a lagrangean relaxation algorithm for multi item lot sizing problems with joint piecewise linear resource costs abstract in this paper we study a class of multi item lot sizing problems with dynamic demands as well as lower and upper bounds on a shared resource with a piecewise linear cost the shared resource might be supply production or transportation capacity the model is particularly applicable to problems with joint shipping and or purchasing cost discounts the problem is formulated as a mixed integer program lagrangean relaxation is used to decompose the problem into a set of simple sub problems a heuristic method based on sub gradient optimization is then proposed to solve a particular case often encountered in the consumer goods wholesaling and retailing industry our tests show that the heuristic proposed is very efficient in solving large real life supply planning problems

tracking distortions in agriculture china and its accession to the world trade organization this article examines the impacts of china s accession to the world trade organization wto on prices in its agricultural sector the analysis uses a new methodology to estimate nominal protection rates in china s agricultural sector before its accession to the wto these new measures account for differences in commodity quality within china and between china and world markets the analysis shows that some of china s agricultural commodities are well above world market prices and others are well below the article also assesses market integration and efficiency in china it finds high degrees of integration between coastal and inland markets and between regional and village markets the remarkable improvements in market performance in recent years mean that if increased imports or exports affect china s domestic price near the border producers throughout most of china will feel the price shifts

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

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

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

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

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

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

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

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

equilibrium prices in a vertically coordinated fishery abstract competition among processing firms is analyzed in a fishery that is managed under a total allowable catch constraint firms compete first in the ex vessel market for round fish and then in the downstream consumer market nash equilibrium prices are characterized at each stage of the vertical market when the number of processors is sufficiently large equilibrium prices are approximately walrasian the ex vessel price is close to the processor marginal valuation of the round fish and the consumer price clears the total quantity of processed fish implications for market structure conduct and performance and fisheries management policy are drawn

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

a note on market power in itq fisheries abstract individual transferable quotas itqs in fisheries are analogous to transferable pollution permits in environmental policy however they are different in that the right to produce is for the final product the fish whereas pollution permits are for a non market joint product i e sulfur dioxide of the good produced for sale in both cases the actual economic efficiency effects of creating the property rights depend upon the workings of the market for both the final product and the rights there has been considerable work on market failures for pollution permits and this paper extends the analysis to itqs it is shown that the difference between pollution permits and itqs can change the type and occurrence of failure in the market for the final product but it does not affect the potential for failure in the market for permits

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

biotechnology boosts to crop productivity in china trade and welfare implications genetically modified gm cotton is widely adopted and the list of gm technologies in trials is impressive in china at the same time there is an active debate on when china should commercialize its gm food crops this paper provides an economy wide assessment of some of the issues surrounding the adoption and commercialization of biotechnology based on unique data from empirical micro level study and field trials in china and a modified gtap model our results indicate that the development of biotechnology has an important impact on china s production trade and welfare welfare gains far outweigh the public biotechnology research expenditures most gains occur inside china and can be achieved independently from biotech unfriendly polices adopted in some industrialized countries

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

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

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

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

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

multiple items procurement under stochastic nonstationary demands abstract in the consumer goods wholesaling and retailing industry a large number of stock keeping units must be managed on a regular basis the items are typically purchased in families each family being associated with a specific external vendor and usually there are some constraints on family order quantities and there are frequent opportunities to buy at a temporary low price the demand for an item is often stochastic and not stationary in this paper by computing procurement plans over rolling planning horizons we transform this difficult sequential decision problem into a multi period static decision problem under risk the problem is initially formulated as a stochastic program with simple recourse and a branch and bound algorithm is designed to solve an equivalent deterministic program a piecewise concave approximation is proposed to reduce this program to a linear program with one 0 1 variable per planning period the performances of the algorithms are studied in two simulation experiments the simulations show that when planning over a rolling horizon the approach proposed yields excellent results

capacity expansion planning for a single facility product line abstract in this paper we describe a deterministic multiperiod capacity expansion model in which a single facility serves the demand for many products potential applications for the model can be found in the capacity expansion planning of communication systems as well as in the production planning of heavy process industries the model assumes that each capacity unit simultaneously serves a prespecified though not necessarily integer number of demand units of each product costs considered include capacity expansion costs idle capacity holding costs and capacity shortage costs all cost functions are assumed to be nondecreasing and concave given the demand for each product over the planning horizon the objective is to find the capacity expansion policy that minimizes the total cost incurred we develop a dynamic programming algorithm that finds optimal policies the required computational effort is a polynomial function of the number of products and the number of time periods when the number of products equals one the algorithm reduces to the well known algorithm for the classical dynamic lot size problem

