlogging we first prove that the optimal replenishment schedule not only exists but also is unique for any given selling price next we show that the total profit is a concave function of p when the replenishment number and schedule are given we then provide a simple algorithm to find the optimal selling price replenishment number and replenishment timing for the proposed model finally we use a couple of numerical examples to illustrate the algorithm

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

an inventory model with deteriorating items quantity discount pricing and time dependent partial backlogging abstract wee international journal of production economics 59 1999 511 in his interesting paper presented a deterministic inventory model with the following characteristics quantity discount schemes for the unit cost partial backlogging at a fixed rate deterioration of stock in time and demand rate being a linear function of the selling price in this article we generalize the work of wee 1999 more specifically we consider a model where the demand rate is a convex decreasing function of the selling price and the backlogging rate is a time dependent function which ensures that the rate of backlogged demand increases as the waiting time to the following replenishment point decreases

an application of tournament genetic algorithm in a marketing oriented economic production lot size model for deteriorating items abstract the goal of this research is to discuss an application of tournament genetic algorithm tga for solving an economic production lot size epl model in this model the production rate of the item is finite and it is assumed to be a decision variable the demand rate is also a deterministic function of selling price and the marketing cost the selling price per unit item is determined by a mark up over the unit production cost the deterioration rate at any instant is a linear increasing decreasing function of time partial backlogging shortages are allowed with a variable rate dependent on the length of the waiting time up to the starting of next production this model is formulated as a highly non linear constrained optimization problem to solve this problem a tga with steady state selection whole arithmetic crossover and non uniform mutation has been developed and applied the model has been illustrated with three numerical examples finally sensitivity analyses have been shown graphically to study the variations of the average profit with respect to the different parameters

flexible exchange rates prices and the role of news lessons from the 1970s recent experience with flexible exchange rate systems has led to renewed interest in the operation of foreign exchange markets as reflected in many recent studies of the principal determinants of exchange rates the 1970s witnessed the dramatic alteration of the international monetary system from a regime of pegged exchange rates which prevailed for about a quarter of a century since the bretton woods conference into a regime of flexible though managed rates as a consequence of the emergence of the new legal and economic system traders national governments and international organisations were confronted with new economic problems choices and instruments during the 1970s ex change rates fluctuated widely and inflation rates accelerated the international monetary system had to accommodate extraordinarily large oil related shocks which affected trade flows in goods and assets huge oil payments had to be recycled uncertainties concerning future developments in international politics reached new heights and the prospects for the world economy got gloomier these developments placed unprecedented pressures on the markets for foreign exchange as well as on other asset markets they were associated with a large slide in the value of the us dollar and resulted in speeding up the creation of new institutions like the european monetary system which provided the formal framework for the management of exchange rates among members

on an eoq model for perishable items under stock dependent selling rate and time dependent partial backlogging by dye and ouyang in 2005 dye and ouyang proposed an eoq model for perishable items under stock dependent selling rate and time dependent partial backlogging and then established the unique optimal solution to the problem when building up inventory is not profitable however they did not provide the optimal solution to the problem when building up inventory is profitable in this note we establish an appropriate model in which building up inventory is profitable and then provide an algorithm to find the optimal solution to the problem a numerical example is used to illustrate the proposed model

optimal replenishment policies for non instantaneous deteriorating items with stock dependent demand abstract wu et al 2006 an optimal replenishment policy for non instantaneous deteriorating items with stock dependent demand and partial backlogging international journal of production economics 101 369 384 established an inventory model for non instantaneous deteriorating items with stock dependent demand and obtained the optimal replenishment policy in this paper we first amend wu et al s model by changing the objective to maximizing the total profit secondly we set a maximum inventory level in the model to reflect the facts that most retail outlets have limited shelf space thirdly we relax the restriction of zero ending inventory when shortages are not desirable we then establish the theoretical results and provide an algorithm to find the optimal solution finally we present some numerical examples to illustrate the results

