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

exclusive contracts and protection of investments we consider the effect of a renegotiable exclusive contract restricting a buyer to purchase from only one seller on the levels of noncontractible investments undertaken in their relationship contrary to some informal claims in the literature we find that exclusivity has no effect when all investments are fully specific to the relationship i e are purely internal exclusivity does matter when investments affect the value of the buyer s trade with other sellers i e have external effects we examine the effects of exclusivity on investments and aggregate welfare and the private incentives of the buyer seller coalition to use it

patent pools litigation and innovation this article analyzes patent pools and their effects on litigation incentives overall royalty rates and social welfare when patent rights are probabilistic and can be invalidated in court with probabilistic patents the license fees reflect the strength of the patents we show that patent pools of complementary patents can be used to discourage infringement by depriving potential licensees of the ability to selectively challenge patents and making them committed to a proposition of all or nothing in patent litigation if patents are sufficiently weak patent pools with complementary patents reduce social welfare as they charge higher licensing fees and chill subsequent innovation incentives

research joint venture with technology transfer kamien et al 1992 show that an industry wide research joint venture rjv compared to the case without any rjv does not lead to better technological development or a higher consumer surplus in contrast we show that every non industry wide rjv leads to strict improvements in both measures and it also results in higher production efficiency furthermore when technology transfer is possible after making rd et lorsque l efficacite de la recherche est faible ces ameliorations s amplifient davantage les gouvernements devraient promouvoir l innovation par l entremise de collaborations independantes avec transfert de technologie comme alternative a l etablissement de consortiums de recherche a l echelle de tout un secteur

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

why are small firms different managers views do incentives differ between large and small organizations results from a representative survey of compensation managers are used to shed light on the issues i find that i small establishments rely less on pecuniary incentives and have a significantly more hostile attitude towards incentive schemes based on competition and relative rewards ii large units are more vulnerable to mechanisms of efficiency wages effects that remain even after controlling for differences in monitoring ability iii large units are more prone to indicate that negative reciprocity is important and that their employees care about relative pay i argue that these findings fit with behavioral stories of incentives and motivation in particular those stressing group interaction effects inequity aversion and gift exchange

patenting in the shadow of competitors this article empirically examines the patenting behavior of new biotechnology firms that have different litigation costs i show that firms with high litigation costs are less likely to patent in subclasses with many other awards particularly those of firms with low litigation costs this pattern is consistent with the literature on costly litigation which suggests that firms that have high litigation costs will take greater precautions to avoid litigation these results are robust to a variety of control variables and modifications that seek to test alternative explanations

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

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

the e correspondence principle we present a new application of samuelson s correspondence principle to the analysis of comparative dynamics in stochastic rational expectations models our version which we call the e correspondence principle applies to rational expectations equilibria that are stable under least squares and closely related learning rules with this technique it is sometimes possible to study without explicitly solving for the equilibrium how qualitative properties of the equilibrium are affected by changes in the model parameters applications to overlapping generations and new keynesian models illustrate the potential of the technique

efficient division of profits from complementary innovations abstract many products including microprocessors telecommunications devices computer software and on line auction services make use of multiple technologies each of which is essential to make or sell the product the owner of one technology benefits from the existence of complementary technologies we show that despite this externality the structure of payoffs that support efficient r d investment by duopolists racing to discover a single innovation generalizes to the structure that supports efficient investment for complementary innovations the paper also examines how alternative intellectual property regimes and legal institutions affect r d investment in complementary technologies the results have policy implications for the organization of r d the assessment of damages for patent infringement and allocations of value in patent pools

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

optimal licensing of uncertain patents in the shadow of litigation this paper investigates the choice of a licensing mechanism by the holder of a patent whose validity is uncertain we provide sufficient conditions of a general nature under which the licensor prefers to use a per unit royalty contract in particular we show that this is the case for the holders of weak patents if the strategic effect of an increase in a potential licensee s unit cost on the equilibrium industry profit is positive the latter condition is shown to hold in a cournot resp bertrand oligopoly with homogeneous resp differentiated products under general assumptions on the demands faced by firms as a byproduct of our analysis we contribute to the literature on the cost paradox in oligopoly by offering some new insights of independent interest regarding the effects of cost variations on cournot and bertrand equilibria

