exact and heuristic solutions of the global supply chain problem with transfer pricing we examine the example of a multinational corporation that attempts to maximize its global after tax profits by determining the flow of goods the transfer prices and the transportation cost allocation between each of its subsidiaries vidal and goetschalckx vidal c j goetschalckx m 2001 a global supply chain model with transfer pricing and transportation cost allocation european journal of operational research 129 1 134 158 proposed a bilinear model of this problem and solved it by an alternate heuristic we propose a reformulation of this model reducing the number of bilinear terms and accelerating considerably the exact solution we also present three other solution methods an implementation of variable neighborhood search vns designed for any bilinear model an implementation of vns specifically designed for the problem considered here and an exact method based on a branch and cut algorithm the solution methods are tested on artificial instances these results show that our implementation of vns outperforms the two other heuristics the exact method found the optimal solution of all small instances and of 26 of medium instances

optimality of myopic policies in disposing excess inventory in a recent article the author presented results for the optimum levels of inventory to dispose and keep in an excess inventory situation this note shows that these levels do not change when additional disposal opportunities are presented in the future in this sense the optimal policy is myopic in that the decision can be made without any examination of future decisions

optimal policies for a capacitated two echelon inventory system this paper demonstrates optimal policies for capacitated serial multiechelon production inventory systems extending the clark and scarf 1960 model to include installations with production capacity limits we demonstrate that a modified echelon base stock policy is optimal in a two stage system when there is a smaller capacity at the downstream facility this is shown by decomposing the dynamic programming value function into value functions dependent upon individual echelon stock variables we show that the optimal structure holds for both stationary and nonstationary stochastic customer demand finite horizon and infinite horizon results are included under discounted cost and average cost criteria

order quantity and timing flexibility in supply chains the role of demand characteristics we study how differences in product demand characteristics affect the strategic value of different types of supply chain flexibility for accurate response we propose a single period inventory modelling framework with two ordering opportunities the second order reflects updated demand information and potentially capitalizes on supply chain flexibility we consider two complementary forms of flexibility quantity flexibility in production and timing flexibility in scheduling in this framework we analyze the total inventory cost of a firm for alternate demand types we model functional products through the standard assumption of independent demand over the period fashion driven innovative products through a bayesian model and innovative products with evolving demand through a martingale process the three demand processes exhibit very different behavior with respect to the value of the alternate forms of flexibility we observe that quantity flexibility is of moderate value for functional goods and of high value for fashion driven products for all lead times quantity flexibility is of low value for goods with evolving demand with long lead times but of high value for short lead times alternately we observe timing flexibility is of highest value for functional goods especially for cases of high holding cost and is of lesser value for fashion driven goods it is of least value for goods with evolving demand both quantity and timing flexibility capabilities are required to significantly reduce the relevant supply chain costs for evolving demand innovative goods when the lead times are long

integrating replenishment decisions with advance demand information there is a growing consensus that a portfolio of customers with different demand lead times can lead to higher more regular revenues and better capacity utilization customers with positive demand lead times place orders in advance of their needs resulting inadvance demand information this gives rise to the problem of finding effective inventory control policies under advance demand information we show that state dependent s s and base stock policies are optimal for stochastic inventory systems with and without fixed costs the state of the system reflects our knowledge of advance demand information we also determine conditions under which advance demand information has no operational value a numerical study allows us to obtain additional insights and to evaluate strategies to induce advance demand information

measuring the opportunity cost of holding money more evidence on the term structure of interest rates abstract this paper tests the statistical importance and forecasting performance of a term structure money demand equation relative to two competing specifications the evidence indicates that the term structure specification is preferred to one using a long term interest rate but not a short term rate forecasts for 1981 1982 reveal that the term structure model is preferable to both alternatives

critical number policies for inventory models with periodic data we consider an infinite horizon in problem with stochastic demands where the data vary periodically karlin karlin s 1960a dynamic inventory policy with varying stochastic demands management sci 6 231 258 karlin s 1960b optimal policy for dynamic inventory process with stochastic demands subject to seasonal variations j siam8 611 629 shows that a periodic critical number policy is optimal and presents an algorithm for computing the critical numbers assuming discounted costs here we develop an alternative conceptually simpler approach to these problems the results include a proof of the optimality of such policies for the average cost case and a qualitative description of the behavior of the optimal policy as smoothing fluctuations in the data

classroom experiments not just fun and games i introduction historically economics was the classic example of a science in which laboratory methods are impossible consistent with this view economics has traditionally been taught as a theory intensive science rather than as an experimental one however the view that economics is not a laboratory science has been changing in large part due to the increase in research conducted using experimental methods in addition as evidence of the benefits of active learning for students has been gathered leaders in the field of education have been urging faculty to actively engage students in the process of learning introducing experimental methods into the economics classroom is a natural step warranted both by the evolution of the discipline itself and the need to more actively involve students in the learning process this paper presents results from a research project examining the effectiveness of using economics experiments in the classroom the project involved designing course packages for the principles of microeconomics and principles of macroeconomics classes that integrate basic economic experiments into the curricula and then evaluating their success as a teaching tool the evaluation phase focused on assessing the impact of this curriculum on student performance student attitudes towards economics and economic knowledge retention the project was conducted over a three year period during the initial phase of the research project both the course materials and an assessment instrument for evaluating the effectiveness of those materials were developed 1 next a controlled experiment using students at the university of arkansas was conducted students who enrolled in principles of macroeconomics and principles of microeconomics courses were separated into control and treatment classes both groups were taught using a general lecture class discussion format but experiments designed to illustrate specific economic concepts were used in the treatment sections in place of the additional lecture class discussion and examples used in the control classes for those topics relative performance on the assessment instrument serves as the basis for evaluating the impact of the new curricula on student learning while controlling for other factors that might affect student performance an attitude survey was administered to the students at the beginning and at the end of the courses in both the treatment and control groups to gain insight into their attitudes towards the study of economics and whether those attitudes changed over the course of the semester 2 in addition to assessing the impact of classroom experiments on student performance and attitudes towards economics their impact on knowledge retention was also investigated students were tracked into a required advanced business course where their performance on a test of material covered in the introductory economics courses was used to evaluate the impact of classroom experiments on their retention of this material although we had no a priori expectations of what the specific outcomes from the evaluative portion would be we hypothesized that students would benefit overall from the use of experiments and that this benefit would be dispersed differentially based on student learning styles we also anticipated that we would find an improved attitude towards the study of economics and an increase in knowledge retention when experiments were implemented as active learning tools ii background in their 1985 edition of principles of economics samuelson and nordhaus argued one possible way of figuring out economic laws is by controlled experiments economists unfortunately cannot perform the controlled experiments of chemists or biologists because they cannot easily control other important factors like astronomers or meteorologists they generally must be content largely to observe

