financing flexibility the case of outsourcing abstract we investigate the relationship between the extent and timing of vertical flexibility and the financial choices of a firm by vertical flexibility we mean partial total and reversible outsourcing of a necessary input a firm simultaneously selects the vertical setting and the financial sources of investment in flexibility in particular debt and venture capital a loan may come from a lender that requires the payment of a fixed coupon over time and an option to buy out the firm in certain circumstances debt leads to the same level of flexibility of an unlevered firm yet investment occurs earlier the injection of venture capital reduces the quest for vertical flexibility and speeds up investment then there arises a fresh substitutability between a financial venture capital and a real variable vertical flexibility

inventory management under market size dynamics we investigate the situation where a customer experiencing an inventory stockout at a retailer potentially leaves the firm s market in classical inventory theory a unit stockout penalty cost has been used as a surrogate to mimic the economic effect of such a departure in this study we explicitly represent this aspect of consumer behavior incorporating the diminishing effect of the consumers leaving the market upon the stochastic demand distribution in a time dynamic context the initial model considers a single firm we allow for consumer forgiveness where customers may flow back to the committed purchasing market from a nonpurchasing latent market the per period decisions include a marketing mix to attract latent and new consumers to the committed market and the setting of inventory levels we establish conditions under which the firm optimally operates a base stock inventory policy the subsequent two models consider a duopoly where the potential market for a firm is now the committed market of

multinomial approximating models for options with k state variables contingent claims whose values depend on multiple sources of uncertainty arise in many financial contracts and in the analysis of real projects unfortunately closed form solutions for these options are rare and numerical methods can be computationally expensive this article extends the literature on multinomial approximating models specifically new multinomial models are presented that include as special cases existing models the more general models are shown to be computationally more efficient

non cooperative and cooperative game theoretic models for usage based lease contracts abstract in this paper we study game theoretic models for lease contracts by which the owner lessor rents a piece of equipment to a user lessee the lessee decides on the optimal lease period and usage rate and the lessor is responsible for developing a maintenance policy for the equipment two non cooperative game theoretic models and a cooperative model are developed to describe the relationships between the two decision makers in the non cooperative simultaneous move game the lessee and the lessor act simultaneously and independently to make their decisions in the leader follower non cooperative game the lessor is the leader who specifies the maintenance policy first and the lessee as the follower decides on the lease period and usage rate accordingly for these two games the nash and stackelberg equilibria are obtained respectively for the cooperative game we derive the solution targeting on total profit maximization and show that this solution can be implemented as an equilibrium using a nonlinear transfer payment contract besides we compare the nash equilibrium stackelberg equilibrium and the total maximum solution to each other and our results show that the lessee and lessor can gain more profit from the cooperative contract than from the non cooperative alternatives numerical examples are provided to demonstrate the different solution methodologies and the value of cooperation

competitive and cooperative inventory policies in a two stage supply chain we investigate a two stage serial supply chain with stationary stochastic demand and fixed transportation times inventory holding costs are charged at each stage and each stage may incur a consumer backorder penalty cost e g the upper stage the supplier may dislike backorders at the lower stage the retailer we consider two games in both the stages independently choose base stock policies to minimize their costs the games differ in how the firms track their inventory levels in one the firms are committed to tracking echelon inventory in the other they track local inventory we compare the policies chosen under this competitive regime to those selected to minimize total supply chain costs i e the optimal solution we show that the games nearly always have a unique nash equilibrium and it differs from the optimal solution hence competition reduces efficiency furthermore the two games equilibria are different so the tracking method influences strategic behavior we show that the system optimal solution can be achieved as a nash equilibrium using simple linear transfer payments the value of cooperation is context specific in some settings competition increases total cost by only a fraction of a percent whereas in other settings the cost increase is enormous we also discuss stackelberg equilibria

promised lead time contracts under asymmetric information we study the important problem of how a supplier should optimally share the consequences of demand uncertainty i e the cost of inventory excesses and shortages with a retailer in a two level supply chain facing a finite planning horizon in particular we characterize a multiperiod contract form the promised lead time contract that reduces the supplier s risk from demand uncertainty and the retailer s risk from uncertain inventory availability under the contract terms the supplier guarantees on time delivery of complete orders of any size after the promised lead time we characterize the optimal promised lead time and the corresponding payments that the supplier should offer to minimize her expected inventory cost while ensuring the retailer s participation in such a supply chain the retailer often holds private information about his shortage cost or his service level to end customers hence to understand the impact of the promised lead time contract on the supplier s and the retailer s performance we study the system under local control with full information and local control with asymmetric information by comparing the results under these information scenarios to those under a centrally controlled system we provide insights into stock positioning and inventory risk sharing we quantify for example how much and when the supplier and the retailer overinvest in inventory as compared to the centrally controlled supply chain we show that the supplier faces more inventory risk when the retailer has private service level information we also show that a supplier located closer to the retailer is affected less by information asymmetry next we characterize when the supplier should optimally choose not to sign a promised lead time contract and consider doing business under other settings in particular we establish the optimality of a cutoff level policy finally under both full and asymmetric service level information we characterize conditions when optimal promised lead times take extreme values of the feasible set yielding the supplier to assume all or none of the inventory risk hence the name all or nothing solution we conclude with numerical examples demonstrating our 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

review of renewable energy investment and financing in china status mode issues and countermeasures abstract with the support of national policies china s renewable energy generation industry has experienced a rapid development period and entered the world forefront level especially in the aspects of installed capacity and speed of newly installed capacity however with the rapid development of renewable energy the power generation industry is facing more and more challenges particularly in investment and financing as for wind power industry there are also some problems such as single financing channels blindness of projects investment and so on which will result in financing difficulties for some advanced projects in addition the problems for the investment of photovoltaic pv power generation leads to vicious competition and a tumble in international market thus the overcapacity of china s entire pv industry emerges generally speaking the renewable energy industry is facing a seemingly contradictory predicament of funding deficiencies and blind investment which is derived from the government centered renewable energy investment and financing this government centered mode has promoted the development of renewable energy industry in the early stage but it cannot be adapted to the requirements of sustainable development in view of these the problems of renewable energy investment and financing are deeply studied in this paper this paper proceeds as follows firstly the overview of the development of china s renewable energy industry is briefly introduced secondly the status quo of china s renewable energy investment and financing is explored in detail based on overview of the following five perspectives investment situation investment and financing bodies investment and financing means sources of funding and financing channels secondly the patterns and characteristics of renewable energy financing are summarized and a comparative analysis of wind power and photovoltaic power generation financing means is carried out finally renewable energy investment and financing issues are discussed and further feasible proposals are put forward in all this paper is of great significance in the sustainable and healthy development of china s renewable energy

decentralizing cross functional decisions coordination through internal markets a firm faces many problems that are inherently cross functional to solve them successfully requires the coordinated actions of many functional representatives acting in a decentralized setting functional managers however respond to their own individual incentives and may consequently fail to maximize the overall profits of the firm we examine this issue in a setting in which the output of early actions limits the range of later actions and we propose an incentive scheme that allows the system to be successfully decentralized our mechanism is based on linear transfer prices for the intermediate output that are implemented through an internal market a market maker buys the output from one function and sells it to another she is not obliged to sell at the same price at which she bought and may set prices solely to provide incentives we illustrate the flexibility of the scheme by applying it to several models in the operations management literature

