option bounds with finite revision opportunities this article generalizes the single period linear programming bounds on option prices by allowing for a finite number of revision opportunities it is shown that in an incomplete market the bounds on option prices can be derived using a modified binomial option pricing model tighter bounds are developed under more restrictive assumptions on probabilities and risk aversion for this case the upper bounds are shown to coincide with the upper bounds derived by perrakis while the lower bounds are shown to be tighter in 1984 perrakis and ryan 6 derived upper and lower bounds on european option prices in discrete time and under modest assumptions on preferences and

valuing catastrophe derivatives under limited diversification a stochastic dominance approach abstract we present a new approach to the pricing of catastrophe event cat derivatives that does not assume a fully diversifiable event risk instead we assume that the event occurrence and intensity affect the return of the market portfolio of an agent that trades in the event derivatives based on this approach we derive values for a cat option and a reinsurance contract on an insurer s assets using recent results from the option pricing literature we show that the assumption of unsystematic event risk seriously underprices the cat option last we present numerical results for our derivatives using real data from hurricane landings in florida

upper and lower bounds of put and call option value stochastic dominance approach applying stochastic dominance rules with borrowing and lending at the risk free interest rate we derive upper and lower values for an option price for all unconstrained utility functions and alternatively for concave utility functions the derivation of these bounds is quite general and fits any kind of stock price distribution as long as it is characterized by a nonnegative beta transaction costs and taxes can be easily incorporated in the model presented here since investors are not required to revise their portfolios continuously the price that is paid for this generalization is that a range of values rather than a unique value is obtained in the last decade there has been an increasing interest in the options market by both academicians and practitioners the most well known valuation models are the black scholes 4 model the jump stochastic process model see cox and ross 6 the binomial model see cox ross and rubinstein 7 rendleman and bartler 19 and sharpe 22 and rubinstein s discrete model 21 recently perrakis and ryan 18 using rubinstein s approach have derived upper and lower bounds for option prices the relative pricing theory of contingent claims differs in the continuous time and discrete time models in a continuous time framework the instantaneous expected rate of return of the option and that of the underlying stock must follow a certain market equilibrium condition in this case the equilibrium condition is easily determined by a continuous hedging strategy in the discrete time case there is no hedging strategy to provide a simple relationship between the option and the stock price however for a given value distribution of the stock the value distribution of the option is uniquely determined by the option exercise price and this suggests some possible relationships between the stock and option values

quote inefficiency in options markets in an arbitrage free economy with non zero bid ask spreads the existence of payoffs whose price is lower than the price of a dominated payoff cannot be discarded in general however when the former price corresponds to trivial portfolios which involve buying or selling one unit of the basis assets its presence although not an arbitrage is a severe market anomaly which we refer to as an inefficient quote in an empirical study we report evidence that indicates that in options markets both the frequency and the magnitude of these anomalies are substantial and we document puzzling patterns in their behavior

evaluating jointly constrained order quantity complexities for incremental discounts abstract in this paper we consider the purchasing decisions facing a buying firm which receives incrementally discounted price schedules for a group of items in the presence of constraints such as budgets and space limitations the constraints take the form of upper bounds on positively weighted linear combinations of order size dollar volume unit price and order frequency we adapt the solution procedures from an earlier paper naval res logis 40 2 1993 255 to treat this case the results show that simultaneous order quantities for multiple items offered with separate incremental discounts and subject to joint resource constraints can be calculated efficiently using a combination of lagrangean relaxation and as needed partial enumeration this problem proved to be no more and no less tractable than its counterpart with all units discounts

an improved model for supplier selection under capacity constraint and multiple criteria abstract ghodsypour and o brien 2001 the total cost of logistics in supplier selection under conditions of multiple sourcing multiple criteria and capacity constraint international journal of production economics 73 1 15 27 study multiple sourcing problem with multiple criteria and capacitated suppliers considering the buyer s quality requirements as a constraint they develop a mixed integer non linear programming model to find the least cost cyclic ordering policy for the buyer they propose to solve the model by enumerating over all possible supplier combinations although the problem is interesting and their analysis is correct we point out two issues with their assumptions namely capacitated suppliers and cyclic ordering policy we discuss two different capacitated supplier settings i long run average annual capacity and ii exact annual capacity first under long run average annual capacity assumption we propose a model which provides the same or a better solution and is much easier to solve than their model then we discuss how to modify our and their models to handle exact annual capacity assumption