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

efficient patent pools the paper builds a tractable model of patent pools agreements among patent owners to license sets of their patents it provides a necessary and sufficient condition for patent pools to enhance welfare and shows that requiring pool members to be able to independently license patents matters if and only if the pool is otherwise welfare reducing the paper allows patents to differ in importance asymmetric blocking patterns and licensors to also be licensees we undertake some initial exploration of the impact of pools on innovation the analysis has broader applicability than pools being relevant to a number of co marketing arrangements

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

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

mixed strategy trade equilibria textabstractconsiders the hybrid situation where some customers care only about the price while others have a brand preference or care about product characteristics

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

decentralized taxation and the size of government evidence from swiss state and local governments according to the leviathan model fiscal federalism is seen as a binding constraint on a revenue maximizing government the competitive pressure of fiscal federalism is supposed to reduce public sector size as compared to unitary states however empirical results concerning the leviathan hypothesis are mixed this study uses a state and local level panel data set of swiss cantons from 1980 to 1998 to empirically analyze the effect of different federalist institutions on the size and structure of government revenue because of the considerable tax autonomy of sub national swiss governments it is possible to investigate different mechanisms by which fiscal federalism may influence government size the results indicate that tax exporting has a revenue expanding effect whereas tax competition favors a smaller size of government fragmentation has essentially no effect on the size of government revenue for swiss cantons the overall effect of revenue decentralization leads to fewer tax revenue but higher user charges thus revenue decentralization favors a smaller size of government revenue and shifts government revenue from taxes to user charges

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 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 settlement of patent litigation in this article i develop a model to analyze patent licensing that is induced as part of a settlement agreement to avoid litigation of the issue of patent validity the patentee possesses private information about patent validity and makes a take it or leave it settlement offer to a single potential rival an essentially unique sequential equilibrium exists if out of equilibrium beliefs are restricted appropriately the model analyzes the effect of the probability of settlement and litigation

characteristics of patent litigation a window on competition we examine the patenting behavior of firms in an industry characterized by rapid technological change and cumulative innovation recent survey evidence suggests that semiconductor firms do not rely heavily on patents to appropriate returns to r d yet the propensity of semiconductor firms to patent has risen dramatically since the mid 1980s we explore this apparent paradox by conducting interviews with industry representatives and analyzing the patenting behavior of 95 u s semiconductor firms during 1979 1995 the results suggest that the 1980s strengthening of u s patent rights spawned patent portfolio races among capital intensive firms but it also facilitated entry by specialized design firms copyright 2001 by the rand corporation

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

trade restrictions as facilitating practices abstract the effect of quantitative restrictions in oligopolistic markets is shown to depend on whether imports are substitutes or complements for domestic products in the former case they have profound effects even when set at free trade levels because they impede the ability of the foreign firm to compete in the domestic market thereby acting to facilitate collusion and raise prices and profits for this reason tariffs and quotas are fundamentally non equivalent with substitute goods when goods are complements a voluntary export restriction ver at the free trade level has no effect and tariffs and quotas are equivalent

cross licensing and competition we study bilateral cross licensing agreements between n 2 firms that engage in competition after the licensing phase it is shown that the most collusive cross licensing royalty i e the one that allows the industry to achieve the monopoly profit is sustainable as the outcome of bilaterally efficient agreements in a symmetric setting if the terms of the cross licensing agreements are not observable to third parties the monopoly royalty is the unique symmetric bilaterally efficient royalty however when the terms of the agreements are public the most competitive royalty i e zero can also be bilaterally efficient policy implications regarding the antitrust treatment of cross licensing agreements are derived from these results