on manufacturing marketing incentives stereotypically marketing is mainly concerned about satisfying customers and manufacturing is mainly interested in factory efficiency using the principal agent agency paradigm which assumes that the marketing and manufacturing managers of the firm will act in their self interest we seek incentive plans that will induce those managers to act so that the owner of the firm can attain as much as possible of the residual returns one optimal incentive plan can be interpreted as follows the owner subcontracts to pay the manufacturing manager a fixed rate for all capacity he delivers each marketing manager receives all of the returns from his product in turn all managers pay a fixed fee to the owner under this plan the marketing managers will often complain about the stock level decisions even though these levels are announced in advance under a revised plan the owner can eliminate such complaints by delegating the stocking decisions to the respective marketing managers without any loss this plan is interpreted as requiring the owner to make a futures market for manufacturing capacity paying the manufacturing manager the expected marginal value for each unit of capacity delivered receiving the realized marginal value from the marketing managers and losing money on average in the process

dynamic investment and capital structure under manager shareholder conflict abstract this paper investigates the interactions between the investment and financing decisions of a firm under manager shareholder conflicts arising from asymmetric information in particular we extend the manager shareholder conflict problem in a real options model by incorporating debt financing we show that manager shareholder conflicts over investment policy increase not only the investment and default triggers but also coupon payments which lead to a decrease in the equity value moreover given the presence of manager shareholder conflicts debt financing increases investment and decreases total social welfare as a result there is a trade off between the efficiency of investment and total social welfare with debt financing these results fit well with the findings of previous empirical work in this area

supplier manufacturer coordination in capacitated two stage supply chains abstract manufacture to order is an increasingly popular strategy in commodity electronics and other similar markets where many different product configurations can be produced from common components to succeed in this environment manufacturers need to keep both cost and order fulfillment time low in this article we compare three different mechanisms that a manufacturer whose revenues depend on order delays may use to affect its component supplier s inventory decisions these mechanisms are specifying components inventory level offering a share of the earned revenues to the supplier called simple revenue sharing and offering a two part revenue sharing scheme we show that whereas the first two approaches do not lead to supply chain coordination the two part scheme does we demonstrate with numerical experiments that up to a point the component supplier benefits from having a high utilization of its production facility whereas the manufacturer benefits from having excess production capacity

a discrete time model of american put option in an uncertain environment abstract a discrete time mathematical model for american put option with uncertainty is presented and the randomness and fuzziness are evaluated by both probabilistic expectation and fuzzy expectation defined by a possibility measure from the viewpoint of fuzzy expectation taking account of decision maker s subjective judgment an optimality equation for the optimal stopping problem in a fuzzy stochastic process is derived and an optimal exercise time is given for the american put option it is shown that the optimal fuzzy price is a solution of the optimality equation under a reasonable assumption the permissible range of the writer s seller s optimal expected price in the american put option is presented and the meaning and properties of the optimal expected prices are discussed in numerical examples in a numerical example the discrete time approximation model is discussed for the continuous time model

coordinated decisions for substitutable products in a common retailer supply chain abstract this paper studies coordination mechanisms in a supply chain which consists of two suppliers with capacity uncertainties selling differential yet substitutable products through a common retailer who faces price sensitive random demand of these two products we develop in a noncompetitive setting three coordination models revenue sharing return policy and combination of revenue sharing and return policy and contrast them with a basic and uncoordinated model we are able to establish the ordinal relationship among the retailer s ordering and pricing decisions and analytically compare the performances between certain models when two suppliers are identical we find that the retailer s ordering and pricing decisions in the model with return policy in the case of identical suppliers are independent of demand or supply uncertainty our numerical results reveal that the performances of coordination models in the case of nonidentical suppliers resemble those in the case of identical suppliers we find that the retailer will place a larger order quantity in models where her average cost per unit sold is smaller we also find that product substitutability and uncertainties have different effects on chain performances

supply chain choice on the internet internet companies extensively use the practice of drop shipping where the wholesaler stocks and owns the inventory and ships products directly to customers at retailers request under the drop shipping arrangement the supply chain benefits from risk pooling because the inventory for multiple retailers is stocked at the same location the wholesalers another more traditional channel alternative on the internet is one in which retailers stock and own the inventory these two supply chain structures which predominate on the internet result in different inventory risk allocation stocking decisions and profits for channel members moreover the two channel alternatives can be combined into a dual strategy whereby the retailer uses local inventory as a primary source and relies on drop shipping as a backup we model the dual strategy as a noncooperative game among the retailers and the wholesaler analyze it and obtain insights into the structural properties of the equilibrium solution to facilitate development of recommendations for practicing managers finally we characterize situations in which each of three channels is preferable by specifying appropriate ranges of critical parameters including demand variability the number of retailers in the channel wholesale prices and transportation costs

optimal ordering and pricing strategies in the presence of a b2b spot market abstract in the current paper we examine the effect of a b2b spot market on the strategic behavior and the performance of a reseller who continues to use the traditional channel while participating in a b2b spot market we analyze the case in which a risk neutral reseller faces an additive or multiplicative demand function and identify sufficient conditions under which the optimal order quantity and retail price exist and are unique we then analytically examine the case in which a risk averse reseller participates in a fully liquid spot market we also study numerically how varying liquidity spot price volatility demand variability and correlation coefficient affect a firm s strategies and performance we find that demand variability significantly affects both pricing and ordering strategies whereas the spot price volatility has less influence on pricing decisions our results also show that for a risk averse reseller to charge a lower retail price when the spot market liquidity increases is desirable we further show that a b2b spot market cannot always improve a reseller s utility these findings shed light on how resellers can adjust their procurement and pricing strategies to align with the new business environment created by the emergence of b2b spot markets as well as have obvious implications for the development of a b2b spot market

numerical evaluation of multivariate contingent claims we develop a numerical approximation method for valuing multivariate contingent claims the approach is based on an n dimensional extension of the lattice binomial method closed form solutions for the jump probabilities and the jump amplitudes are obtained the accuracy of the method is illustrated in the case of european options when there are three underlying assets article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

a lattice framework for option pricing with two state variables a procedure is developed for the valuation of options when there are two underlying state variables the approach involves an extension of the lattice binomial approach developed by cox ross and rubinstein to value options on a single asset details are given on how the jump probabilities and jump amplitudes may be obtained when there are two state variables this procedure can be used to price any contingent claim whose payoff is a piece wise linear function of two underlying state variables provided these two variables have a bivariate lognormal distribution the accuracy of the method is illustrated by valuing options on the maximum and minimum of two assets and comparing the results for cases in which an exact solution has been obtained for european options one advantage of the lattice approach is that it handles the early exercise feature of american options in addition it should be possible to use this approach to value a number of financial instruments that have been created in recent years

capacitated inventory problems with fixed order costs some optimal policy structure abstract almost 40 years ago h scarf the optimality of s s policies in dynamic inventory problems in k arrow s karlin p suppes eds mathematical models in the social sciences stanford university press stanford 1960 established the optimal s s policy structure for the periodic review inventory problem with fixed ordering costs and no capacity constraint since then the capacitated problem has resisted characterization in the present paper we partially bridge this gap using a generalization of scarf s k convexity we show that the optimal capacitated policy has an s s like structure to do so we divide the parameter space into four regions in two of these regions the optimal policy is completely specified while in the other two it is partially specified we complement these findings with a computational study this study suggests that a still simpler optimal policy structure exists

