optimal pricing shipment and payment policy for an integrated supplier buyer inventory model with two part trade credit abstract in this article we develop an integrated supplier buyer inventory model with the assumption that the market demand is sensitive to the retail price and the supplier adopts a trade credit policy the trade credit policy discussed in this paper is a two part strategy cash discount and delayed payment that is if the buyer pays within m1 the buyer receives a cash discount otherwise the full purchasing price must be paid before m2 where m 2 m 1 0 the objective of this research is to determine the optimal pricing ordering shipping and payment policy to maximize the joint expected total profit per unit time an iterative algorithm is established to obtain the optimal strategy furthermore numerical examples and sensitivity analysis are presented to illustrate the results of the proposed model and to draw managerial insights

inventory and credit decisions for time varying deteriorating items with up stream and down stream trade credit financing by discounted cash flow analysis abstract in today s competitive markets most firms in united kingdom and united states offer their products on trade credit to stimulate sales and reduce inventory trade credit is calculated based on time value of money on the purchase cost i e discounted cash flow analysis recently many researchers use discounted cash flow analysis only on the purchase cost but not on the revenue which is significantly larger than the purchase cost and the other costs for a sound and rigorous analysis we should use discounted cash flow analysis on revenue and costs in addition expiration date for a deteriorating item e g bread milk and meat is an important factor in consumer s purchase decision however little attention has been paid to the effect of expiration date hence in this paper we establish a supplier retailer customer supply chain model in which a the retailer receives an up stream trade credit from the supplier while grants a down stream trade credit to customers b the deterioration rate is non decreasing over time and near 100 percent particularly close to its expiration date and c discounted cash flow analysis is adopted for calculating all relevant factors revenue and costs the proposed model is an extension of more than 20 previous papers we then demonstrate that the retailer s optimal credit period and cycle time not only exist but also are unique thus the search of the optimal solution reduces to a local one finally we run several numerical examples to illustrate the problem and gain managerial insights

a unified bilevel programming framework for price based market clearing under marginal pricing market clearing in restructured power systems is mostly implemented through an offer based setting with the goal of maximizing social welfare this approach leads to sound results from an economic viewpoint when generation offers reflect true production costs however offers may significantly differ from actual costs in practice thus yielding undesired distortion under a marginal pricing scheme this paper presents a general bilevel programming framework for alternative market clearing procedures dependent on market clearing prices rather than on offers the resulting nonlinear mixed integer bilevel programming formulation is transformed into an equivalent single level mixed integer linear program suitable for efficient off the shelf software the bilevel formulation is investigated through a particular instance of price based market clearing driven by consumer payment minimization this problem has recently received considerable attention due to the open challenges posed from both modeling and computational perspectives numerical results are provided to illustrate the performance of the proposed approach

the optimal ordering policy in a dcf analysis for deteriorating items when trade credit depends on the order quantity abstract in this paper an inventory system for deteriorating items under the conditions of using the discounted cash flows dcf approach to the permissible to delay payment will be considered as a matter of fact the supplier usually is willing to provide the retailer a permissible delay of payments if the retailer orders a large quantity as a result we consider that the delay in payments depends on the quantity ordered that is when the order quantity is less than that at which the delay in payments is permitted the payment for the item must be made immediately otherwise the fixed trade credit period is permitted this paper incorporates all concepts of a dcf approach and the trade credit linked to ordering quantity and develops a new inventory model for deteriorating items to generalize jaggi and aggarwal int j prod econ 34 1994 151

core equilibria and incentives in large asymmetric information economies we consider a perfectly competitive ex ante economy with a continuum of agents and negligible asymmetric information for such an economy we recast the basic classical results on the existence of walrasian equilibrium core equivalence and the blocking size of coalitions moreover we examine the incentive compatibility of the ex ante pareto core and walrasian allocations

integrated inventory models considering the two level trade credit policy and a price negotiation scheme abstract this paper develops the integrated inventory models with permissible delay in payment in which customers demand is sensitive to the buyer s price the models consider the two level trade credit policy in the vendor buyer and buyer customer relationships in supply chain management a simple recursive solution procedure is proposed for the integrated models to determine the buyer s optimal pricing and production order strategy although the total profit from the buyer and vendor increases together the buyer s share lessens to compensate the buyer s loss due to the cooperative relationship a negotiation system is presented in order to allocate the profit increase to the vendor and buyer to determine the pricing and production order strategy a numerical example and sensitivity analysis are provided to illustrate the proposed model the results indicate that the total profit from the buyer and vendor together can increase although a price discount is given to the buyer in the proposed models