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

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

patent pools and cross licensing in the shadow of patent litigation this paper develops a framework to analyze the incentives to form a patent pool or engage in cross licensing arrangements in the presence of uncertainty about the validity and coverage of patents that makes disputes inevitable it analyzes the private incentives to litigate and compares them with the social incentives it shows that pooling arrangements can have the effect of sheltering invalid patents from challenges this result has an antitrust implication that patent pools should not be permitted until after patentees have challenged the validity of each other s patents if litigation costs are not too large

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

predation mergers and incomplete information this article examines the strategic pricing of duopolists in anticipation of a takeover of one by the other in equilibrium the acquiring firm may expand its output to signal that it is a low cost rival and thereby improve the takeover terms if the merged firm willface potential entry a premerger expansion of output may be necessary to deter entry and to make the merger profitable in that case the acquiringjirm s output expansion increases industry concentration by facilitating the takeover and by deterring entry this establishes the rationality of predatory output expansions even when a merger or a takeover is possible and indeed anticipated a voluminous literature is devoted to exploring the role of pricing in altering industry structure to achieve monopoly power that literature discusses both price cutting to drive existing rivals from the industry predatory pricing and setting low prices to deter potential entrants limit pricing the former has received the lion s share of the attention of antitrust commentators and enforcers but the rationality of predatory pricing has been seriously questioned the major criticism has two parts i takeovers are a superior means of achieving monopoly power and where legal should therefore be used instead of price cutting and ii if a takeover is anticipated premerger price cutting merely dissipates some of the value of the merging parties and would thus be irrational the first argument was originally advanced by mcgee 1958 and later by telser 1965 and bork 1978 the essential idea is that since predation is costly firms should realize that a more profitable arrangement in the form of a merger exists and ought to be negotiated the second argument is a natural extension of the first in response to this criticism yamey 1972 provides two arguments first the aggressor knows that he may face other rivals in the future entrants into this or other markets those potential rivals may draw inferences from his current behavior about the response they will face if they enter in that case the aggressor may wish to develop a reputation for aggressive behavior second even if a takeover is anticipated the terms of the takeover may be affected by the pretakeover pricing

competitive promotional strategies this article analyzes the equilibrium pricing strategies of brands engaged in a pricing game each brand has a monopoly market loyal consumers and competes with others in a common market called brand switchers in the case of a duopoly it is shown that the behavior of the brand switchers characterizes the equilibrium behavior of the duopolists this article focuses on two key comparative statics namely the depth of discounts away from a regular high price and the probability of giving a deal or the frequency of deals how these properties vary with the size of the loyal markets and the behavior of the brand switching population is discussed copyright 1988 by the university of chicago

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

intertemporal price competition alternating price competition between firms selling differentiated products to nonhomogeneous consumers can yield two different types of equilibria one which we call disciplined arises when products are close substitutes another which we call spontaneous emerges when products are more differentiated in disciplined equilibria an implicit threat to cut price further in response to an initial price cut supports quite collusive outcomes which become less collusive as product differentiation increases in spontaneous equilibria no such threat is needed consumers in the smaller market tend to pay a higher price as do consumers served by the more efficient firm copyright 1990 by the econometric society

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

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

how strong are weak patents economists usually conceive of patents as property rights that prevent others from practicing the patenting technology unless they first obtain a license from the patent holder even for ironclad patents i e for patents that are certain to be valid the existing literature has shown that the analysis of equilibrium licensing contracts is surprising subtle and complex 1 for example the analysis is quite different depending upon whether one firm s licensing contract is observable to the other firms likewise equilibrium outcomes are quite different if royalties must be linear than in the case where two part tariffs and other non linear royalties are permitted in that literature a downstream firm that refuses to sign a contract with the upstream supplier either exits the industry in the case that the upstream supplier controls an essential input or must rely on more costly inputs in the case of a non essential input in other words the downstream firm s threat point is to use some backstop technology in practice however patents are issued after a brief examination by the patent office to see if they meet the statutory requirements for novelty and non obviousness mounting evidence indicates that many weak patents i e patents unlikely to be found valid if challenged in court are issued by the u s patent and trademark office uspto 2 some observers view this with great alarm arguing that uspto is handing out undeserved monopolies others by contrast have suggested that these weak patents are of little concern because they will have little commercial impact because they will be licensed at commensurately low royalty rates or not enforced at all we study the commercial impact of weak patents more precisely we define a patent s strength as the probability that it will be found valid if challenged in court and we examine the relationship between a patent s strength and the royalties that it can command the distinctive