managing a noncooperative supply chain with limited capacity we consider a two stage serial supply chain with capacity limits where each installation is operated by managers attempting to minimize their own costs a multiple period model is necessitated by the multiple stages capacity limits stochastic demand and the explicit consideration of inventories with appropriate salvage value functions a markov equilibrium policy is found intuitive profit dominance allows for existence of a unique equilibrium solution which is shown to be a modified echelon base stock policy this equilibrium policy structure is sustained in the infinite horizon a numerical study compares the behavior of the decentralized system with the first best integrated capacitated system the performance of this decentralized system relative to the integrated system across other parameters can be very good over a broad range of values this implies that an acceptable system performance may be attained without the imposition of a contract or other coordinating mechanism which themselves may encounter difficulties in implementation in the form of negotiation execution or enforcement of these agreements we find instances where tighter capacities may actually enhance channel efficiency we also examine the effect of capacity utilization on the system suboptimality

modelling imperfect advance demand information and analysis of optimal inventory policies we consider an inventory control problem where it is possible to collect some imperfect information on future demand we refer to such information as imperfect advance demand information adi which may occur in different forms of applications a simple example is a company that uses sales representatives to market its products in which case the collection of sales representatives information as to the number of customers interested in a product can generate an indication about the future sales of that product hence it constitutes imperfect adi other applications include internet retailing vendor managed inventory vmi applications and collaborative planning forecasting and replenishment cpfr environments we develop a model that incorporates imperfect adi with ordering decisions under our system settings we show that the optimal policy is of order up to type where the order level is a function of imperfect adi we also provide some characterizations of the optimal solution we develop an expression for the expected cost benefits of imperfect adi for the myopic problem our analytical and empirical findings reveal the conditions under which imperfect adi is more valuable

disposal of excess inventory this paper deals with the problem of disposal of slow moving or obsolete inventory for many reasons companies will find themselves in an overstock situation where the potential sales value of excess stock less the expected storage costs does not match the salvage value we present relationships for the optimum number of items to keep under conditions of stochastic demand and perishing

do online homework tools improve student results in principles of microeconomics courses recent technological advances in education have made it possible for instructors to use new tools in their attempt to enhance student interest and improve understanding of economic principles a substantial body of economic education literature has examined the effectiveness of these tools in influencing student performance generally these studies compare student performance between a control group and a test group in the last decade or so these new tools have tended to focus on different aspects of computer technology and whether or not use of the technology enhances student learning along these lines agarwal and day 1998 found that use of the internet in economics instruction had a positive effect on student learning as measured by improvement in the test of understanding in college economics tuce scores in both graduate and undergraduate economics courses similarly sosin et al 2004 suggest that tuce scores of students in classes using extensive technology showed a small but significant improvement over those students in classes using little technology this paper contributes to and extends the literature by reporting the results of an empirical study investigating the effect on student learning of an online homework tool aplia compared to the more traditional instructor assigned and graded homework do online homework tools improve student results in principles of microeconomics courses

an inventory model for slow moving items subject to obsolescence in this paper we consider a continuous review inventory system of a slow moving item for which the demand rate drops to a lower level at a known future time instance the inventory system is controlled according to a one for one replenishment policy with a fixed lead time adapting to lower demand is achieved by changing the control policy in advance and letting the demand take away the excess stocks we show that the timing of the control policy change primarily determines the tradeoff between backordering penalties and obsolescence costs we propose an approximate solution for the optimal time to shift to the new control policy minimizing the expected total cost during the transient period we find that the advance policy change results in significant cost savings and the approximation yields near optimal expected total costs

optimal policies and approximations for a serial multiechelon inventory system with time correlated demand since clark and scarf s pioneering work most advances in multiechelon inventory systems have been based on demand processes that are time independent this paper revisits the serial multiechelon inventory system of clark and scarf and develops three key results first we provide a simple lower bound approximation to the optimal echelon inventory levels and an upper bound to the total system cost for the basic model of clark and scarf second we show that the structure of the optimal stocking policy of clark and scarf holds under time correlated demand processes using a martingale model of forecast evolution third we extend the approximation to the time correlated demand process and study in particular for an autoregressive demand model the impact of lead times and autocorrelation on the performance of the serial inventory system

optimal strategy for an integrated system with variable production rate when the freight rate and trade credit are both linked to the order quantity abstract this paper presents an integrated inventory model with variable production rate and price sensitive demand rate the buyer s purchases trade credit linked to the order quantity offered by the supplier in addition the buyer pays the freight charge according to a weight schedule this paper attempts to offer a best policy that aims at maximizing the joint total profit while the trade credit and freight rate are simultaneously linked to the order quantity the same policy also incorporates considerations on the optimal retail price order quantity and delivery decision we provide possible solutions for the buyer and the supplier to collaboratively agree on inventory control warehouse management transportation logistics delivery and billing our study demonstrates that significant profit increase for the entire supply chain can be achieved by linking both trade credit policy and freight rate policy to order quantities an algorithm is furnished to determine the optimal solution in addition numerical examples and sensitivity analysis are presented to illustrate the theoretical results

optimal policies for multiechelon inventory problems with markov modulated demand this paper considers a multistage serial inventory system with markov modulated demand random demand arises at stage 1 stage 1 orders from stage 2 etc and stage n orders from an outside supplier with unlimited stock the demand distribution in each period is determined by the current state of an exogenous markov chain excess demand is backlogged linear holding costs are incurred at every stage and linear backorder costs are incurred at stage 1 the ordering costs are also linear the objective is to minimize the long run average costs in the system the paper shows that the optimal policy is an echelon base stock policy with state dependent order up to levels an efficient algorithm is also provided for determining the optimal base stock levels the results can be extended to serial systems in which there is a fixed ordering cost at stage n and to assembly systems with linear ordering costs

the stabilizing effect of inventory in supply chains this paper presents a hierarchical model framework for the analysis of the stabilizing effect of inventories in multiechelon manufacturing distribution supply chains this framework is used to compare the variance of demand to the variance of replenishment orders at different echelons of the system e g retailer wholesaler empirical data and experience with management games suggest that in most industries inventory management policies can have a destabilizing effect by increasing the volatility of demand as it passes up through the chain the bullwhip effect our model helps to explain these observations and indicates mechanisms that can promote stabilization the analysis results also define sufficient conditions for the existence of stabilization and relate these conditions to the optimality of myopic control policies