on option pricing bounds the purpose of this article is to compare the perrakis and ryan bounds of option prices in a single period model with option bounds derived using linear programming it is shown that the upper bounds are identical but that the lower bounds are different a comparison of these bounds together with merton s bounds and the black scholes prices in a lognormal securities market is presented the black scholes 1 option pricing model is preference free its simplicity derives from the continuous trading assumption which enables a portfolio of stock and bonds to be constructed so as to replicate the payouts of the option in an incomplete market with only finite opportunities to revise portfolios no preference free option price can be constructed 3 6 for this case preferencedependent prices can be established rather than place restrictive assumptions on preferences perrakis and ryan pr 5 have recently derived upper and lower bounds for a single and multiple period call option price the development of these bounds is based on the single price law and arbitrage arguments and requires modest assumptions on preferences the bounds exist as equilibrium values given a consensus on stock price distributions in this article we shall develop bounds for option prices based on primitive prices in incomplete markets and compare these bounds to the single period bounds derived by perrakis and ryan towards this goal we first review the pricing approach for primitive securities and proceed to re express the pr bounds as derived from their arbitrage portfolios then using linear programming bounds on option prices are derived linear programming approaches for obtaining relationships among option prices have been investigated garman 2 for example established an algebra for evaluating hedge portfolios using this algebra a one period linear program can be established that provides a way to search for arbitrage opportunities over an infinite number of portfolio strategies one of the features of the algebra is that only one linear program need be solved to determine if riskless arbitrage strategies can be established by investigating the dual of the linear program garman obtained necessary and sufficient conditions for rational option pricing in a one period setting these bounds were shown to be consistent with the bounds determined by merton 4 unlike garman s approach the linear programming approach presented here places constraints on time preferences risk aversion and state probabilities under specific sets of assumptions linear programs are formulated where the objective function to be optimized is the call price minimization and maximi

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

replenishment decisions under an all units discount schedule and stepwise freight costs in this study we analyze the replenishment decisions under a general replenishment cost structure that includes stepwise freight costs and all units quantity discounts we first formulate a general model that accounts for a larger class of problems and prove several useful properties of the expected profit function we later utilize these properties to develop a computational solution approach to find the optimal order quantity as an application of the general results we study the replenishment decisions in the single period i e the newsboy problem considering several scenarios that model the cost considerations either for the buyer or for both the buyer and the vendor

a generalized quantity discount pricing model to increase supplier s profits in this paper the joint problem of ordering and offering price discount by a supplier to his sole major buyer is analyzed the objective is to induce the buyer to alter his order schedule and size so that the supplier can benefit from lower set up ordering and inventory holding costs we generalize the quantity discount pricing model of monahan monahan j p 1984 a quantity discount pricing model to increase vendor profits management sci 30 6 720 726 to 1 explicitly incorporate constraints imposed on the amount of discount that can be offered and 2 relax the implicit assumption of a lot for lot or order for order policy adopted by the supplier an algorithm is developed to solve the supplier s joint ordering and price discount problem

note comment on a generalized quantity discount pricing model to increase supplier s profits lee and rosenblatt lee h l m j rosenblatt 1986 a generalized quantity discount pricing model to increase supplier s profits management sci 32 9 1177 1185 considered the joint problem of ordering and offering discount by a supplier to his sole buyer the objective of the supplier being to induce the buyer to alter his order quantities in order to increase the supplier s yearly profit they determined the optimal ordering and pricing policy for the supplier under the constraint on the amount of discount offered to the purchaser this restriction on the amount of price discount seems unreasonable when the objective of the supplier in all likelihood is to increase his own profits it is possible that higher discounts in purchase price may lead to greater economies for the supplier in this note a much simpler approach is being offered for determining the optimal ordering and pricing policy for the supplier

a heuristic for single warehouse multiretailer supply chains with all unit transportation cost discounts abstract in supply chain management research transportation costs if explicitly considered at all are frequently assumed to be linear these costs often have a more complex form such as an all unit discount structure this piecewise cost function adds significant complexity when included in supply chain management problems and is therefore often ignored due to solution time or tractability concerns we present and evaluate a new heuristic procedure which provides good solutions to problems involving all unit discount cost functions while significantly reducing solution times the general nature of this procedure does not require assumptions about the supply chain structure or policies and is therefore applicable in a wide range of settings

