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

eco thermodynamics economics and the second law the laws of physics especially the first and second laws of thermodynamics have significant implications for economic theory the major implications of the first law conservation of mass energy are straightforward and have been discussed at length elsewhere in brief raw material inputs to economic processes are not consumed having been extracted from the environment in the first place they eventually return to the environment as wastes the economic implications of the second law entropy law are far more subtle there is considerable literature initiated by the work of georgescu roegen on the supposed constraints on economic growth imposed by the fact that economic processes utilize low entropy raw materials fossil fuels and high grade metal ores and discard high entropy wastes however as a practical matter the flux of available low entropy energy exergy from the sun is extremely large and certainly adequate to sustain economic activity in the solar system indefinitely even though fossil fuel and metal ore stocks may eventually be exhausted it is argued in this paper that the real economic significance of the second law lies in the fact that exergy is i not conserved and ii is a useful common measure of resource quality as well as quantity applicable to both materials and energy thus exergy can be used to measure and compare resource inputs and outputs including wastes and losses this is potentially important in itself moreover since exergy is not conserved it is truly consumed i e used up in economic processes hence exergy is no less a factor of production than labor or capital this fact has strong implications for economic growth theory especially with regard to assessing the role of technical progress

impact of loss aversion on the newsvendor game with product substitution abstract this paper studies a newsvendor game in which two substitutable products are sold by two different retailers newsvendors with loss averse preferences each loss averse retailer facing stochastic customer demand and deterministic substitution rate will make an order quantity decision to maximize his expected utility since product substitution causes two retailers to make decisions in a competitive environment game theory is used to find the retailers optimal order quantities it is shown that under certain conditions there exists a unique nash equilibrium in the newsvendor game under a symmetry assumption each retailer s equilibrium order quantity is decreasing in the loss aversion coefficient and increasing in the substitution rate further if the effect of loss aversion on the order quantity is strong enough to dominate the effect of competition the total inventory level of a decentralized supply chain will be lower than that of a centralized supply chain numerical experiments are conducted to illustrate our results

dynamic capacity management with substitution we examine a multiperiod capacity allocation model with upgrading there are multiple product types corresponding to multiple classes of demand and the firm purchases capacity of each product before the first period within each period after demand arrives products are allocated to customers customers who arrive to find that their product has been depleted can be upgraded by at most one level we show that the optimal allocation policy is a simple two step algorithm first use any available capacity to satisfy same class demand and then upgrade customers until capacity reaches a protection limit so that in the second step the higher level capacity is rationed we show that these results hold both when all capacity is salvaged at the end of the last demand period as well as when capacity can be replenished in the latter case an order up to policy is optimal for replenishment although finding the optimal protection limits is computationally intensive we describe bounds for the optimal protection limits that take little effort to compute and can be used to effectively solve large problems using these heuristics we examine numerically the relative value of strictly optimal capacity and dynamic rationing the value of perfect demand information and the impact of demand and economic parameters on the value of optimal substitution

joint pricing and production decisions with yield uncertainty and downconversion abstract we consider a firm who supplies two types of products high end and low end because of the uncertainty in the production process the yield rate of the high end products is uncertain the substandard high end products caused by the yield uncertainty can be transformed into the low end products with a certain cost we characterize the optimal pricing and production decisions and develop an algorithm to compute the optimal solution we also investigate the impact of the yield uncertainty on the firm s performance and explore how stability of market demand emergent fulfillment costs and downconversion cost influence this effect we find that i the profit of the firm deteriorates when the risk of the yield uncertainty is high in the face of yield uncertainty the firm prefers to decrease increase the production quantity of the high end low end products ii when the market demands are quite unstable the emergent fulfillment costs are low or the downconversion cost is high the firm has a low incentive to eliminate the yield uncertainty