optimal shared savings contracts in supply chains linear contracts and double moral hazard in many supply chains consumption of indirect materials sold by a supplier to a customer for use in her production process can be reduced by efforts exerted by either party since traditional supply contracts provide no incentive for the supplier to exert such effort shared savings contracts have been proposed as a way to improve incentives in the channel leading to more efficient effort choices by the two parties such shared savings contracts typically combine a fixed service fee with a variable component based on consumption volume we formalize this situation using the double moral hazard framework in which both parties decide how much effort to exert by trading off the cost of their effort against the benefits that they will obtain from reduced consumption we also extend the double moral hazard framework to analyze a broader class of cost of effort functions than considered so far including the linear cost of effort functions commonly found in practice we show that the supplier can still always induce the optimal second best equilibrium with a linear shared savings contract under this broader class of functions however the behavior of the optimal contract as a function of the problem parameters becomes more complex we illustrate how small changes in the problem parameters can turn profits from being a well behaved to a poorly behaved function of the contract and provide some theoretical characterization of this phenomenon the practical significance of this is that simple linear contracts are sufficient in many double moral hazard contexts even for the broader class of functions we consider but care must be taken in selecting the optimal contract parameters

investment uncertainty and liquidity we analyze the dynamic investment decision of a firm subject to an endogenous financing constraint the threat of future funding shortfalls lowers the value of the firm s timing options and encourages acceleration of investment beyond the first best optimal level as well as highlighting another way by which capital market frictions can distort investment behavior this result implies that 1 the sensitivity of investment to cash flow can be greatest for high liquidity firms and 2 greater uncertainty has an ambiguous effect on investment

real options agency conflicts and optimal capital structure abstract we examine the impact of a stockholder bondholder conflict over the timing of the exercise of an investment option on firm value and corporate financial policy we find that an equity maximizing firm exercises the option too early relative to a value maximizing strategy and we show how this problem can be characterized as one of overinvestment in risky investment projects equityholders incentive to overinvest significantly decreases firm value and optimal leverage and significantly increases the credit spread of risky debt numerical solutions illustrate how the agency cost of overinvestment and its effect on corporate financial policy vary with firm and project characteristics

technology choice under several uncertainty sources abstract we analyze a model of irreversible investment with two sources of uncertainty a risk neutral decision maker has the choice between two mutually exclusive projects under input price and output price uncertainty we propose a complete study of the shape of the rational investment region and we prove that it is never optimal to invest when the alternative investments generate the same payoff independently of its size a key feature of this bidimensional degree of uncertainty is thus that the payoff generated by each project is not a sufficient statistic to make a rational investment in this context our analysis provides a new motive for waiting to invest the benefits associated with the dominance of one project over the other as an illustration we apply our methodology to power generation under uncertainty

serial supply chains with economies of scale bounds and approximations we consider two models of stochastic serial inventory systems with economies of scale for which the forms of optimal policies are known in the first model each stage has a fixed order quantity while in the second model there is a fixed order cost for external supplies for each model we show that the optimal policy parameters can be bounded and approximated by a series of independent single stage optimal policy parameters we further construct closed form bounds and approximations for the single stage solutions and apply them to the serial systems these results provide simple and effective solutions that will help to facilitate implementations in practice they also allow us to see the connections between the serial and single stage systems and sharpen our intuition on optimal policy parameters and system behavior

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

generalised soft binomial american real option pricing model fuzzy stochastic approach abstract the stochastic discrete binomial models and continuous models are usually applied in option valuation valuation of the real american options is solved usually by the numerical procedures therefore binomial model is suitable approach for appraising the options of american type however there is not in several situations especially in real option methodology application at to disposal input data of required quality two aspects of input data uncertainty should be distinguished risk stochastic and vagueness fuzzy traditionally input data are in a form of real crisp numbers or crisp stochastic distribution function therefore hybrid models combination of risk and vagueness could be useful approach in option valuation generalised hybrid fuzzy stochastic binomial american real option model under fuzzy numbers t numbers and decomposition principle is proposed and described input data up index down index growth rate initial underlying asset price exercise price and risk free rate are in a form of fuzzy numbers and result possibility expected option value is also determined vaguely as a fuzzy set illustrative example of equity valuation as an american real call option is presented

capacity decisions with debt financing the effects of agency problem abstract this paper studies the capacity management problem for a firm that uses debt financing this is done by analyzing the effect of the associated agency problem when making capacity decisions the agency problem arises when there are potential conflicts of interest between the firm owner and the lender we show that this agency problem can constrain the firm s optimal capacity decision because the borrowing rate will increase as the risk of default increases with capacity level chosen the firm will therefore try to optimally choose the level so as to reduce the risk of bankruptcy which the lender will take into account and as a consequence the firm will try to control the risk associated with potentially high borrowing costs however even when the expected bankruptcy cost is carefully controlled the optimal capacity decision is still made at the risk of incurring considerable agency costs in addition the corporate tax level can also play a significant role in capacity choice we show that although a higher tax rate leads to bigger tax benefit of debt and lower agency cost it also gives rise to a higher tax liability after balancing the tax benefit of debt with the agency cost the firm can make an optimal decision on the capacity level required the efficacy of financial hedging for mitigating the agency cost is also analyzed finally we compare and contrast our analysis with existing studies and it appears that we have been able to obtain a deeper insight into the problem

integrated optimization of procurement processing and trade of commodities we consider the integrated optimization problem of procurement processing and trade of commodities in a multiperiod setting motivated by the operations of a prominent commodity processing firm we model a firm that procures an input commodity and has processing capacity to convert the input into a processed commodity the processed commodity is sold using forward contracts while the input itself can be traded at the end of the horizon we solve this problem optimally and derive closed form expressions for the marginal value of input and output inventory we find that the optimal procurement and processing decisions are governed by price dependent inventory thresholds we use commodity markets data for the soybean complex to conduct numerical studies and find that approximating the joint price processes of multiple output commodities using a single composite output product and using the approximate price process to determine procurement and processing decisions is near optimal compared to a myopic spread option based heuristic the optimization based dynamic programming policy provides significant benefits under conditions of tight processing capacities and high price volatilities finally we propose an approximation procedure to compute heuristic policies and an upper bound to compare the heuristic against when commodity prices follow multifactor processes

optimal inventory policy with two suppliers we analyze a periodic review inventory model where the decision maker can buy from either of two suppliers with the first supplier the buyer incurs a high variable cost but negligible fixed cost with the second supplier the buyer incurs a lower variable cost but a substantial fixed cost consequently ordering costs are piecewise linear and concave we show that a reduced form of generalized s s policy is optimal for both finite and discounted infinite horizon problems provided that the demand density is log concave this condition on the distribution is much less restrictive than in previous models in particular it applies to the normal truncated normal gamma and beta distributions which were previously excluded we concentrate on the situation in which sales are lost but explain how the policy cost assumptions and proofs can be altered for the case where excess demand is backordered in the lost sales case the optimal policy will have one of three possible forms a base stock policy for purchasing exclusively at the high variable cost hvc supplier an slvc slvc policy for buying exclusively from the low variable cost lvc supplier or a hybrid s shvc slvc policy for buying from both suppliers