on the mean variance tradeoff in option replication with transactions costs this paper analyzes the tradeoff between cost and risk of discretely rebalanced option hedges in the presence of transactions costs i present closed form solutions for expected hedging error transactions costs and variance of the cash flow from a time based hedging strategy similar to that analyzed by leland 1985 furthermore i characterize the cost and risk of a move based hedging strategy without resorting to monte carlo simulations all results are sufficiently general to accommodate the use of a transactions costs adjusted hedging volatility and an asset rate of return that differs from the risk free rate of return

option replication in discrete time with transaction costs option replication is discussed in a discrete time framework with transaction costs the model represents an extension of the cox ross rubinstein binomial option pricing model to cover the case of proportional transaction costs the method proceeds by constructing the appropriate replicating portfolio at each trading interval numerical values of these prices are presented for a range of parameter values the paper derives a simple black scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values

planning and approximation models for delivery route based services with price sensitive demands abstract classical vehicle routing problems typically do not consider the impact of delivery price on the demand for delivery services existing models seek the minimum sum of tour lengths in order to serve the demands of a given set of customers this paper proposes approximation models to estimate the impacts of price on delivery services when demand for delivery service is price dependent such models can serve as useful tools in the planning phase for delivery service providers and can assist in understanding the economics of delivery services these models seek to maximize profit from delivery service where price determines demand for deliveries as well as the total revenue generated by satisfying demand we consider a variant of the model in which each customer s delivery volume is price sensitive as well as the case in which customer delivery volumes are fixed but the total number of customers who select the delivery service provider is price sensitive a third model variant allows the delivery service provider to select a subset of delivery requests at the offered price in order to maximize profit

incorporating transport cost in the lot size and pricing decisions with downward sloping demand abstract there is an increased emphasis in supply chain management on making all costs transparent this has led to greater scrutiny of freight costs by the resellers who want to control their inbound logistics costs an astute reseller may opt for paying freight when he sees an opportunity for savings in some cases a supplier may only sell on conditions of fob origin in this paper we consider a reselling situation wherein the final demand is sensitive to the selling price and the reseller is responsible for paying for the freight given that transportation costs can be almost 50 of the logistics cost s r swenseth m r godfrey int j prod econ 77 2002 113 there is a need for coordination between the reseller s purchasing function and his pricing policy in this study we formulate a model for determining the optimal lot size and the selling price for the reseller existing models for the problem have treated freight breakpoints in the same way as price breakpoints in a quantity discount schedule in doing so they have ignored the option of over declaring the weight of the shipment which is routinely available to the buyer shipper in practice in this paper we assume that the reseller has such an option we also assume that in setting the size of the order shipment the reseller can choose between less than full truckload or full truckload shipment

managing channel profits a channel of distribution consists of different channel members each having his own decision variables however each channel member s decisions do affect the other channel members profits and as a consequence actions a lack of coordination of these decisions can lead to undesirable consequences for example in the simple manufacturer retailer consumer channel uncoordinated and independent channel members decisions over margins result in a higher price paid by the consumer than if those decisions were coordinated in addition the ensuing suboptimal volume leads to lower profits for both the manufacturer and the retailer this paper explores the problems inherent in channel coordination we address the following questions what is the effect of channel coordination what causes a lack of coordination in the channel how difficult is it to achieve channel coordination what mechanisms exist which can achieve channel coordination what are the strengths and weaknesses of these mechanism what is the role of nonprice variables e g manufacturer advertising retailer shelf space in coordination does the lack of coordination affect normative implications from in store experimentation can quantity discounts be a coordination mechanism are some marketing practices actually disguised quantity discounts we review the literature and present a simple formulation illustrating the roots of the coordination problem we then derive the form of the quantity discount schedule that results in optimum channel profits this article was originally published in marketing science volume 2 issue 3 pages 239 272 in 1983

a classification of literature on determining the lot size under quantity discounts abstract determining a lot size in the presence of either all units or incremental discounts has represented one of major interests of materials managers it is a common practice that the suppliers offer quantity discount to entice the buyers to purchase more and to achieve economies of scale for transportation and processing costs this paper will classify the literature on lot sizing determination under several types of discount schemes and discuss some of the significant literature in this area over two decades also some future research areas have been identified