global energy modelling a biophysical approach gemba part 1 an overview of biophysical economics abstract economists investors and policy makers need to understand energy systems and the potential for investment in both alternative energy supply and demand side technologies biophysical economics has contributed to conventional economics by incorporating thermodynamic and ecological principles and emphasising the importance of natural resources to economic processes this paper is presented in two parts part 1 gives a historic review of biophysical economics and discusses some previous models of the energy economy system built around the principles of biophysical economics part 2 presents the gemba model a new modelling methodology in the biophysical economics tradition the methodology proposes a new and important contribution to the field of biophysical economics a lifetime evolving function for the dynamics of the energy return on investment eroi the dynamic eroi function was incorporated into the gemba model and implemented in vensim the model is calibrated using historical energy production data i e trained to historical data the trained model is run to 2100 under a variety of assumptions regarding availability of energy resources and corresponding eroi s the main finding of the model is that growth of the renewable energy sector may impact investment in other areas of the economy and thereby stymie economic growth

a general equilibrium analysis of price controls and subsidies on food in mexico abstract in this paper we present a general equilibrium model that permits a thorough analysis of the effects of government pricing policies in particular we study the effects of price controls and subsidies on agricultural and food items in mexico we analyze alternative policies for reducing the government deficit by cutting subsidies and increasing indirect taxes our results indicate that although food subsidies need to be reduced maintaining some subsidies would have a favorable impact on income distribution

a computational general equilibrium model with endogenous unemployment an analysis of the 1980 fiscal reform in mexico abstract in this paper we develop a general equilibrium model of the mexican economy in which unemployment and government deficits play important roles the unemployment rate depends on a downwardly rigid real wage in the urban sector the government runs a deficit simply by selling bonds that consumers consider perfect substitutes for physical capital as savings instruments the model is used to analyze the impact of the 1980 fiscal reform the presence of the rigid real wage and alternative specifications of government policies regarding the size of the deficit are found to have significant effects on the comparative statics results whether or not the reform improves the welfare of rural households compared to urban households for example depends on whether government policy is to keep the deficit constant or keep expenditures constant in response to changes in tax revenues

terms of trade and class conflict in a computable general equilibrium model for mexico a computable general equilibrium model for mexico is constructed in which class conflict over the distribution of the surplus is the principal determinant of the terms of trade the model consists of seven social classes and eight productive sectors classes are distinguished as fundamental or subsumed according to whether their incomes are primarily determined by conscious class struggle or by the resulting system of relative prices flexible prices are assumed to clear markets for which non produced means of production such as agricultural land limit supply while output in the remaining sectors is determined by the level of effective demand for the latter sectors two theories of price formation are compared and are seen to differ radically in their implicit conception of the nature of class conflict a keynes kalecki closure is considered in which prices are determined by a fixed mark up on costs this enables capitalists to protect themselves from incursions on the rate of profit due to labou

optimal myopic policy for a stochastic inventory problem with fixed and proportional backorder costs in this paper we consider a single product periodic review stochastic demand inventory problem where backorders are allowed and penalized via fixed and proportional backorder costs simultaneously fixed backorder cost associates a one shot penalty with stockout situations whereas proportional backorder cost corresponds to a penalty for each demanded but yet waiting to be satisfied item we discuss the optimality of a myopic base stock policy for the infinite horizon case critical number of the infinite horizon myopic policy i e the base stock level is denoted by s if the initial inventory is below s then the optimal policy is myopic in general i e regardless of the values of model parameters and demand density otherwise the sufficient condition for a myopic optimum requires some restrictions on demand density or parameter values however this sufficient condition is not very restrictive in the sense that it holds immediately for erlang demand density family we also show that the value of s can be computed easily for the case of erlang demand this special case is important since most real life demand densities with coefficient of variation not exceeding unity can well be represented by an erlang density thus the myopic policy may be considered as an approximate solution if the exact policy is intractable finally we comment on a generalization of this study for the case of phase type demands and identify some related research problems which utilize the results presented here

physical energy cost serves as the invisible hand governing economic valuation direct evidence from biogeochemical data and the u s metal market abstract energy supply is mandatory for the production of economic value nevertheless tradition dictates that an enigmatic invisible hand governs economic valuation physical scientists have long proposed alternative but testable energy cost theories of economic valuation and have shown the gross correlation between energy consumption and economic output at the national level through input output energy analysis however due to the difficulty of precise energy analysis and highly complicated real markets no decisive evidence directly linking energy costs to the selling prices of individual commodities has yet been found over the past century the us metal market has accumulated a huge body of price data which for the first time ever provides us the opportunity to quantitatively examine the direct energy value correlation here by analyzing the market price data of 65 purified chemical elements mainly metals relative to the total energy consumption for refining them from naturally occurring geochemical conditions we found a clear correlation between the energy cost and their market prices the underlying physics we proposed has compatibility with conventional economic concepts such as the ratio between supply and demand or scarcity s role in economic valuation it demonstrates how energy cost serves as the invisible hand governing economic valuation thorough understanding of this energy connection between the human economic and the earth s biogeochemical metabolism is essential for improving the overall energy efficiency and furthermore the sustainability of the human society