stockpiling under price uncertainty and storage capacity constraints abstract a model is presented for the operation of an agent whose responsibility is to purchase and perhaps stockpile sufficient quantities of a certain commodity in order to satisfy an exogenous constant demand per time period this is the situation faced by a state agency which is responsible for the purchasing of oil products to satisfy the demand of a country in which demand for energy has stabilized at a certain level an important feature of the model is that the price of the commodity is described by a stochastic process this reflects the volatility of prices of oil products furthermore the model takes storage capacity constraints explicitly into account and thus can help to assess the optimal level of storage capacity expansion the relevant stochastic dynamic programming equations are derived and solved for the least cost function which turns out to be piecewise linear in the inventory level the storage capacity enters only in the computation of the constant term of the value function the solution of the dynamic programming equation leads also to the optimal purchasing strategy of agencies with different levels of flexibility in their policy in the model an agency can be allowed or not to resell from the stock and it can have finite or infinite storage capacity

nash game model for optimizing market strategies configuration of platform products in a vendor managed inventory vmi supply chain for a product family this paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies platform product configuration and inventory policies in a vmi vendor managed inventory supply chain the manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers multiple types of products are substitutable each other to end customers the manufacturer makes its decision on raw materials procurement platform product configuration product replenishment policies to retailers with vmi price discount rate and advertising investment to maximize its profit retailers in turn consider the optimal local advertising investments and retail prices to maximize their profits this problem is modeled as a dual simultaneous non cooperative game as a dual nash game model with two sub games one is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers this paper combines analytical iterative and ga genetic algorithm methods to develop a game solution algorithm to find the nash equilibrium a numerical example is conducted to test the proposed model and algorithm and gain managerial implications

the effects of external financing costs on investment timing and sizing decisions abstract we develop a dynamic model in which a firm exercises an option to expand production on either a small or large scale with cash reserves and costly external funds an intermediate level of cash reserves which is insufficient for the large scale investment but sufficient for the small scale investment provides an incentive for the firm to invest early in the small scale project these results fill the gap between two types of results i empirical findings of a u shaped relation between the investment volume and internal funds and ii empirical predictions of a u shaped relation between the investment timing and internal funds in addition our results have real world implications for investment in alternative projects

technical note optimal inventory policy in the presence of a long term supplier and a spot market we consider a stochastic inventory control problem in which a buyer makes procurement decisions while facing periodic random demand and two supply sources namely a long term contract supplier and a spot market the contract between the buyer and the supplier partially shields the latter from the vicissitudes of the spot market in that the price paid by the buyer to the supplier is only partially linked to the spot price at the moment after fulfilling the minimum order commitment with the supplier the buyer has the full freedom to source from both the supplier and the market procurement from the spot market also incurs a fixed setup cost we show that an optimal policy consists of three different policy forms with the realization of each depending on the buyer s inventory level and the prevalent spot price certain conditions are identified under which monotone trends exist between policy parameters and the current spot price

analysis of batch ordering inventory models with setup cost and capacity constraint abstract stochastic periodic review batch ordering inventory problems appear in many industrial settings however few literature deals with the optimal ordering polices for such problems no mention to the inclusion of the fixed ordering cost and the production capacity in this paper we consider a single item periodic review batch ordering inventory system with the consideration of the setup cost and the capacity constraint for each order over a finite planning horizon by proposing several new convex notions we show that a batch based s s policy is optimal for the unlimited ordering capacity case while for the limited ordering capacity case a modified r q policy is optimal for the setting with zero ordering setup cost and a batch based x y band policy for the setting with positive ordering setup cost moreover we analytically study the sensitivity of the policy parameters with respect to the capacity and batch order size and derive the bounds on the optimal policy parameters we further extend our analysis to the infinite horizon setting and show that the structure of the optimal policy remains similar finally the numerical experiments provide some insights into the impact of model parameters on the benefit of reducing the batch size and increasing the ordering capacity and indicate that ignoring batch requirement may lead to a significant cost increment

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

optimal ordering decisions with uncertain cost and demand forecast updating we determine the optimal ordering policy for a retailer who has two instants to order a seasonal product from a manufacturer prior to a single selling season while the demand is uncertain the retailer can improve the forecast by utilizing the market signals observed between the first and second instants however because of the nature of the manufacturing environment the unit cost at the second instant is uncertain and could be higher or lower than the unit cost at the first instant to determine the profit maximizing ordering strategies at both instants the retailer has to evaluate the trade off between a more accurate forecast and a potentially higher unit cost at the second instant we present a nested newsvendor model for determining the optimal order quantity at each instant and characterize the conditions under which it is optimal for the retailer to delay its order until the second instant

inventory sharing and rationing in decentralized dealer networks an increasing number of manufacturers have started to pursue a strategy that promotes inventory sharing among the dealers in their distribution network in this paper we analyze a decentralized dealer network in which each independent dealer is given the flexibility to share his inventory we model inventory sharing as a multiple demand classes problem in which each dealer faces his own customer demand with high priority and inventory sharing requests from other dealers with low priority assuming that each dealer uses a base stock and threshold rationing policy for his inventory stocking and inventory sharing decisions we explicitly model the interactions between the dealers through inventory sharing and obtain aclosed form cost function for each dealer based on the steady state distribution of the inventory levels at the two dealers we then provide a detailed supermodularity analysis of the inventory sharing and inventory rationing game in which each dealer has a two dimensional strategy set stocking level and rationing level we show that the full sharing game in which dealers precommit to sharing all of their on hand inventory and the fixed sharing level game in which dealers precommit to sharing a portion of their on hand inventory are supermodular and thus a pure strategy nash equilibrium is guaranteed to exist for the rationing game in which dealers precommit to their stocking levels we show that there exists a dominant strategy equilibrium on the dealers sharing rationing levels finally a comprehensive computational study is conducted to highlight the impact of the manufacturer s incentives subsidies and or transshipment fees on the dealers sharing behavior

all or nothing ordering under a capacity constraint we consider a special case of the single item periodic review inventory control problem with fixed plus linear ordering costs and an upper bound on production capacity we assume that the fixed cost is large relative to the variable cost and restrict our analysis to full capacity orders we show that the optimal policy is a threshold policy with respect to the inventory position for a class of cost to go functions that include the class of convex functions

the multinomial option pricing model and its brownian and poisson limits the cox ross and rubinstein binomial model is generalized to the multinomial case limits are investigated and shown to yield the blacks scholes formula in the case of continuous sample paths for formula in the case of complete market structures in the discontinuous case a merton type formula is shown to result provided jump probabilities are replaced by their corresponding arrow debreu prices article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

evaluating natural resource investments notwithstanding impressive advances in the theory of finance over the past 2 decades practical procedures for capital budgeting have evolved only slowly the standard technique which has remained unchanged in essentials since it was originally proposed see dean 1951 bierman and smidt 1960 derives from a simple adaptation of the fisher 1907 model of valuation under certainty under this technique expected cash flows from an investment project are discounted at a rate deemed appropriate to their risk and the resulting present value is compared with the cost of the project this standard textbook technique reflects modern theoretical developments only insofar as estimates of the discount rate may be obtained from crude application of single period asset pricing theory but see brennan 1973 bogue and roll 1974 turnbull 1977 constantinides 1978 the inadequacy of this approach to capital budgeting is widely acknowledged although not widely discussed its obvious deficiency is its the evaluation of mining and other natural resource projects is made particularly difficult by the high degree of uncertainty attaching to output prices it is shown that the techniques of continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing managing and abandoning them the approach may be adapted to a wide variety of contexts outside the natural resource sector where uncertainty about future project revenues is a paramount concern