limits to economic growth as shown by a computable general equilibrium model abstract economic growth is distinguished from commercial growth and is defined in this article as the growth of the value a society puts in monetary terms on all commercial and non commercial goods and values it possesses during a certain period a computable general equilibrium model is used to show the impact of changes in the endowments preferences and production possibilities on economic income which in the model comprises all wealth besides land with its natural resources and labor energy is the key endowment to drive an economy the model leads in an intuitive way to the following conclusions 1 societies should start to use appropriate indicators for true economic growth rather than just for commercial growth as measured by gross national product 2 all types of economic growth are limited no matter if based on endowment growth production efficiency growth or changes in preferences 3 economic growth should be oriented more towards increasing production efficiency and less towards using more natural resources 4 human population growth puts at risk the possibilities for average economic growth per person 5 we should get better prepared to use solar energy in the future 6 besides economic growth there exists pure utility growth which is not measurable in monetary terms it includes much of scientific progress in the long run and is of great importance even though it cannot be included in an indicator of economic growth

an approach for developing an optimal discount pricing policy this paper addresses the problem of why and how a seller should develop a discount pricing structure even if such a pricing structure does not alter ultimate demand the situation modeled is most appropriate where the seller s product does not represent a major component of the buyer s final product where the demand for the product is derived or where the price is only one of many factors considered in making a purchase decision a model of buyer reaction to any given pricing scheme is developed to show that there exists a unified pricing policy which motivates the buyer to increase its ordering quantity per order thereby reducing the joint buyer and seller ordering and holding costs as a result the seller is able to reduce its costs while leaving the buyer no worse off and often better off the model is extended to handle variable ordering and shipping costs and situations where the seller faces numerous groups of buyers each having different ordering policies finally a case study is presented explicitly showing how the proposed pricing policy can be applied to the situation of a large seller selling to a number of different buyer groups

the concave cost supply problem abstract this paper is divided in two parts in the first part we consider the case where several providers feed a single manufacturing unit periodically in order to satisfy a given demand the cost incurred when a provider feeds the manufacturing unit is a concave function of the quantity delivered furthermore each provider either delivers a quantity that lies between a minimum and maximum value or do not deliver anything we are introducing some properties of an optimal solution and derive a heuristic algorithm from these properties a numerical example illustrates this approach in the second part of the paper we consider the case where several providers feed periodically several manufacturing units in order to satisfy given demands a heuristic algorithm is proposed the results provided by this algorithm are compared with the optimal solution in the case when the costs are linear for a strictly positive quantity and equal to zero otherwise

heuristics for sourcing from multiple suppliers with alternative quantity discounts in this paper we analyze the impact of supplier pricing schemes and supplier capacity limitations on the optimal sourcing policy for a single firm we consider the situation where the total quantity to be procured for a single period is known by the firm and communicated to the supplier set in response to this communication each supplier quotes a price and a capacity limit in terms of a maximum quantity that can be supplied to the buyer based on this information the buyer makes a quantity allocation decision among the suppliers and corresponding to this decision is the choice of a subset of suppliers who will receive an order based on industry observations a variety of supplier pricing schemes from the constituent group of suppliers are analyzed including linear discounts incremental units discounts and all units discounts given the complexity of the optimization problem for certain types of pricing schemes heuristic solution methodologies are developed to identify a quantity allocation decision for the firm through an extensive computational comparison we find that these heuristics generate near optimal solutions very quickly data from a major office products retailer is used to illustrate the resulting sourcing strategies given different pricing schemes and capacity limitations of suppliers in this industry we find for the case of capacity constrained suppliers the optimal quantity allocations for two complex pricing schemes linear discount and incremental units discount are such that at most one selected supplier will receive an order quantity that is less than its capacity

economic lot size model for price dependent demand under quantity and freight discounts abstract previous studies have developed procedures which determine optimal lot size and selling price when demand depends on price and all unit quantity discounts are offered further recent studies have addressed the concepts of quantity and freight discounts for constant demand in this paper we incorporate quantity and freight discounts in inventory decision making when demand rather than being constant is considered to be dependent upon price an algorithm is developed to determine the optimal lot size and selling price for a class of demand functions including constant price elasticity and linear demand a numerical example is provided to illustrate the model and a computer program is developed to implement the model derived in the paper