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

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

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

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

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

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

production efficiency and exit in rights based fisheries economic theory predicts that the least efficient vessels are more likely to exit a fishery following the transition to an individual transferable quota itq management regime tools are needed to help analysts predict the likely degree and distribution of consolidation prior to implementing itq programs this research utilizes a one stage estimation procedure to determine the degree to which one s technical inefficiency preceding an itq regime influences the likelihood of exiting our results indicate that a vessel s measure of technical inefficiency is a significant and positive factor in explaining whether it exits the fishery following the implementation of itqs jel q22

the tradable permits approach to protecting the commons lessons for climate change tradable permit approaches for rationing access to the commons have been applied to many different types of resources in many different countries this essay reviews the experience with three main applications of tradable permit systems air pollution control water supply and fisheries management as well as some unique related programmes the purpose of the review is to draw together what we have learned about tradable permits in practice that might offer some useful insights for the implementation of the three tradable permit mechanisms that are part of the kyoto protocol copyright 2003 oxford university press

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

exclusionary manipulation of markets for pollution rights abstract strategic price manipulation can affect the distribution of transferable pollution rights across polluters and the efficiency of pollution control efforts prior research has concentrated on market manipulation by firms seeking only to minimize the sum of pollution rights costs and pollution abatement costs in this paper we explore the potential for the exclusionary manipulation of pollution permit markets intended to drive up the costs of one s rivals and we distinguish between the resource allocation effects of exclusionary manipulation and cost minimizing manipulation we find that exclusionary manipulation can sometimes worsen and sometimes ameliorate the abatement inefficiency which occurs under cost minimizing manipulation and that an overbuying rule can obviate or at least limit damages from this form of strategic behavior

instrument choice in a fishery abstract this paper considers the choice of regulatory instruments in a fishery fishing captains consumers and input suppliers each attempt to influence the regulator s choice of instruments the regulator chooses among instruments such as input restrictions entry restrictions or individual transferable quotas itqs regulatory instruments that result in zero fishery rents can only occur if the regulator places an extraordinary weight on the welfare of input suppliers relative to fishing captains and consumers indeed heterogeneity of fishing captains is neither necessary nor sufficient to obtain regulations that fail to generate fishery rents

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

approximation methods for the uncapacitated dynamic lot size problem we provide worst case error bounds for several approximation methods heuristics product aggregation and partitioning of the planning horizon for the uncapacitated dynamic lot size problem we propose two managerially oriented heuristics and show that they have a relative wont case error bound equal to two and develop similar analyses for methods known as the least cost per unit heuristic the part period balancing heuristic and an economic order quantity heuristic expressed in terms of a time supply of demand we also show how errors introduced by partitioning of the planning horizon in multi product multi facility problems are bounded by product set up costs and how errors introduced by product aggregation are bounded by set up costs holding costs and demands the latter results suggest methods for product aggregation that minimize the worst case error bounds

fishing quota markets abstract in 1986 new zealand responded to the open access problem by establishing the world s largest individual transferable quota itq system using a 15 year panel dataset from new zealand that covers 33 species and more than 150 markets for fishing quotas we assess trends in market activity price dispersion and the fundamentals determining quota prices we find that market activity is sufficiently high in the economically important markets and that price dispersion has decreased we also find evidence of economically rational behavior through the relationship between quota lease and sale prices and fishing output and input prices ecological variability and market interest rates controlling for these factors our results show a greater increase in quota prices for fish stocks that faced significant reductions consistent with increased profitability due to rationalization overall this suggests that these markets are operating reasonably well implying that itqs can be effective instruments for efficient fisheries management