risk sharing and information revelation mechanism of a one manufacturer and one retailer supply chain facing an integrated competitor this paper develops an information revelation mechanism model of a one manufacturer and one retailer supply chain facing an outside integrated competitor under demand uncertainty we investigate how the manufacturer designs a wholesale price order quantity contract to induce the retailer to report his risk sensitivity information truthfully we try to explore the effects of the outside competitor and the risk sharing rule on the optimal price service level decisions of the retailer and the optimal wholesale prices of the manufacturer we find that the strategic interaction plays an important role in the effect of risk sensitivity on the order quantity for the retailer when the fraction of the risk cost shared by the manufacturer is sufficiently large small the optimal wholesale price for the high risk averse retailer is higher lower than that for the low risk averse retailer

the competitive newsboy we consider a competitive version of the classical newsboy problem in which a firm must choose an inventory or production level for a perishable good with random demand and the optimal solution is a fractile of the demand distribution and investigate the impact of competition upon industry inventory a splitting rule specifies how initial industry demand is allocated among competing firms and how any excess demand is allocated among firms with remaining inventory we examine the relation between equilibrium inventory levels and the splitting rule and provide conditions under which there is a unique equilibrium our most general result is that if all excess demand is reallocated i e there is perfect substitutability then competition never leads to a decrease in industry inventory

supply chain coordination with multiple shipments the optimal inventory subsidizing contracts we study a supply chain involving a supplier retailer relationship when production lead time is long and the selling season is short the retailer has to place an order ahead of the season which resembles the classical newsvendor model however we consider the situation when the supplier agrees to deliver the order in multiple shipments in the season and then the retailer needs to determine the quantity and or timing of each shipment under a centralized setting we derive the optimal quantity and or timing decisions of the retailer under a decentralized setting incentive misalignment arises from ineffective allocation of inventory costs between the parties in addition to the well known double marginalization effect hence we devise an incentive contract which involves a risk sharing mechanism at the end of the season and an inventory subsidizing scheme for the entire season in practice the inventory subsidizing scheme can be implemented in different ways such as a direct subsidizing scheme o

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

demand information and spot price information supply chains trading in spot markets abstract this paper investigates the effect of information updating on the members of a two stage supply chain in the presence of spot market the supplier decides the contract price new information becomes available as time progresses the manufacturer updates his belief on demand and or spot price and subsequently decides the contract quantity the demand and spot price are correlated thus the new demand information also updates the belief on the spot price and vice versa we model the problem with an information updating stackelberg game and derive unique equilibrium strategies previous studies have considered only the demand information and concluded that improved demand information always benefits the supplier by contrast we demonstrate that improved demand information benefits both the supplier and manufacturer if the correlation coefficient between the two uncertainties has a small positive value and benefits the manufacturer but hurts the supplier otherwise moreover superior spot price information benefits only the manufacturer and always hurts the supplier surprisingly superior information fails to improve the performance of the supply chain and only changes the allocation of the profits between the supplier and manufacturer our findings likewise provide insights into when the supplier intends to use the contract channel and which type of information updating facility or expertise to invest in if a choice must be made

efficient supply contracts for fashion goods with forecast updating and two production modes we examine the problem of developing supply contracts that encourage proper coordination of forecast information and production decisions between a manufacturer and distributor of high fashion seasonal products operating in a two mode production environment the first production mode is relatively cheap but requires a long lead time while the second is expensive but offers quick turnaround we focus on contracts of the form w1 w2 b wherewi is the wholesale price offered for production modei andb is a return price offered for items left over at the end of the season we find that such a contract can coordinate the manufacturer and distributor to act in the best interest of the channel the pricing conditions needed to ensure an efficient solution vary depending on the degree of demand forecast improvement between periods and the manufacturer s access to forecast information we also examine whether these conditions ensure a pareto optimal solution with respect to two traditional production settings

short term variations and long term dynamics in commodity prices in this article we develop a two factor model of commodity prices that allows meanreversion in short term prices and uncertainty in the equilibrium level to which prices revert although these two factors are not directly observable they may be estimated from spot and futures prices intuitively movements in prices for long maturity futures contracts provide information about the equilibrium price level and differences between the prices for the short and long term contracts provide information about short term variations in prices we show that although this model does not explicitly consider changes in convenience yields over time this short term long term model is equivalent to the stochastic convenience yield model developed in gibson and schwartz 1990 we estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil linked assets to demonstrate its use and some of its advantages over the gibson schwartz model

optimal inventory policies when purchase price and demand are stochastic in this paper we consider the problem of a firm that faces a stochastic poisson demand and must replenish from a market in which prices fluctuate such as a commodity market we describe the price evolution as a continuous stochastic process and we focus on commonly used processes suggested by the financial literature such as the geometric brownian motion and the ornstein uhlenbeck process it is well known that under variable purchase price a price dependent base stock policy is optimal using the single unit decomposition approach we explicitly characterize the optimal base stock level using a series of threshold prices we show that the base stock level is first increasing and then decreasing in the current purchase price we provide a procedure for calculating the thresholds which yields closed form solutions when price follows a geometric brownian motion and implicit solutions under the ornstein uhlenbeck price model in addition our numerical study shows that the optimal policy performs much better than inventory policies that ignore future price evolution because it tends to place larger orders when prices are expected to increase

decentralized inventory control in a two component assembly system abstract we investigate a two component assembly system facing stationary stochastic demand with constant component replenishment lead times holding cost are charged for each component inventory which are managed by component suppliers final product demand is backordered when cannot be fulfilled in time and a penalty cost is charged we assume the long lead time component supplier takes normal base stock policy while the short lead time component supplier takes a modified base stock policy static game and stackelberg games are considered equilibria are analyzed and the cost in equilibria are compared with the system optimal solution difference shows the deterioration of system performance caused by decentralized inventory control we try to design a mechanism to coordinate the decentralized system that is to make decentralized system perform as well as system optimal solution though the decisions separated we show that a liner transfer based on the backorder between the component suppliers qualifies this task

a multi stage financial hedging approach for the procurement of manufacturing materials abstract this paper addresses the problem of mitigating procurement risk that arises from volatile commodity prices by proposing a hedging strategy within a multi stage time frame the proposed multi stage hedging strategy requires a commodity futures position to be correctly initialised and rebalanced with adequate volumes of short long positions so as to reduce the volatility in the total procurement cost that would otherwise be generated by varying commodity spot prices the novelty in the approach is the introduction of the rebalancing of commodity futures position at defined intermediate stages to obtain an efficient or near optimal multi stage hedging strategy a discrete time stochastic control model dscm is developed numerical experiments and monte carlo simulation are used to show that the proposed multi stage hedging strategy compares favourably with the minimal variance hedge and the one stage hedge a close form optimal solution is also presented for the case when procurement volume and price are independent

the role of inventory in delivery time competition the paper operationalizes the notion of shortage cost by considering the behavior of customers and competing firms and examines the role of inventory in response time competition we start with a single firm production control model in which customers are characterized by their preferences of price quality and delivery time the optimal production inventory policy and the optimal choice between make to order and make to stock operations are determined in simple newsboy like formulas the basic model is then extended to an n firm market game in which firms compete for orders from the aspect of early delivery one could think of this setting as an oligopoly racing market the analysis shows that competition can breed a demand for produce to stock just as other economic phenomena such as economies of scale uncertainty or seasonality can induce make to stock and that delivery time competition increases the buyer s welfare while decreasing the producer s welfare