option bounds in discrete time extensions and the pricing of the american put in a recent paper perrakis and ryan 1984 upper and lower bounds on european option prices were derived in discrete time these bounds were based on an extension of the discrete time derivation of black scholes pricing first presented in the work of black and scholes 1973 the bounds are functions of the stock and exercise prices the riskless rate of interest the time to maturity and the entire distribution of stock returns in other words they need more information than black scholes for their computation and the derived results are weaker on the other hand they are significantly more general in their assumptions insofar as they do not rely on the continuous time riskless hedge of the original black scholes derivations or on the assumption of a binomial distribution of stock returns used in cox ross and rubinstein 1979 and rendleman and bartter 1979 for this reason they are likely to be particularly useful in valuing options on assets for which the black scholes methodology is clearly this paper generalizes and tightens the discrete time bounds for european options and develops similar bounds for american puts the stock return has a distribution with a finite range and is subject to the restriction that the stock be nonnegative beta the bounds are derived from arbitrage portfolios using the stock the option and the riskless asset they converge to the previous ones when the range coincides with the nonnegative real line and they both become equal to the binomial option model under a two state stock return upper and lower bounds for the american put are derived recursively by the same method with arbitrage portfolios involving the stock the riskless asset and american and european puts an example is provided with a trinomial return distribution part of this research was done while i was a visiting professor 1983 84 ecole superieure de commerce et d administration des entreprises reims france i wish to thank peter ryan albert madansky and a referee of this journal for helpful advice and comment while retaining all responsibility for any remaining errors or omissions 1 note however that this is also true of other blackscholes generalizations such as merton 1976

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

a note on an economic lot size model for price dependent demand under quantity and freight discounts abstract in this study we revisit research contributed by burwell et al 1997 international journal of production economics 48 141 155 where an economic lot size model for price dependent demand under quantity and freight discounts was proposed specifically for the cases of mixed discounts in which the quantity discounts are either of the incremental or all units variety and the freight discounts are of the opposite type we first provide counterexamples to show that adopting the existing algorithm to determine overall optimal lot size and selling price may not achieve the goal of maximizing profit we then propose an easy to understand computational algorithm to obtain an exact solution

joint inventory replenishments with group discounts based on invoice value the study focuses attention on a grouping procedure for the purpose of joint inventory replenishments from a single supplier the grouping procedure exploits the group discounts available on the total purchase value of a group of index and the economies of scale of order placing costs in particular it is shown that the optimal groups are formed such that the annual dollar usage values of the items do not decrease may increase or stay the same from the first to the last group this is similar in concept to the well known abc classification of inventory items the grouping problem is modeled as a shortest path using the above property

a generalized discount structure and some dominance rules for selecting the price break eoq abstract this paper introduces a generalized discount structure that combines the features of incremental and all units quantity discount policies general properties of the eoq model under this discount structure are studied and dominance rules for comparing order quantity intervals under either type of discount policy are established in addition procedures for developing an iso cost function and the minimal feasible set for optimal order quantity are proposed

option pricing bounds in discrete time upper and lower bounds are derived for call options traded at discrete intervals these bounds are independent of assumptions on the stock price distribution other than a restriction satisfied by the stock being non negative beta the development of the bounds relies on the single price law and arbitrage arguments both single period and multiperiod results are produced and put option bounds follow by extension the bounds exist as equilibrium values given a consensus on stock price distribution they are also valid for empirical studies being adjustable for dividends and commissions following the impetus of the black scholes pricing model the majority of option analyses have been in continuous time such approaches have relied on the formation of perfect riskless hedges involving the option its underlying security and a riskless asset since the hedge must be continuously revised and maintained while actual trading opportunities are discrete this crucial assumption limits the accuracy and applicability of the black scholes and related formulae in fact the black scholes formula can only be considered as a valid approximation to the discrete time solution merton 8 p 663 while the closeness of that approximation has not been ascertained in general 1 earlier discrete models such as boness 3 and samuelson 12 have been succeeded by those of brennan 5 cox et al 6 and rubinstein 11 in which distributional restrictions are imposed on share returns usually the discrete formula converges to the black scholes expression under appropriate limit conditions using the rubinstein 11 approach we derive upper and lower bounds for option prices with both a general price distribution and discrete trading opportunities the bounds are functions of the share and exercise prices the riskless rate of interest the distribution of the share price change per period and the number of periods of expiration of the option the lower bound is tighter than that of merton 7 derived from more general arbitrage considerations while being less exact than the results already mentioned for restricted distributions