a deterministic order level inventory model for deteriorating items with two storage facilities abstract in this paper a deterministic inventory model is developed for a single deteriorating item which is stored in two different warehouses a rented warehouse is used to store the excess units over the fixed capacity w of the own warehouse the rented warehouse is assumed to charge higher unit holding cost than the own warehouse but to offer a better preserving facility resulting in a lower rate of deterioration for the goods than the own warehouse the optimal stock level for the beginning of the period is found and the model developed is shown to agree with the order level model for non deteriorating items with a single storage facility an illustration to show the applicability of the model is also presented

efficiency in the use of technology in economic education some preliminary results this paper reports preliminary results of a project funded by the andrew f mellon foundation that is intended to ascertain whether technology enhanced introductory economics courses are more effective and also more efficient than traditionally taught courses blecha s 2000 survey of faculty at different types of institutions of higher education documents that economics instructors now use a continuum of technological enhancements ranging from e mail web sites presentation software computerized games and spreadsheets to computerized instruction and distance learning while several studies investigate the consequences of using technology on student performance there has been little attempt to compare the efficacy and efficiency of the various types of available technologies

optimal policy for a two stage assembly system under random demand this paper considers an inventory system in which an end product is assembled from two components each of which is ordered from an external supplier only the end product has final demand which is assumed to be random using the functional equation approach of dynamic programming we characterize the forms of both the optimal order policy for the components and the optimal assembly policy of the end product for a multiperiod problem of arbitrary but finite length we believe that this work represents the only exact analysis of an mrp type assembly system when demand is stochastic

a general unconstrained model for transfer pricing in multinational supply chains multinational supply chains operate in more than one country or tax jurisdiction and face decision problems concerned with trade flows of resources products and services transfer prices and allocation of transport costs between their divisions these decisions must consider for the sake of optimality corporate and governmental parameters such as the payment of dividends and royalties ownership of and control over subsidiaries income taxes differentials duties and quotas etc in this paper we generalize and extend the theory of the multinational firm to the case of multinational supply chains we propose a model that is more general and comprehensive than the previous ones proposed in the literature to be more specific our model integrates many of the previous research factors and includes new ones such as transport costs and duty drawbacks which are critical for supply chains that operate under international trade regulations under the maximization of the repatriated earnings objective we study the optimality conditions of the corporate decision variables to derive managerial guidelines and to determine how decisions regarding trade quantities transfer prices and transport cost allocations affect the amount of taxes to be paid to host governments as well as the total after tax repatriated earnings of the corporation

risk sharing in supply chains using order bands analytical results and managerial insights abstract this work generalizes and extends a number of basic production inventory models we study a periodic review non stationary markovian production inventory model with stochastic demand and holding and penalty costs all state dependent where goods can be procured from up to two suppliers each supplier quotes a state dependent minimum order quantity moq order capacity c and unit price we concentrate on a base stock policy that is defined by a vector of numbers one for each lead time indexed by the states of the markov chain in certain cases our policy is optimal for the general case we show that there is no simple optimal policy we use infinitesimal perturbation analysis to compute inventory levels within this class for an application motivated by international trade for this application we find that the imposition of minimum and or maximum order quantities provides an effective mechanism for risk sharing the customer guarantees the supplier a minimum order every period at an increased unit price and in exchange the supplier grants an increase in capacity this can more effectively match supply with demand making the entire supply chain more profitable

an eoq model with noninstantaneous receipt and exponentially deteriorating items under two level trade credit abstract this paper considers the impact of the trade credit policy on the classical economic production quantity epq model for an item subject to exponential decays essentially this study focuses on an exponentially deteriorating item under the conditions of the retailer receiving the supplier trade credit and providing the customer trade credit simultaneously so as to minimize the average total cost a theorem is developed to determine the optimal replenishment policies the main contribution to literature is the inclusion of the latter type of payment delay finally through numerical examples sensitive analysis shows the influence of key model parameters

lower bounds for multi echelon stochastic inventory systems we establish lower bounds on the minimum cost of managing certain production distribution networks with setup costs at all stages and stochastic demands these networks include serial assembly and one warehouse multi retailer systems we obtain the bounds through novel cost allocation schemes we evaluate the bounds performance for one warehouse multi retailer systems by comparing them with simple heuristic policies the bounds are quite tight for systems with a small number of retailers we also present simplified proof of known optimality results for serial and assembly systems

large deviations based asymptotics for inventory control in supply chains we consider a model of a capacitated single class supply chain consisting of production facilities stages in tandem external demand is met from the available finished goods inventory maintained in front of the most downstream facility unsatisfied demand is backlogged every stage orders from its upstream facility thus production is constrained by the local production capacity and the availability of upstream inventory we propose production policies in two separate cases 1 when each facility has information about its local inventory only and 2 when each facility has knowledge of the total downstream inventory in case 1 the proposed policy guarantees that stockout probabilities at each stage stay bounded below given constants service level constraints in case 2 the proposed policy minimizes total expected inventory cost subject to desirable service level constraints in both cases the parameters of the proposed policies are obtained analytically based on large deviations asymptotics which leads to drastic computational savings compared to simulation an important feature of our model is that it accommodates autocorrelated demand and service processes both critical features of modern failure prone manufacturing systems we demonstrate that detailed distributional information on demand and service processes which is incorporated into large deviations asymptotics is critical in inventory control decisions we discuss extensions to a multiclass setting and to a model where unsatisfied demand is lost instead of backordered

review of inventory systems with deterioration since 2001 abstract this paper presents an up to date review of the advances made in the field of inventory control of perishable items deteriorating inventory the last extensive review on this topic dates back to 2001 goyal s k and giri b c recent trends in modeling of deteriorating inventory european journal of operational research 134 1 16 since then over two hundred articles on this subject have been published in the major journals on inventory control indicating the need for a new review we use the classification of goyal and giri based on shelf life characteristics and demand characteristics contributions are highlighted by discussing main system characteristics including price discounts backordering or lost sales single or multiple items one or two warehouses single or multi echelon average cost or discounted cash flow and payment delay

inventory control in directed networks a note on linear costs we consider periodic review inventory control problems in directed networks primary examples of which are distribution systems and assembly systems external demand could occur at each node when inventory is insufficient to meet requirements at a node a portion of this demand is backordered and the remaining is lost external demands as well as lead times for inventory purchase assembly and transportation are stochastic in each period linear sales revenues and the following costs all linear are charged at each node a inventory purchase assembly transfer cost to receive inventory b holding cost c backorder cost and d lost sales cost when the objective function of interest is a discounted sum of profits over a finite planning horizon it is shown that the sales prices and the inventory purchase assembly transfer cost parameters can be assumed to be zero without loss of generality the result is proved for every realization of demands and lead times some extensions to these results are discussed during this process we also generalize the concept of echelon inventories to directed networks