loss averse newsvendor model with two ordering opportunities and market information updating abstract a fashion supply chain characterized by a long lead time and a short selling season is considered in this paper facing demand uncertainty the risk averse retailer has two opportunities to make order decisions before the demand is realized the risk aversion is modelled as a penalty to the decision maker the retailer if a target profit is not attained we derive the retailer s optimal ordering decisions and analyze the monotonicity behaviours of the critical market signal the optimal first stage order quantity and the optimal expected payoff with respect to the penalty coefficient we also examine the impact of demand forecast quality on the retailer s decisions and extend the study to the case where order cancellation is allowed

integrating long term and short term contracting in beef supply chains this paper analyzes the optimal procurement processing and production decisions of a meat processing company hereafter a packer in a beef supply chain the packer processes fed cattle to produce two beef products program premium boxed beef and commodity boxed beef in fixed proportions but with downward substitution of the premium product for the commodity product the packer can source input fed cattle from a contract market where long term contracts are signed in advance of the required delivery time and from a spot market on the spot day contract prices are taken to be of a general window form linear in the spot price but capped by upper and lower limits on realized contract price our analysis provides managerial insights on the interaction of window contract terms with processing options we show that the packer benefits from a low correlation between the spot price and product market uncertainties and this is independent of the form of the window contract although the expected revenues from processing increase in spot price variability the overall impact on profitability depends on the parameters of the window contract using a calibration based on the report by the gipsa grain inspection packers and stockyards administration 2007 gipsa livestock and meat marketing study vol 3 fed cattle and beef industries report u s department of agriculture washington dc this paper elucidates for the first time the value of long term contracting as a complement to spot sourcing in the beef supply chain our comparative statics results provide some rules of thumb for the packer for the strategic management of the procurement portfolio in particular we show that higher variability higher spot price variability product market variability and correlation increases the profits of the packer but decreases the reliance on the contract market relative to the spot market this paper was accepted by yossi aviv operations management

vertical contracts in a supply chain and the bullwhip effect this paper shows that decentralized supply chains in which upstream firms use linear wholesale prices may experience lower upstream production and downstream sales volatility than vertically inte

evaluating corporate bonds with complicated liability structures and bond provisions this paper presents a general and numerically accurate lattice methodology to price risky corporate bonds it can handle complex default boundaries discrete payments various asset sales assumptions and early redemption provisions for which closed form solutions are unavailable furthermore it can price a portfolio of bonds that accounts for their complex interaction whereas traditional approaches can only price each bond individually or a small portfolio of highly simplistic bonds because of the generality and accuracy of our method it is used to investigate how credit spreads are influenced by the bond provisions and the change in a firm s liability structure due to bond repayments

side payment contracts in two person nonzero sum supply chain games review discussion and applications this paper investigates supply chain coordination with side payment contracts we first summarize specific side payment contracts and present our review on the literature that developed general side payment schemes to coordinate supply chains following our review we discuss two criteria that a proper side payment contract must satisfy and accordingly introduce a decision dependent transfer payment function and a constant transfer term we present the condition that the transfer function must satisfy and use nash arbitration scheme and shapley value to compute the constant transfer term and derive its closed form solution next we provide a five step procedure for the development of side payment contract and apply it to four supply chain games cournot and bertrand games a two retailer supply chain game with substitutable products and a one supplier one retailer supply chain more specifically for the cournot game we construct a linear transfer function and a constant side payment to coordinate two producers for the bertrand game we build a nonlinear transfer function which is equivalent to a revenue sharing contract and show that the constant term is zero and two firms in the game equally share the system wide profit for a supply chain with substitutable products we present a side payment contract to coordinate two retailers for a two echelon supply chain we develop a proper side payment scheme that can coordinate the supply chain and also help reduce the impact of forward buying on supply chain performance

multiechelon procurement and distribution policies for traded commodities we consider a firm that procures and distributes a commodity from spot and forward markets under randomly fluctuating prices the commodity is distributed downstream to a set of nonhomogeneous retailers to satisfy random demand we formulate a model that allows one to compute approximate but near optimal procurement and distribution policies for this system and we explore the value of the commodity s market in providing managers with a additional flexibility in procurement and b information on price dynamics generated through the trading of futures contracts our results indicate that the presence of the commodity market and the information that it conveys may lead to significant reductions in inventory related costs however to obtain these benefits both the spot procurement flexibility and the term structure of prices generated by the commodity market must be incorporated in the formulation of the operating policy managerial insights on the procurement strategy as a function of variability in prices and demand are also discussed this paper was accepted by john birge focused issue editor

the quantity flexibility contract and supplier customer incentives consider a supply chain consisting of two independent agents a supplier e g a manufacturer and its customer e g a retailer the latter in turn serving an uncertain market demand to reconcile manufacturing procurement time lags with a need for timely response to the market such supply chains often must commit resources to production quantities based on forecasted rather than realized demand the customer typically provides a planning forecast of its intended purchase which does not entail commitment benefiting from overproduction while not bearing the immediate costs the customer has incentive to initially overforecast before eventually purchasing a lesser quantity the supplier must in turn anticipate such behavior in its production quantity decision this individually rational behavior results in an inefficient supply chain this paper models the incentives of the two parties identifying causes of inefficiency and suggesting remedies particular attention is given to the quantity flexibility qf contract which couples the customer s commitment to purchase no less than a certain percentage below the forecast with the supplier s guarantee to deliver up to a certain percentage above under certain conditions this method can allocate the costs of market demand uncertainty so as to lead the individually motivated supplier and customer to the systemwide optimal outcome we characterize the implications of qf contracts for the behavior and performance of both parties and the supply chain as a whole

investment based financing constraints and debt renegotiation we consider how equity holders bargaining power during financial distress influences the interactions between financing and investment decisions when the firm faces the upper limit of debt issuance we obtain four results first weaker equity holders bargaining power is more likely that the firm is financially constrained second the investment quantity is independent of equity holders bargaining power third the constrained credit spreads are increasing with equity holders bargaining power contrary to the unconstrained ones fourth higher volatility and weaker equity holders bargaining power are likely that the firm prefers to issue debt with renegotiation compared with debt without renegotiation c 2014 elsevier b v all rights reserved

the valuation of european options in uncertain environment abstract a new model on european options with uncertainty of both randomness and fuzziness in output is presented by introducing fuzzy logic to the stochastic financial model the randomness and fuzziness in the systems are evaluated by both probabilistic expectation and fuzzy expectation taking account of seller s buyer s subjective judgment prices of european call put options with uncertainty are given and their valuation and properties are discussed under a reasonable assumption this paper demonstrates black scholes formula to give rational expected price of the european options and buyer s writer s seller s permissible range of expected prices the meaning and properties of rational expected prices are discussed in a numerical example the hedging strategies are also considered for marketability of the european options for portfolio selection