productive efficiency in the middle east and north africa productive efficiency and factors affecting it in 11 countries in the middle east and north africa region were evaluated over the period 1980 to 1999 using fare s nonparametric approach the results indicate that oil producing countries are more efficient in terms of production compared with non oil producing countries tobit analyses indicate that previous levels of efficiency the degree of economic openness consumption of domestically produced goods and the limited availability of credit have a positive impact on production efficiency a sensitivity analysis using the bias corrected bootstrap technique shows that allocative efficiency and economic efficiency are more sensitive to the returns to scale assumption and sample size than pure technical efficiency

shared resource capacity expansion decisions for multiple products with quantity discounts abstract when multiple products compete for the same storage space their optimal individual lot sizes may need to be reduced to accommodate the storage needs of other products this challenge is exacerbated with the presence of quantity discounts which tend to entice larger lot sizes under such circumstances firms may wish to consider storage capacity expansion as an option to take full advantage of quantity discounts this paper aims to simultaneously determine the optimal storage capacity level along with individual lot sizes for multiple products being offered quantity discounts either all units discounts incremental discounts or a mixture of both by utilizing lagrangian techniques along with a piecewise linear approximation for capacity cost our algorithms can generate precise solutions regardless of the functional form of capacity cost i e concave or convex the algorithms can incorporate simultaneous lot sizing decisions for thousands of products in a reasonable solution time we utilize numerical examples and sensitivity analysis to understand the key factors that influence the capacity expansion decision and the performance of the algorithms the primary characteristic that influences the capacity expansion decision is the size of the quantity discount offered but variability in demand and capacity per unit influence the expansion decision as well furthermore we discover that all units quantity discounts are more likely to lead to capacity expansion compared to incremental quantity discounts our analysis illuminates the potential for significant savings available to companies willing to explore the option of increasing storage capacity to take advantage of quantity discount offerings for their purchased products

quantity discounts managerial issues and research opportunities marketing managers frequently administer pricing policies involving substantial quantity discounts however our understanding of the precise role of these discounts and their design is quite limited this paper reviews and integrates the economics and marketing literature and presents a detailed analysis of the policies of four firms in order to i specify the variety of motivations for quantity discounts ii provide guidelines to managers in designing quantity discount schedules and iii set out the most fruitful directions for future research

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

multi buyer discount pricing abstract this article gives an exact optimal solution to the problem of finding the optimal discount price and price break quantity for a seller dealing with one buyer it also gives a method for solving the problem when one seller offers a single quantity discount schedule to many buyers the discount is of the all quantity type and the model of the cost structure was originally proposed by crowther

an incremental discount pricing schedule with multiple customers and single price break abstract this paper analyzes how a supplier can formulate the terms of a quantity discount pricing schedule assuming a single incremental discount system a model is developed from which an algorithm is derived for an optimal discount schedule the cases are investigated in which both the discount rate and the break point are unknown and either one is prescribed a numerical example is presented to illustrate the algorithm developed

productive efficiency and growth policies for the caribbean productive economic efficiency and factors affecting it was evaluated in the caribbean between 1983 to 1992 results from non parametric programming indicated that efficiency i e pure technical allocative and economic measures were lower and more variable in caribbean than in other western hemisphere countries i e north america and latin america tobit regression analysis indicated higher levels of private and foreign investments productive infrastructure credit availability education level and consumption of domestically produced goods had positive impacts on the efficiency measures on the other hand higher levels of public expenditure income tax and export taxes and higher inflation rates had negative effects these results support the current trend towards advocating more open economies i e letting the free market work and encouraging governments to confine their functions to facilitative regulatory type roles and to undertaking tasks that are not generally undertaken by the privat

option pricing and replication with transactions costs transactions costs invalidate the black scholes arbitrage argument for option pricing since continuous revision implies infinite trading discrete revision using black scholes deltas generates errors which are correlated with the market and do not approach zero with more frequent revision when transactions costs are included this paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision hedging errors are uncorrelated with the market and approach zero with more frequent revision the technique permits calculation of the transactions costs of option replication and provides bounds on option prices

multi item single source ordering problem with transportation cost a lagrangian decomposition approach as a part of supply chain management literature and practice it has been recognized that there can be significant gains in integrating inventory and transportation decisions the problem we tackle here is a common one both in retail and production sectors where several items have to be ordered from a single supplier we assume that there is a finite planning horizon to make the ordering decisions for the items and in this finite horizon the retailer or the producer knows the demand of each item in each period in addition to the inventory holding cost an item base fixed cost associated with each item included in the order and a piecewise linear transportation cost are incurred we suggest a lagrangean decomposition based solution procedure for the problem and carry out numerical experiments to analyze the value of integrating inventory and transportation decisions under different scenarios