a capacitated production inventory model with periodic demand for a single product single stage capacitated production inventory model with stochastic periodic cyclic demand we find the optimal policy and characterize some of its properties we study the finite horizon the discounted infinite horizon and the infinite horizon average cases a simulation based optimization method is provided to compute the optimal parameters based on a numerical study several insights into the model are also provided

fair transfer price and inventory holding policies in two enterprise supply chains abstract a key issue in supply chain optimisation involving multiple enterprises is the determination of policies that optimise the performance of the supply chain as a whole while ensuring adequate rewards for each participant in this paper we present a mathematical programming formulation for fair optimised profit distribution between echelons in a general multi enterprise supply chain the proposed formulation is based on an approach applying the nash bargaining solution for finding optimal multi partner profit levels subject to given minimum echelon profit requirements the overall problem is first formulated as a mixed integer non linear programming minlp model a spatial and binary variable branch and bound algorithm is then applied to the above problem based on exact and approximate linearisations of the bilinear terms involved in the model while at each node of the search tree a mixed integer linear programming milp problem is solved the solution comprises inter firm transfer prices production and inventory levels flows of products between echelons and sales profiles the applicability of the proposed approach is demonstrated by a number of illustrative examples based on industrial processes

a global supply chain model with transfer pricing and transportation cost allocation abstract we present a model for the optimization of a global supply that maximizes the after tax profits of a multinational corporation and that includes transfer prices and the allocation of transportation costs as explicit decision variables the resulting mathematical formulation is a non convex optimization problem with a linear objective function a set of linear constraints and a set of bilinear constraints we develop a heuristic solution algorithm that applies successive linear programming based on the reformulation and the relaxation of the original problem our computational experiments investigate the impact of using different starting points the algorithm produces feasible solutions with very small gaps between the solutions and their upper bound ub

inventory control in a fluctuating demand environment we present an inventory model where the demand rate varies with an underlying state of the world variable this variable can represent economic fluctuations or stages in the product life cycle for example we derive some basic characteristics of optimal policies and develop algorithms for computing them in addition we show that certain monotonicity patterns in the problem data are reflected in the optimal policies

a multiechelon inventory problem with secondary market sales we consider a finite horizon multiechelon inventory system in which the surplus of stock can be sold i e disposed in the secondary markets at each stage in the system what are called nested echelon order up to policies are shown to be optimal for jointly managing inventory replenishments and secondary market sales under a general restriction on model parameters we establish that it is optimal not to both sell off excess stock and replenish inventory secondary market sales complicate the structure of the system so that the classical clark and scarf echelon reformulation no longer allows for the decomposition of the objective function under the optimal policy we introduce a novel class of policies referred to as the disposal saturation policies and show that there exists a disposal saturation policy determined recursively by a single base stock level at each echelon that achieves the decomposition of this problem the resulting optimal replenishment policy is shown to be the echelon base stock policy we demonstrate the heuristic performance of this disposal saturation policy through a series of numerical studies except at extreme ranges of model parameters the policy provides a very good approximation to the optimal policy while avoiding the curse of dimensionality we also conduct numerical studies to determine the value of the secondary markets for multistage supply chains and assess its sensitivity to model parameters the results provide potentially useful insights for companies seeking to enter or develop secondary markets for supply chains this paper was accepted by martin lariviere operations management

an operational profit sharing and transfer pricing model for network manufacturing companies abstract new age companies are forging partnerships with other firms to market products that have been assembled through manufacturing activities distributed at different locations these locations belong to more than one company and the product passes through these different sites during its manufacturing stages this manufacturing collaboration is known as network manufacturing according to the network philosophy companies form alliances to manufacture a product and share in its operating profits this paper proposes a framework and methodology for profit sharing and transfer pricing between network companies we propose a paradigm that enables maximization of operating profits by the manufacturing network in its larger supply chain suggesting a departure from the model that maximizes profits for the individual company within the sphere of its own supply chain

impact of trade credit and inflation on retailer s ordering policies for non instantaneous deteriorating items in a two warehouse environment with the advent of better technologies in manufacturing and retail industry consumer beliefs and needs have been altered supermarkets are expected to sell fresh products in good conditions which have a longer shelf life or do not begin to deteriorate immediately termed known as non instantaneous deteriorating items this characteristic is now usually observed in almost all food stuffs fashionable items electronic products among others in order to sustain in the retail sectors the managers are moving forward to store these items in warehouses moreover due to increasing competition in business world supplier offers a permissible delay in payments to retailer in order to increase demand this encourages the retailer to order a large quantity which in turn entitles the organization to rent out an additional storage space considering the importance of such a scenario the present research work develops a two warehouse inventory model for non instantaneous deteriorating items with permissible delay in payments under inflationary conditions shortages are allowed and partially backlogged since customers willingness to wait decreases over time the objective of this paper is to determine the retailer s optimal replenishment policies that maximize the present worth of total optimal profit per unit time finally the proposed inventory model has been validated with the help of numerical example sensitivity analysis of the optimal solution with respect to key parameters of the inventory system has been also presented which provides important managerial implications

an inventory model with deteriorating items under inflation when a delay in payment is permissible abstract this study develops an inventory model for initial stock dependent consumption rate when a delay in payment is permissible in the inventory model shortages are not allowed the effect of the inflation rate deterioration rate initial stock dependent consumption rate and delay in payment are discussed in the study mathematical models are also derived under two different circumstances i e case i the credit period is less than or equal to the cycle time for settling the account and case ii the credit period is greater than the cycle time for settling the account besides expressions for an inventory system s total cost are derived for these two cases moreover a computational procedure and gino lasdon et al acm transactions mathematical software 4 1978 34 50 are proposed to obtain the optimal order size and cycle time the results can help managers determine the optimal total cost finally a numerical example demonstrates the applicability of the proposed model

scarf s state reduction method flexibility and a dependent demand inventory model we consider a finite horizon inventory model with linear holding shortage and ordering costs the demand random variables are dependent and average demand is described by an exponential smoothing formula this model can be formulated as a two state variable inventory level weighted past demands dynamic program using a procedure first developed by scarf for a bayesian inventory model we are able to reformulate the model as a one state variable dynamic program resulting in a considerable computational saving over the two state variable formulation we also show that this dependent demand model orders less than or equal the amount ordered by a comparable independent demand model we establish this result under the assumption that demand represents failures that are repaired by the beginning of the next period