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

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

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

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

market power and transferable property rights the appeal of using markets as a means of allocating scarce resources stems in large part from the assumption that a market will approximate the competitive ideal when competition is not a foregone conclusion the question naturally arises as to how a firm might manipulate the market to its own advantage this paper analyzes the issue of market power in the context of markets for transferable property rights first a model is developed that explains how a single firm with market power might exercise its influence this is followed by an examination of the model in the context of a particular policy problem the control of particulate sulfates in the los angeles region

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

will the biosafety protocol hinder or protect the developing world learning from china s experience abstract uncertainties about the effect of biosafety protocol bsp on global agricultural trade have caused concern among those with a stake in agrifood imports and exports the primary goal of this paper is to analyze the potential economic impacts of the bsp on both importing countries with a specific emphasis on china and exporting countries of soybean and maize the results show that in absolute terms the bsp will require large investments internationally and will induce compliance costs the bsp will increase the international price and domestic production in importing countries and lower international trade and domestic production in the exporting countries in absolute terms the impacts are large amounting for each commodity into the tens of millions of dollars and varying largely among different scenarios but in the percentage the impacts are small much smaller impacts are found in china because china has already invested in a system that provides almost all of the services that could be required by the bsp other developing nations may need more help and that it will be more costly

the effects of itq management on fishermen s welfare when the processing sector is imperfectly competitive in this paper we use a general model of imperfect competition to predict welfare changes within an open access fishery after it transitions to individual transferable quota itq management although related research has explored the effects of market power in the harvesting sector on itq performance none has considered the implications of an imperfectly competitive processing sector addressing this question we find that although fishermen should expect to gain from itqs under perfect competition they may suffer welfare losses if the processing sector is imperfectly competitive

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

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

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

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

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

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

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

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

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

rolling horizon procedures for the facilities in series inventory model with nested schedules this paper develops rolling horizon procedures for solving a multistage inventory problem with facilities in series in such an inventory system we assume that the raw material is processed successively through several facilities before reaching the customer the input to a facility comes from one preceding facility or the raw material and the output from the facility goes to one succeeding facility or the customer the rolling horizon procedures form rolling production schedules by solving a finite horizon multiperiod problem and implementing only the first period s decisions one period later the multiperiod problem is updated as better forecasts become available and the process is repeated the paper considers a simple case when holding costs are linear production costs on a facility consist of a setup cost and a constant marginal cost of production and production and holding costs are stationary in time demand is allowed to be nonstationary in time several rolling horizon procedures are deve

a coordinated production planning model with capacity expansion and inventory management motivated by a problem faced by a large manufacturer of a consumer product we explore the interaction between production planning and capacity acquisition decisions in environments with demand growth we study a firm producing multiple items in a multiperiod environment where demand for items is known but varies over time with a long term growth and possible short term fluctuations the production equipment is characterized by significant changeover time between the production of different items while demand growth is gradual capacity additions are discrete therefore periods immediately following a machine purchase are characterized by excess machine capacity we develop a mathematical programming model and an effective solution approach to determine the optimal capacity acquisition production and inventory decisions over time through a computational study we show the effectiveness of the solution approach in terms of solution quality and investigate the impact of product variety cost of capital and other important parameters on the capacity and inventory decisions the computational results bring out some key insights increasing product variety may not result in excessive inventory and even a substantial increase in set up times or holding costs may not increase the total cost over the horizon in a significant manner due to the ability to acquire additional capacity we also provide solutions and insights to the real problem that motivated this work

using history dependence to design a dynamic tradeable quota system under market imperfections a transferable quota system is analysed in a two period model with market power so far the management mechanisms presented in the literature to remedy market power have either not succeeded in securing efficiency in the distribution of quota within and across time periods or have resulted in only one of the two inefficiencies being eliminated in this paper a new mechanism is introduced where allocation of quota is made dependent upon historic quota acquisitions this opens for a trade off between distributional and time efficiency or under specific circumstances securing overall efficiency

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

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

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

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

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

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

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

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