managing an available to promise assembly system with dynamic short term pseudo order forecast we study an order promising problem in a multiclass available to promise atp assembly system in the presence of pseudo orders a pseudo order refers to a tentative customer order whose attributes such as the likelihood of an actual order order quantity and confirmation timing can change dynamically over time a unit demand from any class is assembled from one manufactured unit and one inventory unit where the manufactured unit takes one unit of capacity and needs a single period to produce an accepted order must be filled before a positive delivery lead time the underlying order acceptance decisions involve trade offs between committing resources production capacity and component inventory to low reward firm orders and reserving resources for high reward orders we develop a markov chain model that captures the key characteristics of pseudo orders including demand lumpiness nonstationarity and volatility we then formulate a stochastic dynamic program for the atp assembly system that embeds the markov chain model as a short term forecast for pseudo orders we show that the optimal order acceptance policy is characterized by class prioritization resource imbalance based rationing and capacity inventory demand matching in particular the rationing level for each class is determined by a critical value that depends on the resource imbalance level defined as the net difference between the production capacity and component inventory levels extensive numerical tests underscore the importance of the key properties of the optimal policy and provide operational and managerial insights on the value of the short term demand forecast and the robustness of the optimal policy this paper was accepted by martin lariviere operations management

optimal policies for inventory systems with priority demand classes we consider a periodic review inventory system with two priority demand classes one deterministic and the other stochastic the deterministic demand must be met immediately in each period however the units of stochastic demand that are not satisfied during the period when demand occurs are treated as lost sales at each decision epoch one has to decide not only whether an order should be placed and how much to order but also how much demand to fill from the stochastic source the firm has the option to ration inventory to the stochastic source i e not satisfy all customer demand even though there is inventory in the system we first characterize the structure of the optimal policy we show that in general the optimal order quantity and rationing policy are state dependent and do not have a simple structure we then propose a simple policy called s k s policy wheres ands ordering policy determine when and how much to order whilek rationing policy specifies how much of the stochastic demand to satisfy we report the results of a numerical study which shows that this simple policy works extremely well and is very easy to compute

effects of subsidized wheat consumption by state in india this paper reports the results of a study of the effects of the indian government s consumer subsidies on wheat demand results indicate consumption of subsidized wheat is higher in urban areas than in rural areas the public distribution of wheat in most states had little effect on demand in the commercial market which suggests the government is effective in targeting subsidized wheat to poor consumers

inventory decisions for substitutable products with stock dependent demand abstract we study a retailer s inventory policy for two products the products are substitutable and have inventory dependent demand so a higher inventory level of a product increases its sales we model the joint effect of demand stimulation and product substitution on inventory decisions by considering a single period stochastic demand setting we provide the first order optimality conditions for the profit maximizing order quantities and interpret them using marginal analysis we also consider two heuristic solutions that separately account for either demand stimulation or product substitution our numerical analysis reveals that the optimal policy by appropriately using sales information that quantifies substitution and demand stimulation can produce significantly higher profits the profit benefits are lessened under certain circumstances such as when the two products have similar critical fractile values suggesting that in such instances the heuristics may be used effectively

component rationing for available to promise scheduling in configure to order systems abstract we address the problem of rationing common components among multiple products in a configure to order system with order configuration uncertainty the objective of this problem is to maximize expected revenue by implementing a threshold rationing policy under this policy a product is available to promise if fulfilling the order for the product will not cause the inventory of any one of its required components to fall below the component s threshold level for that product the problem is modeled as a two stage stochastic integer program and solved using the sample average approximation approach a heuristic is developed to generate good feasible solutions and lower bound estimates using industry data we examine the benefit of component rationing as compared to a first come first served policy and show that this benefit is correlated to the average revenue per product and the variability in the revenue across products whose components are constrained