benefits of leadtime information and of its combination with demand forecast information abstract this paper studies both the benefits of leadtime information and the interrelationships among demand forecast information leadtime uncertainty and leadtime information for improving inventory control performance to this end it explicitly incorporates both leadtime information and demand forecast information into an inventory model although they have conventionally been dealt with individually in the literature specifically it considers a periodic review inventory model with uncertain leadtimes in which both leadtime information and demand forecast information are available the leadtime information is modeled as the information of the arrival of outstanding orders and the demand forecast information as the martingale model of forecast evolution mmfe the paper analyzes the way to use both leadtime information and demand forecast information for inventory control operations specifically under certain conditions the optimality of the state dependent base stock policy is shown and an effective heuristic policy is developed it also derives some managerial insights for exploiting both leadtime information and demand forecast information in the case where leadtimes are uncertain for instance while leadtime information itself significantly improves inventory control performance it also enhances the benefits of demand forecast information specifically the benefits of demand forecast information may significantly decrease as leadtime uncertainty increases however the decrease of the benefits of demand forecast information may be alleviated with leadtime information

simultaneous capacity and production management of short life cycle produce to stock goods under stochastic demand this paper derives the optimal simultaneous capacity and production plan for a shortlife cycle produce to stock good under stochastic demand capacity can be reduced as well as added at exogenously set unit prices in both cases studied with and without carryover of unsold units a target interval policy is optimal there is a usually different target interval for each period such that capacity should be changed as little as possible to bring the level available into that interval our contribution in the case of no carry over is a detailed characterization of the target intervals assuming demands increase stochastically at the beginning of the life cycle and decrease thereafter in the case of carry over we establish the general result and show that capacity and inventory are economic substitutes the target intervals decrease in the initial stock level and the optimal unconstrained base stock level decreases in the capacity level in both cases optimal service rates are not necessarily constant over time a numerical example illustrates the results

newsvendor bounds and heuristic for optimal policies in serial supply chains we consider the classicn stage serial supply systems with linear costs and stationary random demands there are deterministic transportation leadtimes between stages and unsatisfied demands are backlogged the optimal inventory policy for this system is known to be an echelon base stock policy which can be computed through minimizingn nested convex functions recursively to identify the key determinants of the optimal policy we develop a simple and surprisingly good heuristic this method minimizes 2 n separate newsvendor type cost functions each of which uses the original problem data only these functions are lower and upper bounds for the echelon cost functions their minimizers form bounds for the optimal echelon base stock levels the heuristic is the simple average of the solution bounds in extensive numerical experiments the average relative error of the heuristic is 0 24 with the maximum error less than 1 5 the bounds and the heuristic which can be easily obtained by simple spreadsheet calculations enhance the accessibility and implementability of the multiechelon inventory theory more importantly the closed form expressions provide an analytical tool for us to gain insights into issues such as system bottlenecks effects of system parameters and coordination mechanisms in decentralized systems

classroom experiments is more more studies have demonstrated that classroom experiments have a positive effect on student achievement in economics courses questions remain regarding the appropriate number of experiments in the current study we attempt to determine whether more intensive use of classroom experiments is associated with greater student achievement our data contains variation in the number of experiments administered in a principles of microeconomics course we find that participation in classroom experiments has a positive but diminishing marginal benefit on students final course scores we also find that classroom experiments can bridge some achievement gaps between older and younger students between whites and minorities

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

comments on the eoq model under retailer partial trade credit policy in the supply chain abstract huang and hsu 2007 an eoq model under retailer partial trade credit policy in supply chain international journal of production economics doi 10 1016 j ijpe 2007 05 014 investigate the inventory system as a cost minimization problem to determine the retailer s optimal inventory policy under the supply chain they develop two easy to use theorems to locate the optimal inventory policy for the retailer although their inventory models are correct and interesting processes of arguments to derive those theorems to find the optimal inventory policy are not complete so the main purpose of this paper is to overcome these shortcomings and present complete proofs for huang and hsu 2007

competition and cooperation in a two stage supply chain with demand forecasts we consider a serial supply chain with one supplier and one retailer each obtains some demand forecast information which may be shared or not we investigate the members benefits from sharing information the forecasts follow a variant of the martingale model of forecast evolution mmfe we construct a simple transfer payment scheme to align the players incentives with that of the overall system the main finding is that unless the players incentives are aligned in this way sharing information makes little sense it might hurt one or the other player and the system as a whole

optimal price discounting and lot sizing policies for perishable items in a supply chain under advance payment scheme and two echelon trade credits abstract many researchers have assumed that a retailer announces price discount to motivate market sales when he has competition in markets unanticipated surplus in inventory or change in the production run of a product but in real life situations there are retailers who announce price discount offer under advance payment ap scheme prior to the selling period due to the advancement of internet and on line money transactions the ap scheme is common and useful to decrease the estimation error in demand and to increase the market sales when the items are arrived to the inventory the priority will be given to the customers who use ap scheme this paper considers a supply chain where the supplier provides the retailer a full trade credit period for payments whereas the retailer offers the partial trade credit to his customers i intend to develop an economic order quantity eoq based model with perishable items in order to investigate the retailer s inventory system as a cost minimization problem under ap scheme and two echelon trade credit option mathematical theorems are developed to determine optimal price discounting and lot sizing policies and a lot of managerial phenomena are obtained through numerical examples

technology improves learning in large principles of economics classes using our wits much recent innovation in teaching economics has focused on active learning strategies and on the use of technology at the same time budget realities make large lecture classes a fact of life for principles of economics courses at many universities unfortunately neither active learning strategies nor teaching with technology tend to work well in large classes active learning is difficult to facilitate with many students and learning with technology in economics has been limited for the most part to classes small enough to fit in computer labs we have developed a system that uses handheld devices and wireless technology to facilitate interactive learning in large classes by putting technology in the hands of the students during class the wireless interactive teaching system wits consists of handspring visors a hand held pda equipped with wireless capabilities a laptop server a wireless access point and projector and proprietary software this intranet uses the 802 11b wireless standard wits allows students to trade in markets play standard economics games prisoner s dilemma public goods 2 2 matrix etc take multiple choice quizzes and communicate with the instructor during class see http lshta vt edu index html for a sample exercise and instructional material we report the results of a controlled experiment to test the impact of wits facilitated active learning exercises our study differs from previous work in three important ways first use of the wits system allows us to implement experiments in larger classes than previous studies using hand run exercises second we measure learning using exam scores rather than the test of understanding in college economics tuce so that improved results are understandable in terms of students grades the metric that students and universities use to evaluate performance finally to isolate whether changes in learning are from substituting experiment based material for standard lectures or whether gains are the result of active learning the control class held parallel research days where students discussed the same experiment students in the wits class earned final grades that averaged 3 2 points higher than the control class though impact varies by gender and class level the impact on learning is highest for freshmen and women groups that often struggle with introductory economics and lowest for male seniors who in our sample tend to be engineering majors satisfying a general education requirement teaching evaluations are also significantly higher in the experimental class