optimal pricing and return policies for perishable commodities this paper considers the pricing decision faced by a producer of a commodity with a short shelf or demand life a hierarchical model is developed and the results of the single period inventory model are used to examine possible pricing and return policies the paper shows that several such policies currently in effect are suboptimal these include those where the manufacturer offers retailers full credit for all unsold goods or where no returns of unsold goods are permitted the paper also demonstrates that a policy whereby a manufacturer offers retailers full credit for a partial return of goods may achieve channel coordination but that the optimal return allowance will be a function of retailer demand therefore such a policy cannot be optimal in a multi retailer environment it is proven however that a pricing and return policy in which a manufacturer offers retailers a partial credit for all unsold goods can achieve channel coordination in a multi retailer environment this article was originally published in marketing science volume 4 issue 2 pages 166 176 in 1985

buy now and price later supply contracts with time consistent mean variance financial hedging abstract we consider a two stage supply chain comprising one risk neutral manufacturer he and one risk averse retailer she where the manufacturer procures consumption commodities in spot market as major inputs for production and sells the final products to the retailer the retailer then sells the final products to the market at a stochastic clearance price we investigate a flexible price contract that allows the manufacturer to determine the product wholesale price and the retailer to determine the order quantity based on the future spot price of consumption commodities compared with the simple wholesale price contract a win win situation can be achieved under the flexible price contract when the manufacturer s postponed processing cost is lower than a threshold however under this flexible price contract the retailer may suffer from the commodity price volatility even if she does not procure the commodities directly we further investigate how the risk averse retailer conducts mean variance financial hedging by purchasing consumption commodity futures contracts we formulate the problem using a dynamic programming model and derive a closed form time consistent financial hedging policy through numerical experiments we show that the commodity price risk from the manufacturer to the retailer is effectively mitigated with the hedging and the benefits of the flexible price contract are maintained

investment under uncertainty with strategic debt service the presence of a well designed bankruptcy code is an important part of the nancialarchitecture in developed economies by allowing the creditors to seize the assets of theborrowers who fail to make contractual payments the code generates bene cial ex ante e ectson debt capacity and rm value by giving the borrowers options to renegotiate their debtobligations and seek bankruptcy protection the code increases the likelihood that borrowersmay avoid ine cient ex post liquidation as hart 1999 notes the code should balanceex ante rm value maximization with ex post e ciency the bankruptcy codes in di erentcountries weight this tradeo di erently and hence vary in terms of the distribution of rightsand powers between borrowers and lenders in this paper we provide an inter temporal framework to examine how the creditors liquidation rights and the distribution of ex post bargaining powers in uence the rm s in vestment and nancing decisions and a ect ex ante rm value we show that strongerequityholders bargaining power lowers debt capacity reduces rm value and discouragesgrowth option exercising our calibration suggests that the quantitative e ects of ex poststrategic renegotiation on ex ante rm value may be large our paper provides an attempt to integrate nancial architecture into the theory of in vestment growth option exercising by building on two strands of literature investment anddebt pricing we extend the real options approach to investment pioneered by mcdonaldand siegel 1986 and brennan and schwartz 1985 to allow for capital structure decisionsunder strategic debt service we also draw insights from corporate debt pricing capital struc ture literature which focuses on leverage and security pricing after investment has alreadybeen made merton 1974 black and cox 1976 and leland 1994 our paper bridgesthe gap between these two strands of literature by characterizing the optimal investment and nancing decisions and the option value of waiting in closed form we show that the inter action between nancing and investment decisions in the presence of strategic debt servicegenerates new insights and also quantitatively important e ects on ex ante rm value

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

flexible and risk sharing supply contracts under price uncertainty we study supply contracts for deterministic demand but in an environment of uncertain prices we develop valuation methodologies for different types of supply contracts a time inflexible contract requires the firm to specify not only how many units it will purchase but also the timing of the purchase a time flexible contract allows the firm to specify the purchase amount over a given period of time without specifying the exact time of purchase other than time flexibility the suppliers may offer quantity flexibility to the firm as well i e purchase quantities could be within a prespecified quantity window finally risk sharing features can be incorporated in the contract in terms of the purchase price that the firm eventually pays to a supplier within a prespecified price window the firm pays the realized price but outside of it the firm shares in an agreed way added costs or benefits given the structure of a supply contract we study the firm s decision when to purchase and how many units in each purchase such that the expected net present value of the purchase cost plus inventory holding cost is minimized we discuss optimal purchasing strategies for both time flexible and time inflexible contracts with risk sharing features other interesting results include the analysis of two supplier sourcing environments and the exploitation of quantity flexibility in such contracts our discussion illustrates how time flexibility quantity flexibility supplier selection and risk sharing when carefully exercised can effectively reduce the sourcing cost in environments of price uncertainty

firm behaviour under the threat of liquidation abstract we study the optimal behaviour of a firm whose cash flow is determined by a diffusion process facing liquidation if internal cash balances fall below some threshold there is a conflict between the desire to pay dividends to satisfy shareholders and the need to retain cash as a barrier against possible liquidation stochastic optimal control characterises the value function and gives optimal decision rules for the firm the firm has a precautionary motive for retaining earnings the internal cost of funds and local risk aversion are both decreasing functions of cash held and in natural extensions to our model output and investment are both increasing functions of cash balances

coalition formation problem for sourcing contract design in supply networks abstract this article studies a coalition formation problem for cooperative replenishment with a single supplier and multiple firms we consider that a vertical cooperation between the supplier and the set of firms is already set using periodic individual contracts and we investigate the profitability of a horizontal cooperation between firms when designing collaborative contracts given the significant savings that can be realized thanks to horizontal collaboration the main interest of the potential collaborating firms is to figure out how the collaborating group should be formed and how stable alliances and coalitions should be generated in this article the two questions are studied in two business situations focusing either on the collaboration opportunities in the ordering or the transportation process in each collaborative situation a decision making approach is applied to assess the expected profitability of each firm and to determine if firms should form coalitions to maximize their profits an exact solution method based on a game theoretic approach is developed called cooperative replenishment algorithm cra which generates core stable coalitions for cost savings regarding all partner standpoints an analytical study of stability conditions regarding the ordering and transportation cost structures were performed to enhance the cra resolution procedure extensive experiments based on realistic instances are provided to validate the performance of the cra proposed in terms of solution stability and convergence the computational results also confirm the potential benefit of horizontal collaboration between firms in terms of profit maximization compared to the stand alone situation

optimal commodity trading with a capacitated storage asset this paper considers the so called warehouse problem with both space and injection withdrawal capacity limits this is a foundational problem in the merchant management of assets for the storage of commodities such as energy sources and natural resources when the commodity spot price evolves according to an exogenous markov process this work shows that the optimal inventory trading policy of a risk neutral merchant is characterized by two stage and spot price dependent basestock targets under some assumptions these targets are monotone in the spot price and partition the available inventory and spot price space in each stage into three regions where it is respectively optimal to buy and inject do nothing and withdraw and sell in some cases of practical importance one can easily compute the optimal basestock targets the structure of the optimal policy is nontrivial because in each stage the merchant s qualification of high selling and low buying commodity prices in general depends on the merchant s inventory availability this is a consequence of the interplay between the capacity and space limits of the storage asset and brings to light the nontrivial nature of the interface between trading and operations a computational analysis based on natural gas data shows that mismanaging this interface can yield significant value losses moreover adapting the merchant s optimal trading policy to the spot price stochastic evolution has substantial value this value can be almost entirely generated by reacting to the unfolding of price uncertainty that is by sequentially reoptimizing a model that ignores this source of uncertainty