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

preemptive patenting and the persistence of monopoly this article takes a different tack and inquires whether institutions such as the patent system create opportunities for firms with monopoly power to maintain their monopoly power the results apply to other situations such as brand identification spatial location and capacity expansion which share the characteristic that early or preemptive actions may lower the returns to potential competitors

cooperating with competitors patent pooling and choice of a new standard abstract i examine the efficiency of patent pooling in a setting that allows for the interplay between the standards process in which owners of essential intellectual property ip develop a new product and the subsequent pooling decision in which ip prices are coordinated if one of the ip owners is also the incumbent of a product that employs the current competing standard referred to as overlapping ownership then the relationship among the ip owners will be both vertical through their ip and horizontal through their competing interests in the final products consumers are better off when ip owners cooperate even when these owners are effectively competitors because of lower prices and greater product variety consumers prefer however that the agreements not admit firms with overlapping ownership these results inform antitrust policy on cooperative agreements among competitors

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

on the elasticities of harvesting rules abstract in this paper we rank the relative importance of the exogenous parameters upon the optimal harvesting size in a stochastic rotation problem we show that when the tree growth follows geometric brownian motion the harvesting size is most elastic to the harvesting cost followed by the interest rate and is least elastic to the parameters of tree growth similar ranking holds for the linear growth case in both cases the harvesting size is increasing and concave in the harvesting cost bounded between two parallel lines the harvesting decision is made according to a stochastic extension of the faustmann formula

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

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

do patents work thickets trolls and antibiotic resistance this paper connects ideas from recent literature on the economics of intellectual property ip to address the question did the strengthening and broadening of ip rights from important patent policy changes in the us promote greater innovation the analysis rests on the theory of cumulative innovation which shows that if ip rights on a pioneer invention extend to follow on research and impediments to contracting exist then strengthening patents can actually reduce overall innovation recent empirical studies are consistent with the theory patents can significantly deter follow on research in complex technology areas where contracting is difficult computers electronics telecommunications but not in drugs chemicals and human genes i outline remedies from court decisions and antitrust policy for addressing inefficiencies from patent trolling patent thickets and the anti commons of fragmented ownership i then apply the analysis to the antibiotics market drawing on recent research to examine how patent and competition policies can be used to improve incentives for drug development in the battle against antibiotic resistance the literature provides persuasive evidence that the policy changes overreached in broadening and strengthening ip rights and reveals important patent reforms for improving the effectiveness of patent systems in the us and canada

price competition between two international firms facing tariffs abstract this paper examines the effects of tariffs on price setting duopolists selling a homogeneous product the producers cannot segment geographically distinct markets it provides a complete characterization of the equilibrium mixed strategies and analyzes the pattern of competition for different tariffs if a country raises its tariff the profits of both producers increase although the protected firm typically benefits more than its foreign counterpart growth in one market may reduce the profits of the firm located in the other market

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

patent litigation as an information transmission mechanism patent litigation reveals important information about the validity of the contested patent to other potential entrants this paper explores the implications of such informational externalities for entry dynamics in the presence of multiple potential entrants the nature of the entry game can be one of either waiting or preemption depending on the degree of patent protection therefore the payoffs for the patentee and the initial imitator are discontinuous in the degree of patent protection furthermore strengthening intellectual property rights is not necessarily desirable for the patentee the analysis may also help explain the apparently puzzling practice of delaying patent suits copyright 1998 by american economic association

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

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