on the optimal policy structure in serial inventory systems with lost sales we study a periodically reviewed serial inventory system in which excess demand from external customers is lost we derive elementary properties of the vector of optimal order quantities in this system in particular we derive bounds on the sensitivity or more mathematically the derivative of the optimal order quantity at each stage to the vector of the current inventory levels our analysis uses the concept of l natural convexity which was studied in discrete convex analysis and recently used in the study of single stage inventory systems with lost sales we also remark on how our analysis extends to models with capacity constraints and or backordering

the price of reverse factoring financing rates vs payment delays reverse factoring a financial arrangement where a corporation facilitates early payment of its trade credit obligations to suppliers is increasingly popular in industry many firms use the scheme to induce their suppliers to grant them more lenient payment terms by means of a periodic review base stock model that includes alternative sources of financing we explore the following question what extensions of payment terms allow the supplier to benefit from reverse factoring we obtain solutions by means of simulation optimisation we find that an extension of payment terms induces a non linear financing cost for the supplier beyond the opportunity cost of carrying additional receivables furthermore we find that the size of the payment term extension that a supplier can accommodate depends on demand uncertainty and the cost structure of the supplier overall our results show that the financial implications of an extension of payment terms need careful assessment in stochastic settings

joint inventory and cash management for multidivisional supply chains this paper develops a centralized supply chain model that integrates material flows with cash flows the supply chain is owned by a single firm with two divisions the downstream division headquarters facing random customer demand replenishes materials from the upstream division the firm installs a financial services platform that pools the divisions cash into a master account managed by the headquarters in each period cash is received from customers and paid to the outside vendor after materials are delivered the headquarters determines how much cash to retain for inventory replenishment the objective is to determine an optimal joint inventory replenishment and cash retention policy for the entire supply chain we prove that the optimal policy has a surprisingly simple structure both divisions implement a base stock policy for inventory replenishment the headquarters monitors the corporate working capital and implements a two threshold policy for cash retention this result is obtained by exte

inventory decisions for emergency supplies based on hurricane count predictions abstract this paper addresses a stochastic inventory control problem for manufacturing and retail firms who face challenging procurement and production decisions associated with hurricane seasons specifically the paper presents a control policy in which stocking decisions are based on a hurricane forecast model that predicts the number of landfall hurricanes for an ensuing hurricane season the multi period inventory control problem is formulated as a stochastic programming model with recourse where demand during each pre hurricane season period is represented as a convolution of the current period s demand and an updated estimate of demand for the ensuing hurricane season due to the computational challenges associated with solving stochastic programming problems recent scenario reduction techniques are discussed and illustrated through an example problem the proposed model specifies cost minimizing inventory strategies for simultaneously meeting stochastic demands that occur prior to the hurricane season while proactively preparing for potential demand surge during the season

combined pricing and inventory control under uncertainty this paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty more specifically we analyze the following single item periodic review model demands in consecutive periods are independent but their distributions depend on the item s price in accordance with general stochastic demand functions the price charged in any given period can be specified dynamically as a function of the state of the system a replenishment order may be placed at the beginning of some or all of the periods stockouts are fully backlogged we address both finite and infinite horizon models with the objective of maximizing total expected discounted profit or its time average value assuming that prices can either be adjusted arbitrarily upward or downward or that they can only be decreased we characterize the structure of an optimal combined pricing and inventory strategy for all of the above types of models we also develop an efficient value iteration method to compute these optimal strategies finally we report on an extensive numerical study that characterizes various qualitative properties of the optimal strategies and corresponding optimal profit values

optimal policies for multi echelon inventory problems with batch ordering in many production distribution systems materials flow from one stage to another in fixed lot sizes for example a retailer orders a full truckload from a manufacturer to qualify for a quantity discount a factory has a material handling system that moves full containers of parts from one production stage to the next in this paper we derive optimal policies for multi stage serial and assembly systems where materials flow in fixed batches the optimal policies have a simple structure and their parameters can be easily determined this research extends the multi echelon inventory theory in several ways it generalizes the clark scarf model by allowing batch transfers of inventories rosling 1989 shows that assembly systems can be interpreted as serial systems under the assumption that there are no setup costs we show that the series interpretation still holds when materials flow in fixed batches which satisfy a certain regularity condition finally veinott 1965 identifies an optimal policy for a single location inventory system with batch ordering this paper generalizes his result to multi echelon settings

coordination mechanisms in decentralized serial inventory systems with batch ordering this paper studies a periodic review serial supply chain in which materials are ordered and shipped according to r nq policies three information scenarios are considered depending on the level of information available echelon local and quasilocal in the echelon scenario each stage can access the inventory and cost information within its echelon comprising the stage itself and all downstream stages in the local scenario each stage only accesses its own local information finally in the quasilocal scenario each stage knows its local information plus the actual customer demands we propose coordination schemes that regulate the stages to achieve the supply chain s optimal cost under each information setting all these coordination schemes fit comfortably within an emerging practice called supply chain finance which includes the organization and technology needed to implement them

a deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate abstract a deterministic inventory model for deteriorating items with two warehouses is developed when the replenishment rate is finite demand is at a uniform rate and shortages are allowed it is assumed that the rates of deterioration of item in the two warehouses may be different the model is analysed for the case of continuous release pattern several special cases are discussed and a numerical example is provided to illustrate the variation in optimum inventory level and optimum cost for varying shortage cost

the optimal retailer s ordering policies for deteriorating items with limited storage capacity under trade credit financing abstract under permissible delay in payments all previously published models implicitly assumed that the supplier would offer the retailer a delay period but the retailer would not offer the trade credit period to his her customer huang 2003 journal of the operational research society 54 1011 1015 developed a retailer s replenishment model to reflect the real life situations by assuming that the retailer also adopts the trade credit policy to stimulate his her customer demand in huang s model it is assumed that the goods are not perishable and the storage capacity is unlimited based upon the above argument we propose a two warehouse inventory model for deteriorating items under permissible delay in payments three theorems are developed to determine the optimal cycle time and numerical examples are given to illustrate these theorems finally the results in this paper generalize the results presented by huang 2003 journal of the operational research society 54 1011 1015