optimal policy for an inventory system with backlogging and all units discounts application to the composite lot size model this paper examines an inventory model with full backlogging and all units quantity discounts the practical scenario of a salesperson offering compensation to a client so as not to lose the sale is considered the cost of a backorder thus includes both a fixed cost and a further cost which is proportional to the length of time the said backorder exists a first algorithm is developed to determine the optimal policy while some extensions to this algorithm are obtained that include additional conditions on the model in particular the well known composite lot size model developed by tersine is solved incorporating a new stockout cost and a new all units discount numerical examples are provided to illustrate the application of the algorithms

optimal replication of options with transactions costs and trading restrictions this paper analyzes the strategy that minimizes the initial cost of replicating a contingent claim in a market with transactions costs and trading constraints the linear programming and two stage backward recursive models developed are applicable to the replication of convex as well as nonconvex payoffs and to a portfolio of options with different maturities the paper s formulation conveniently accounts for fixed and variable transactions costs lot size constraints and position limits on trading the article shows that in the presence of trading frictions it is no longer optimal to revise one s portfolio in each period at the optimum cash flows in excess of the desired ones may be generated the optimal policy trades off the curvature of the payoff that is generated against the terminal slack

stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs by applying stochastic dominance arguments upper bounds on the reservation write price of european calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security the primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option a tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put these results jointly impose tight upper and lower bounds on the implied volatility

productivity growth technical progress and efficiency change in industrialized countries this paper analyzes productivity growth in 17 oecd countries over the period 1979 1988 a nonparametric programming method activity analysis is used to compute malmquist productivity indexes these are decomposed into two component measures namely technical change and efficiency change we find that u s productivity growth is slightly higher than average all of which is due to technical change japan s productivity growth is the highest in the sample with almost half due to efficiency change jel c43 d24 in this paper we apply recently developed

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

production and shipment lot sizing in a vendor buyer supply chain with transportation cost abstract previous research on the joint vendor buyer problem focused on the production shipment schedule in terms of the number and size of batches transferred between the two parties it is a fact that transportation cost is a major part of the total operational cost however in most joint vendor buyer models the transportation cost is only considered implicitly as a part of fixed setup or ordering cost and thus is assumed to be independent of the size of the shipment as such the effect of the transportation cost is not adequately reflected in final planning decisions there is a need for models involving transportation cost explicitly for better decision making in this study we analyze the vendor buyer lot sizing problem under equal size shipment policy we introduce the complete solution of the problem in an explicit and extended manner that has not existed in the literature we incorporate transportation cost explicitly into the model and develop optimal solution procedures for solving the integrated models all unit discount transportation cost structures with and without over declaration have been considered numerical examples are presented for illustrative purpose

generalized analytical upper bounds for american option prices this paper generalizes and tightens chen and yeh s 2002 analytical upper bounds for american options under stochastic interest rates stochastic volatility and jumps where american option prices are difficult to compute with accuracy we first generalize theorem 1 of chen and yeh 2002 and apply it to derive a tighter upper bound for american calls when the interest rate is greater than the dividend yield our upper bounds are not only tight but also converge to accurate american call option prices when the dividend yield or strike price is small or when volatility is large we then propose a general theorem that can be applied to derive upper bounds for american options whose payoffs depend on several risky assets as a demonstration we utilize our general theorem to derive upper bounds for american exchange options and american maximum options on two risky assets

incorporating quantity discounts and their inventory impacts into the centralized purchasing decision multi site organizations must balance conflicting forces to determine the appropriate degree of purchasing centralization for their respective supplies the ability to garner quantity discounts represents one of the primary reasons that organizations centralize procurement this paper provides methodologies to calculate optimal order quantities and compute total purchasing and inventory costs when products have quantity discount pricing procedures for both all units and incremental quantity discount schedules are provided for four different strategic purchasing configurations scenarios complete decentralization centralized pricing with decentralized purchasing centralized purchasing with local distribution and centralized purchasing and warehousing for ordering decisions under local distribution procedures to determine optimal order quantities and costs are presented in a precise form that could be easily implemented into spreadsheets by practicing managers for the more complicated multi echelon scenarios we introduce a single cycle policy with a tailored aggregation refinement step that performs very well under experimentation when compared to a conservative bound