pre season stocking and pricing decisions for fashion retailers with multiple information updating abstract motivated by the industrial practice we investigate in this paper the pre season inventory and pricing decisions for fashion retailers before the selling season a retailer can place orders for a seasonal fashion product from her supplier at two distinct stages via two different delivery modes market information from the sales of a pre seasonal product is collected and used to update the demand forecast of the seasonal product at the succeeding stages by using bayesian approach we formulate a dynamic optimization problem and obtain the optimal stocking policy after the ordered seasonal product has arrived and just before the start of the selling season the retailer can determine the optimal selling price of the product with respect to the latest demand information and the amount of product on hand we study the pricing policy under different objectives sensitivity analysis is carried out and the features of the policies are revealed managerial insights are generated

valuing risky projects option pricing theory and decision analysis in the academic literature and professional practice there are a number of alternative and apparently competing methods for valuing risky projects in this paper we compare and contrast three different approaches risk adjusted discount rate analysis option pricing analysis and decision analysis focusing on the last two we show that in contrast to some of the claims made in the real options literature when both option pricing and decision analysis methods are correctly applied they must give consistent results we also explore ways in which option pricing and decision analysis methods can be profitably integrated in particular we show how option pricing techniques can be used to simplify decision analysis when some risks can be hedged by trading and conversely how decision analysis techniques can be used to extend option pricing techniques to problems with incomplete securities markets

supply contracts with financial hedging we study the performance of a stylized supply chain where two firms a retailer and a producer compete in a stackelberg game the retailer purchases a single product from the producer and afterward sells it in the retail market at a stochastic clearance price the retailer however is budget constrained and is therefore limited in the number of units that he may purchase from the producer we also assume that the retailer s profit depends in part on the realized path or terminal value of some observable stochastic process we interpret this process as a financial process such as a foreign exchange rate or interest rate more generally the process can be interpreted as any relevant economic index we consider a variation the flexible contract of the traditional wholesale price contract that is offered by the producer to the retailer under this flexible contract at t 0 the producer offers a menu of wholesale prices to the retailer one for each realization of the financial process up to a future time the retailer then commits to purchasing at time a variable number of units with the specific quantity depending on the realization of the process up to time because of the retailer s budget constraint the supply chain might be more profitable if the retailer was able to shift some of the budget from states where the constraint is not binding to states where it is binding we therefore consider a variation of the flexible contract where we assume that the retailer is able to trade dynamically between zero and in the financial market we refer to this variation as the flexible contract with hedging we compare the decentralized competitive solution for the two contracts with the solutions obtained by a central planner we also compare the supply chain s performance across the two contracts we find for example that the producer always prefers the flexible contract with hedging to the flexible contract without hedging depending on model parameters however the retailer might or might not prefer the flexible contract with hedging

the u shaped investment curve theory and evidence we analyze how the availability of internal funds affects a firm s investment we show that under fairly standard assumptions the relation is u shaped investment increases monotonically with internal funds if they are large but decreases if they are very low we discuss the tradeoff that generates the u shape and argue that models predicting an always increasing relation are based on restrictive assumptions using a large data set we find strong empirical support for our predictions our results qualify conventional wisdom about the effects of financial constraints on investment behavior and help to explain seemingly conflicting findings in the empirical literature

hedging long term exposures with multiple short term futures contracts this article analyzes the problem facing an agent who has a long term commodity supply commitment and who wishes to hedge that commitment using short maturity commodity futures contracts as time evolves the agent has to roll the hedge as old futures contracts mature and new futures contracts are listed this gives rise to hedge errors the optimal hedging strategy is characterized in a world where contracts of several different maturities coexist the strategy is independent both of the agent s risk aversion and under certain conditions of beliefs about expected returns from holding futures contracts the methodology is compared with approaches based on dynamic models of the term structure it is tested on data from the oil futures market article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

choosing among alternative discrete investment projects under uncertainty abstract irreversible choice among mutually exclusive projects under output price uncertainty is considered increasing returns are shown to make it optimal to wait for the largest project greater uncertainty of the price process makes it optimal to wait for a larger project

application of the fuzzy stochastic methodology to appraising the firm value as a european call option abstract the valuing of a firm equity as a call option is a crucial problem in financial decision making there are two basic aspects that are studied contingent claim features payoff functions and risk stochastic process of underlying assets however non preciseness vagueness uncertainty of input data is often neglected thus a combination of risk stochastic and uncertainty fuzzy instruments could be a useful approach in calculating a firm value as a call option the black scholes methodology of appraising equity as a european call option is applied fuzzy stochastic methodology under fuzzy numbers t numbers is proposed and described fuzzy stochastic model of appraising a firm equity is proposed input data are in a form of fuzzy numbers and result firm possibility expected equity value is also determined vaguely as a fuzzy set illustrative example is introduced

effects of sourcing structure on performance in a multiple product assemble to order supply chain abstract this paper addresses the strategic pricing decisions of a decentralized assemble to order system and the effects of sourcing structure on system performance we consider an assemble to order system consisting of two substitute products and three components manufactured by different suppliers demand for the products is price sensitive the selling prices for the products are jointly determined by firms in the system we study the system under both centralized and decentralized decision making situations for the centralized system we demonstrate that there exists a unique optimal pricing solution for the decentralized system we show that there exists a unique nash equilibrium in the players pricing game we further analyze the effects of different sourcing structures on the system performance and the assembler s performance we find that reduction of suppliers in the system does not guarantee improvement of system performance different sourcing structures have different impacts on performance when the two dedicated components are sourced from a single supplier and the common component is sourced from another independent supplier the system and the assembler s performance become worse we show that the decentralized system can be effectively coordinated and the system performance can be improved with a simple profit sharing contract finally we provide comprehensive numerical examples to demonstrate some important managerial insights

operational flexibility and financial hedging complements or substitutes we consider a firm that invests in capacity under demand uncertainty and thus faces two related but distinct types of risk mismatch between capacity and demand and profit variability whereas mismatch risk can be mitigated with greater operational flexibility profit variability can be reduced through financial hedging we show that the relationship between these two risk mitigating strategies depends on the type of flexibility product flexibility and financial hedging tend to be complements substitutes i e product flexibility tends to increase decrease the value of financial hedging and vice versa financial hedging tends to increase decrease the value of product flexibility when product demands are positively negatively correlated in contrast to product flexibility postponement flexibility is a substitute to financial hedging as intuitively expected although our analytical results assume perfect flexibility and perfect hedging and rely on a linear approximation of the value of hedging we validate their robustness in an extensive numerical study

capacity acquisition subcontracting and lot sizing the fundamental question encountered in acquiring capacity to meet nonstationary demand over a multiperiod horizon is how to balance the trade off between having insufficient capacity in some periods and excess capacity in others in the former situation part of the demand is subcontracted while in the latter capacity that has been paid for is rendered idle capacity and subcontracting decisions arise in many economic activities ranging from production capacity planning in semiconductor fabs to leasing communication networks from transportation contracts to staffing of call centers in this paper we investigate the trade offs between acquiring capacity subcontracting production and holding inventory to satisfy nonstationary demand over a finite horizon we present capacity acquisition models with holding and without holding inventory and identify forecast robust properties of the models that restrict the dependence of optimal capacity decisions on the demand forecasts we develop algorithms for numerous practical cost structures involving variable and fixed charges and prove that they all have polynomial time complexity for models with inventory we solve a sequence of constant capacity lot sizing and subcontracting subproblems which is also of independent interest