optimal pricing and ordering policy under permissible delay in payments abstract many researchers have assumed that the selling price is the same as the purchase cost and developed various eoq models for a retailer when the supplier offers a permissible delay in payments in this paper we complement the shortcoming of their models by considering the difference between the selling price and the purchase cost we then develop an algorithm for a retailer to determine its optimal price and lot size simultaneously when the supplier offers a permissible delay in payments our theoretical result contradicts to their conclusion that the economic replenishment interval and order quantity generally increases marginally under the permissible delay in payments

stopped myopic policies in some inventory models with generalized demand processes this paper considers single item inventory systems with immediate delivery and no economies of scale bounds are provided on the value loss relative to optimal cost for restricting attention to the class of inventory stocking policies that behave myopically up to a specified stopping time the stopping time may be random and may depend on demand histories as well as information exogenous to the firm the bounds are robust to the nature of the demand process faced after the stopping time so are applicable when the statistics of demand after the stopping time are unknown stopping times that are large with high probability imply that near term decisions are completely specified with high probability the general bounding results allow one to consider demand processes that may otherwise be analytically intractable it is shown that the class of demand models for which the assumption of additive i i d shocks is appropriate is the same class admitting effective myopic stocking policies the bounds also make rigorous the intuitive notion that myopic policies are least effective in systems with precipitous drops in demand coupled with an inability to recover cash invested in inventory the option of selling inventory at discount is a reality in many real systems and enhances the attractiveness of the myopic stocking policy in numerical examples the myopic policy is shown to be an effective competitor in a range of systems for which optimal policies are not known the results suggest that for systems with immediate delivery no economies of scale and no currently known optimal policy the myopic stocking rule is a reasonable default policy to adopt

a decomposition approach for a class of capacitated serial systems we study a class of two echelon serial systems with identical ordering production capacities or limits for both echelons demands are assumed to be integer valued for the case where the lead time to the upstream echelon is one period the optimality of state dependent modified echelon base stock policies is proved using a decomposition approach for the case where the upstream lead time is two periods we introduce a new class of policies called two tier base stock policies and prove their optimality some insight about the inventory control problem in n echelon serial systems with identical capacities at all stages and arbitrary lead times everywhere is also provided we argue that a generalization of two tier base stock policies which we call multitier base stock policies are optimal for these systems we also provide a bound on the number of parameters required to specify the optimal policy

an eoq model with deteriorating items under inflation when supplier credits linked to order quantity abstract this study proposes an inventory model under a situation in which the supplier provides the purchaser a permissible delay of payments if the purchaser orders a large quantity shortages are not allowed and the effect of the inflation rate deterioration rate and delay in payment are discussed as well as a result in this paper we establish an eoq model for deteriorating items under inflation when the supplier offers a permissible delay to the purchaser if the order quantity is greater than or equal to a predetermined quantity we then characterize the optimal solution and provide an easy to use algorithm to find the optimal order quantity and replenishment time finally some numerical examples are given to illustrate the theoretical results and made the sensitivity analysis of parameters on the optimal solutions

optimal control and equilibrium behavior of production inventory systems the relationship between commodity inventory and short term price variations has received considerable attention but the understanding has been limited to single stage cross sectional relation in this paper we aim to deepen our understanding of the inventory price relationship in two dimensions across time and across production stages we first examine an individual firm controlling production and two stages of inventory under uncertain input and output prices and operating costs we next establish and characterize the rational expectations equilibrium for an economy in which competitive production firms link a raw material market and a finished goods market with uncertain and price sensitive supply and demand we characterize the dynamics of inventory market price and gross margin based on theoretical analysis simulation and empirical evidence from the petroleum industry we find that inventory fluctuations lag behind price variations and the length of the lags depend on how far the inventory is from the source of the supply or demand shocks we also find that shocks are both dampened and delayed when propagating through the production stages and that shocks have a prolonged effect on inventories and prices at both stages

optimal centralized ordering policies in multi echelon inventory systems with correlated demands this paper treats a depot warehouse system in which demand occurs at the warehouse or retail level this work differs from a number of other studies in that we allow item demands to be correlated both across warehouses and also correlated in time our motivation for this generalization arises from our experience with an actual system of this type used by a major national producer and distributor of consumer products we observed both high correlations between successive monthly demands around 0 7 and correlations between demands for an item at different locations also about 0 7 in a given time period we derive an explicit expression for the optimal safety stock as a function of the level of correlation through time the analysis requires two assumptions 1 the allocation assumption and 2 the equal coefficient of variation assumption similar assumptions have been used by other researchers finally numerical evaluations are included to illustrate the impact of the various magnitudes of correlation

the impact of classroom experiments on the learning of economics an empirical investigation i introduction in economics experimental research is still less common than in the natural sciences therefore it is not surprising that economists also make much less use of experiments for teaching purposes yet intuitively it is by no means clear that confronting a group of students with rules and incentives and observing what happens has a lower marginal impact on learning than demonstrating what happens when you put some chemicals together in a test tube however fels 1993 365 and deyoung 1993 348 49 recently called on those who actually use classroom experiments to provide evidence of the impact on students learning of economics this paper provides some limited evidence section ii describes the method used to evaluate the impact of classroom experiments section iii describes the experiment and offers some hints for those who want to try it section iv provides the results ii method a first indication that experiments might be useful as a teaching tool comes from isaac and walker s 1991 experiment they found that those with experience in the experiment behave differently from those without presumably due to some reflection on the problem the approach of this study is more straightforward and not confined to those who actually take part in the experiment our hypothesis is that merely following the experiment and its outcome also has an impact on learning seven instructors teaching courses in environmental economics or public finance were asked to give their usual lecture on the tragedy of the commons afterwards the control group about half of the students filled out a multiple choice test on that topic as an incentive to put some thought into that task in each course one of those students with no mistakes won a book on environmental economics namely beckenbach 1991 worth 26 80 german marks 1 the questions are reported in section iv the same questions were answered by the other students following the classroom experiment iii the experiment the experiment itself which takes only five to ten minutes was a simple take some game of which a more general account is given by mitter 1986 it involves five students who volunteer before the rules are explained in order to give the participants a chance to clarify remaining open points the experimenter should not forget to mention that tabular data for table i omitted on average the volunteers will not be worse off or might even carry off a small profit but that nevertheless they need to have some change in their pockets because there might be losers each receives two cards with the stylized picture of one cow on one card and five on the other the rules are explained roughly as follows imagine you are peasants using a common field every one of you has to decide how many cattle to keep on the commons one cow or five cows if you give me the card which shows one cow you receive one german mark if you give me the card which shows five cows you receive five marks however for every five cow card i receive every one of you gets one mark less for example if two of you put five cows on the common those two will each receive three marks i e five minus two for the others the payoff is one mark minus two marks which means they have to pay one mark now you can calculate for yourself what the payoffs for other constellations will be please make your decision secretly the participants were placed at some distance from each other and it was ensured that they could not communicate immediately after the experiment the payments were made and the experiment was repeated once with a different group of students five cows is the dominant strategy but the collective payoff would be greater if no one played it this method of demonstrating the commons dilemma is less complicated than the procedures reported in powers 1987 and tsai 1993