dynamic capacity management with general upgrading this paper studies a capacity management problem with upgrading a firm needs to procure multiple classes of capacities and then allocate the capacities to satisfy multiple classes of customers that arrive over time a general upgrading rule is considered i e unmet demand can be satisfied using multistep upgrade no replenishment is allowed and the firm has to make the allocation decisions without observing future demand we first characterize the structure of the optimal allocation policy which consists of parallel allocation and then sequential rationing specifically the firm first uses capacity to satisfy the same class demand as much as possible then considers possible upgrading decisions in a sequential manner we also propose a heuristic based on certainty equivalence control to solve the problem numerical analysis shows that the heuristic is fast and delivers close to optimal profit for the firm finally we conduct extensive numerical studies to derive insights into the problem it is foun

tactical inventory and backorder decisions for systems with predictable production yield abstract we consider a manufacturing system with stochastic demand and predictable production yield the manufacturer has predetermined prices and limited production capacity in each period the manufacturer also has the option to save some inventory for future periods even if there is demand in the current period the demand that is not met is lost or may be backordered for only one period our objective is to maximize the expected profit by choosing optimal produce up to level y t save s t and backorder quantities b t in each period t we formulate this problem as a markov decision process where the state of the system is represented by the net inventory and the yield rate we show that a modified order up to policy y t s t b t is optimal in each period t we also perform computational analysis to examine the effects of production yield on the optimal decisions

yield and allocation management in a continuous make to stock system with demand upgrade substitution abstract yield management is crucial for high tech industries to reduce over production however it is very challenging for a manufacturer to make a yield decision under the circumstance of uncertain demand and stochastic product quality for example in semiconductor manufacturing industry products are produced in batches within certain production cycle time even if the same raw material is put into the production system the product qualities measured by performance usually are not identical due to random yield in the manufacturing process since products have overlapped performance specifications products of the same batch are classified into different classes according to their qualities at the allocation stage products with higher performance can substitute for demand for products with lower performance this type of production and allocation system can be specified as a make to stock system with single material multi products multi periods upward demand substitution under random yield and uncertain demands in order to maximize profit the manufacturer needs to decide on the optimal input material quantity and the optimal allocation policy the problem is formulated as a stochastic dynamic programming model because manufacturer s profit is affected by the allocation policies atp r allocation policy is proposed to help manufacturer make real time allocation decisions a numerical experiment shows that atp r allocation policy performs better than the traditional myopic allocation policy to reduce the computation burden involved in atp r allocation policy we further propose a simplified algorithm and our experimental studies provide proof of the effectiveness of the proposed simple algorithm

newsvendor model with random supply and financial hedging utility based approach abstract this paper takes a utility based approach to the single period and single item newsvendor model unlike most models in the literature the newsvendor is not necessarily risk neutral and chooses the order quantity that maximizes the expected utility of the cash flow at the end of the period we suppose that there is uncertainty in demand as well as supply furthermore random demand and supply may be correlated with the financial markets the newsvendor exploits this correlation and manages his risks by investing in a portfolio of financial instruments the decision problem therefore includes not only the determination of the optimal ordering policy but also the selection of the optimal portfolio at the same time we first use a minimum variance approach to select the portfolio the analysis results in some interesting and explicit characterizations on the structure of the optimal policy we also present numerical examples to illustrate the effects of the parameters on the optimal order quantity and the importance of financial hedging on risk reduction

co production processes with random yields in the semiconductor industry a wide variety of manufacturing operations can be characterized as co production with substitutable demand that is there are many situations in which the availability of two or more items are related and because of randomness in either supply or demand it can be advantageous to substitute one of these items for another our research was motivated by the semiconductor industry where chips are produced in large batches because of the presence of randomness in the process individual chips in a given batch can perform differently because some customers have stricter specifications than others chips within the same batch can be classified and sold as different products according to their measurable performance we model the production and inventory problem as a stochastic dynamic program in which the objective is to minimize the costs of meeting contractual obligations after developing heuristic methods of solving the problem in practice we validate them against a lower bound on the cost of an optim