arima and cointegration tests of ppp under fixed and flexible exchange rate regimes real exchange rates between the united states and its major trading partners were calculated for the bretton woods and flexible exchange rate periods unit root tests indicate that purchasing power parity performed poorly in both periods tests for cointegration reveal limited instances in which it is possible to estimate the deviations from ppp as an error correcting model the estimated error correcting models indicate that foreign but not u s prices responded to deviations from ppp frenkel s 1981b finding that purchasing power parity ppp worked better during the 1920s than the 1970s caused considerable controversy for example davutyan and pippenger 1985 contend that the socalled collapse of ppp is a result of an increase in the relative importance of real versus monetary shocks they argue that the 1970s as opposed to the 1920s was characterized by real supply shocks and the international coordination of monetary policies the argument is that ppp did not fail rather there was an increase in the volatility of those factors giving rise to deviations from ppp hakkio 1984 reestimated ppp over the 1920s and 1970s using cross country tests i e sure estimates to improve the efficiency of his estimates he was able to support the hypothesis that ppp worked better in the 1970s than in the 1920s on the other hand papers by adler and lehman 1983 dornbusch 1980 frenkel 1981a junge 1985 and krugman 1978 report findings contrary to the ppp hypothesis moreover kenen and rodrik 1986 find that the volatility of real exchange rates has increased throughout the flexible rate period this paper tries to shed some light on the importance and persistence of the observed deviations from purchasing power parity under alternative exchange rate systems while it is interesting to compare ppp in the 1920s versus the 1970s it is equally useful to compare the 1960s versus the 1970s and 1980s if real supply shocks and lack of monetary coordination are characteristic of the latter period ppp should perform better in the 1960s to illustrate the issues involved consider the following econometric model of relative purchasing power

a comparison between two pricing and lot sizing models with partial backlogging and deteriorated items abstract recently abad 2003 optimal pricing and lot sizing under conditions of perishability finite production and partial backordering and lost sale european journal of operational research 144 677 685 studied the pricing and lot sizing problem for a perishable good under finite production exponential decay partial backordering and lost sale in this article we extend his model by adding not only the backlogging cost but also the cost of lost goodwill we then analytically compare the net profits per unit time between abad s 2003 model and goyal and giri s 2003 the production inventory problem of a product with time varying demand production and deterioration rates european journal of operational research 147 549 557 model in abad s model the cycle starts with an instant production to accumulate stocks then stops production to use up stocks and finally restarts production to meet the unsatisfied demands by contrast in goyal and giri s model the cycle begins with a period of shortages then starts production until accumulated inventory reaches certain level and finally stops production and uses up inventory our theoretical results show that there is no dominant one between these two models furthermore we provide certain conditions under which one model has more net profit per unit time than the other finally we give several numerical examples to illustrate the results

purchasing power parity abstract this paper examines the purchasing power parity henceforth ppp using historical data and the cointegration approach the results indicate that the exchange rate is cointegrated with the wholesale price index wpi ratio but not with the consumer price index cpi ratio the cointegrating vector is close to 0 1 for the cpi based real exchange rates however we cannot reject the random walk hypothesis the findings caution us on the use of general price indexes that give a large weight to nontraded goods and are therefore subject to long run deviations from ppp

an optimal replenishment policy for non instantaneous deteriorating items with stock dependent demand and partial backlogging abstract in this study we consider a problem of determining the optimal replenishment policy for non instantaneous deteriorating items with stock dependent demand in the model shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment the necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown as the special cases the results for the models with instantaneous or non instantaneous deterioration rate and with or without shortages are derived further we analytically identify the best circumstance among these special cases based on the minimum total relevant cost per unit time sensitivity analysis of the optimal solution with respect to major parameters is carried out finally four numerical examples are presented to demonstrate the developed model and the solution procedure

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

joint pricing and replenishment policy for deteriorating inventory with declining market abstract this study deals with a deteriorating inventory model where demand decreases linearly with time and cost of items planning horizon is assumed to be finite the replenishment cycles are constant and shortages are partially back ordered the net profit maximizing ordering policy and price are determined for different degree of partial back ordering the reduction in revenue resulted from lost sale is expressed in the lost sale shortage penalty in the total cost formulation a solution method based on nonlinear programming code and the hessian matrix guarantees global optimality of the solution a numerical example is provided to illustrate the theory