interrelating operational and financial performance measurements in inventory control financial supply chain management and working capital management are increasingly receiving attention as important avenues to increase profitability in supply chains by actively managing payment terms and working capital requirements managers can influence financial performance and achieve significant cost savings however measures to improve financial performance implicitly restrict and influence operational performance in our research we elaborate on the benefits of equally considering both operational and financial aspects in decision making for the physical and financial supply chain we develop a mathematical model that determines the optimal purchasing order quantity under working capital restrictions and payment delays we analyze the trade offs between the most commonly used financial and operational measurements such as service level return on investment profit margin and inventory level our results demonstrate the significance of payment delays increases decreases in the upstream downstream payment delays favor the system s operations by decreasing operational costs moreover increases in the working capital employed in the system decrease the total operational cost increase the total financial cost and lower the return on working capital investment c 2009 elsevier b v all rights reserved

myopic policies for some inventory models with uncertain demand distributions the majority of papers on stochastic inventory theory make the assumption that the distribution of consumer demand in each time period is known with certainty while this assumption is unsupported in many applied contexts it is conventionally held that more realistic models are more difficult to solve and will not yield simple operational policies this paper shows that a simple inventory policy based upon a critical fractile can be optimal or near optimal in some inventory models with parameter adaptive demand processes in these some parameter of the demand distribution is not known with certainty and estimates of the parameter are updated in a statistical fashion as demand is observed through time examples include exponentially smoothed forecasts and bayesian updating of parameter estimates bounds on the value loss relative to optimal cost when using the critical fractile policy can be calculated directly from the problem data some numerical examples illustrate the technique

exact and approximate evaluation of batch ordering policies for two level inventory systems we consider a two level inventory system with one warehouse and n identical retailers lead times transportation times are constant and the retailers face independent poisson demand in a previous paper we derived a recursive procedure for determining the policy costs for an average item in case of one for one replenishment policies in this paper we show how these results can be used for the exact or approximate evaluation of more general policies where both the retailers and the warehouse order in batches we compare our methods to the method recently suggested by a svoronos and p zipkin

optimal policy for a two facility inventory problem with storage constraints and two freight modes this paper considers a two facility supply chain for a single product in which facility 1 orders the product from facility 2 and facility 2 orders the product from a supplier in each period the orders placed by each facility are delivered in two possible nonnegative integer numbers of periods the difference between them is one period random demands in each period arise only at facility 1 there are physical storage constraints at both facilities in each period the objective of the supply chain is to find an ordering policy that minimizes the expected cost over a finite horizon and the discounted stationary expected cost over an infinite horizon we characterize the structure of the minimum expected cost and the optimal ordering policy for both the finite and the discounted stationary infinite horizon problems

production and inventory control for a make to stock calibrate to order system with dedicated and shared resources consider a firm that produces multiple products on dedicated production lines stage 1 which are further customized calibrated on a shared resource stage 2 common to all products the dedicated production lines and the shared resource for calibration face capacity uncertainties the firm holds inventory of products that are not yet calibrated and carries out calibration when an order is received we analyze a multiperiod inventory model for two products and derive the optimal production policy at stage 1 as well as the optimal allocation of the shared resource to demands at stage 2 for the shared resource because of its capacity uncertainty not only the total planned production quantities matter but also the sequence in which the products are processed we characterize the optimal allocation of the shared resource and show that the optimal policy keeps the ending inventories of products as close to a so called target path as possible for the dedicated production lines because of their capacit

time phased safety stocks planning and its financial impacts empirical evidence based on european econometric data abstract this paper explores the rationale for planning time phased safety stocks we assert that a single safety stock vector for the entire planning horizon typically based on stationary demand forecast errors and stationary replenishment lead times may be insufficient for hedging against uncertainties we argue that planning time phased safety stocks is prudent when faced with non stationary demand and or non stationary supply we scrutinize particularly whenever non stationarity is due to heteroscedastic demand and resulting heteroscedastic demand forecast errors consequently an empirical evidence on a wide basis is provided that such errors for manufactured products are highly heteroscedastic to test the phenomenon and to estimate its impact at stock keeping unit level we have conducted an econometric analysis using the eurostat data from 1985 onwards specifically we analyze new industrial orders across various industries and types of goods manufactured in the five largest european economies by using eviews 7 0 to demonstrate which inventory savings can accrue when safety stock levels are deliberately planned to vary in accordance with the observed heteroscedasticity we estimate potential safety stock savings reusing the same data sets our findings indicate that one realization of non stationarity i e heteroscedastic demand is indeed pervasive in the european industry thus recognition of this demand nature may add to effective inventory management policies reducing unnecessary safety stocks improving service or both relative to a single valued safety stock regimen

two warehouse inventory models for deteriorating items with shortages under inflation abstract in this paper the two warehouse inventory problem for deteriorating items with constant demand rate and shortages under inflation is considered in contrast to the traditional deterministic two warehouse inventory model with shortages at the end of each replenishment cycle an alternative model in which each cycle begins with shortages and ends without shortages is proposed here the optimal solution not only exists but also is unique comparing these two two warehouse inventory models the study shows that the proposed model is less expensive to operate than the traditional one in the case of the inflation rate is greater than zero hence under the consideration of inflationary effect the proposed model is less expensive finally some numerical examples for illustration are provided

inventory management with asset based financing most of the traditional models in production and inventory control ignore the financial states of an organization and can lead to infeasible practices in real systems this paper is the first attempt to incorporate asset based financing into production decisions instead of setting a known exogenously determined budgetary constraint as most existing models suggest we model the available cash in each period as a function of assets and liabilities that may be updated periodically according to the dynamics of the production activities furthermore our models allow different interest rates on cash balance and outstanding loans which is an enhancement over most traditional models in that inventory financed by a loan may be more expensive than that by out of pocket cash we demonstrate the importance of joint consideration of production and financing decisions in a start up setting in which the ability to grow the firm is mainly constrained by its limited capital and dependence on bank financing we then explain the motivation for asset based financing by examining the decision making at a bank and a set of retailers in a newsvendor setting