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

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

eoq models for perishable items under stock dependent selling rate this paper presents inventory models for perishable items with stock dependent selling rate the selling rate is assumed to be a function of current inventory level and rate of deterioration is taken to be constant under instantaneous replenishment with zero lead time the model incorporates aspects such as complete partial and no backlogging eoq is determined for maximizing the total profit in each of the situations the models developed are illustrated through numerical examples and sensitivity analysis is reported

long run purchasing power parity during the recent float abstract this paper examines the relevance of long run purchasing power parity ppp which allows for measurement errors during the recent floating exchange rate period previous empirical studies generally fail to find support for long run ppp over this period in this paper in this paper the cointegration property of exchange rates and prices is examined using maximum likelihood procedure and we find significant evidence favorable to long run ppp further tests for symmetry and proportionality indicate that these two conditions are not generally with the data the results support the hypothesis of long run ppp with measurement errors in prices

beyond the purchasing power parity testing for cointegration and causality between exchange rates prices and interest rates abstract this paper reexamines the causality between the dollar and the yen in a multivariate framework with the aid of cointegration and error correcting modeling for the 1951 94 period the phillips perron tests and johansen s tests are performed while causality from interest rates to exchange rates is found in the short run no causality between prices and exchange rates is found in the short run however causality is found running from relative prices to exchange rates along with interest rates between the u s and japan in the long run which supports the long run ppp hypothesis

inventory models with the demand rate dependent on stock and shortage levels this paper investigates an inventory system in which the demand rate during stockout periods differs from that during the in stock period by a given amount the previous analysis conducted in this area formulated the model as a cost minimization model this type of formulation will intentionally try to decrease demand by increasing the stockout period in order to decrease costs this paper appropriately considers the model as a profit maximization model and develops a closed form solution the model is then further generalized to incorporate the effect of stock level dependent demand rates and considers initial stock dependent demand as well as instantaneous stock dependent demand rates

cointegration and tests of purchasing power parity nonstationarity in the levels of spot exchange rates and domestic and foreign price indices makes the use of conventional tests of the absolute version of purchasing power parity ppp inappropriate if ppp is true inter country commodity arbitrage ensures that deviations from a linear combination of spot exchange rates and domestic and foreign price levels should be stationary under these conditions exchange rates and price levels should form a cointegrated system we find the null hypothesis of no cointegration cannot be rejected for all five countries thus violating the long run absolute version of ppp

unforeseen contingency and renegotiation with asymmetric information this article considers a buyer seller contracting model in which the seller possesses private information about all relevant aspects of the state of nature including how much each action is worth to the buyer i argue that given asymmetric information the buyer may not entirely dismiss an unforeseen contingency claim by the seller then if the buyer lacks the foresight awareness to expect the unexpected the model admits an equilibrium in which a seemingly complete contract is written and then renegotiated along its outcome path to generate inefficiency ex post

on the flexibility of demand and production rate in the manufacturing practice cycle time is usually optimized in order to plan the batch size and production time among other parameters in certain situations the production rate is decreased in order to have lower inventory levels or to deal with a shelf life constraint this technical note examines the increase decrease in the demand level along with a discussion concerning flexibility of the production rate a generalized problem is also formulated in the context of the costs that are incurred in order to maintain certain demand level

testing purchasing power parity under the null hypothesis of co integration this paper analyzes monthly data on the exchange rates and price indices of the eleven major industrial countries over the modern period of floating exchange rates it presents tests that are based upon the null hypothesis of cointegration the paper finds evidence that most country pairs not involving north american currencies have exchange rates and price indices that are cointegrated it estimates the error correction representation for the series that are cointegrated and it shows that the dynamic adjustment of the relationship between exchange rates and prices is accomplished almost entirely in the market for foreign exchange copyright 1991 by royal economic society

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

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

an empirical examination of long run purchasing power parity using cointegration techniques this paper presents an empirical analysis of long run purchasing power parity ppp for five major exchange rates using recently developed econometric techniques on the cointegration of economic time series our empirical results are extremely unfavourable to the ppp hypothesis as a long run equilibrium condition even with an allowance made for measurement error and or tranportation costs in particular we are unable to reject the hypothesis of non cointegration of the exchange rate and relative prices for any of the countries concerned far from finding a stable long run proportionality between exchange rates and relative prices our results therefore suggest that they tend to drift apart without bound

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

dynamic pricing and ordering decisions by a monopolist this paper considers the relationship between pricing and ordering decisions for a monopolistic retailer facing a known demand function where over the inventory cycle the product may exhibit i physical decay or deterioration of inventory called wastage and ii decrease in market value called value drop associated with each unit of inventory on hand the retailer is allowed to continuously vary the selling price of the product over the cycle we introduce a notion of instantaneous margin and use it to derive profit maximizing conditions for the retailer the model explains the markdown of retail goods subject to decay it also provides guidance in determining when price changes during the cycle are worthwhile due to product aging how often such changes should be made and how such changes affect ordering intervals and quantities