a pure financial explanation for trade credit this paper provided a pure financial explanation for the existence of trade credit and for the values of the credit terms offered to customers two motives for extending trade credit were identified the pure operating flexibility motive arises because the opportunity to change credit policy provides the seller an efficient way to respond to fluctuations in demand this motive was eliminated from consideration in this paper by assuming constant demand the seller must hold a liquid reserve when the financial markets are imperfect and the desire to earn an excess rate of return on this reserve explains the pure financial intermediary motive for trade credit the pure financial incentive to lend this liquid reserve to customers was examined by viewing a market borrowing rate of interest that exceeds the market lending rate of interest as a hindrance to trade or equivalently as a financial market tariff this tariff imposes a wedge between the market prices paid and received for the product plus a loan and thereby inflicts a loss of surplus on the seller and buyers trade credit lending enables the seller and or the buyers to recapture at least part of this loss when the source of the tariff does not apply to direct loans to customers financial market tariffs caused by transactions costs fulfill this requirement because the trade credit lender s familiarity with its customers and product provide it with information and collection cost advantages over financial intermediaries tariffs caused by financial intermediary rents fulfill this requirement as well because the parties to a trade credit loan do not employ the services of a financial intermediary increasing opportunity costs and financial market imperfections in addition to the ones described above establish the limits of credit policy the optimal amount of accounts receivable is derived from the condition that the marginal revenue of trade credit lending is equal to the marginal cost this condition combined with factoring costs produces a unique finite optimal credit period accrual accounting for income tax purposes imposes an additional restriction because the firm is taxed on the recovery of its opportunity costs these limitations on credit policy were examined separately in this paper for clarity but they are in effect simultaneously in practice

thermal plant bids and market clearing in an electricity pool minimization of costs vs minimization of consumer payments the spanish wholesale electricity market started on january 1st 1998 though it is based on simple price quantity bids it incorporates some provisions to take thermal plant running requirements into account this paper presents these rules and its mathematical treatment focusing on a possible implementation of the minimum income condition which allows thermal generators to declare minimum stable loads it also shows another key point in the debate whether the algorithm should minimize costs or consumer payments

on the solution of revenue and network constrained day ahead market clearing under marginal pricing part ii case studies this paper presents the numerical analysis of the bilevel programming approach for revenue and network constrained market clearing developed in its companion paper the impact of minimum revenue conditions and minimum declared profits on generation and consumption levels as well as on locational marginal prices for energy is examined in detail through three case studies first the results from an illustrative example including minimum revenue conditions are comprehensively analyzed the second case study is based on the ieee reliability test system and considers minimum declared profits in the third case study a modified version of the ieee 118 bus system is tested while accounting for minimum revenue conditions in addition the computational behavior of the proposed approach is illustrated with several case studies including the ieee 300 bus system numerical results show the effectiveness of the proposed approach to handle revenue constraints as well as its superiority over the heuristic currently implemented in the iberian electricity market moreover simulations reveal that unlike previous works in the literature generation revenue constraints can be precisely incorporated in day ahead market clearing while explicitly considering the standard economic dispatch based marginal pricing scheme and without requiring price uplifts

supply chain coordination for the joint determination of order quantity and reorder point using credit option abstract decisions regarding order quantity and reorder point are two major challenges in supply chain inventory management in this paper a coordination model of the joint determination of these two decision variables is proposed a decentralized supply chain consisting of one buyer and one supplier in a multi period setting is investigated demand and lead times are uncertain in our model an incentive scheme based on credit option has been developed to encourage the buyer to participate in the coordination model in this model the downstream member has the option of using credit to purchase goods during the credit time subject to its commitment to a jointly agreed order quantity and reorder point the credit time is determined in such a way that the two parties have incentives to participate the proposed incentive scheme can share the benefits of coordination between the two members based on their bargaining power the proposed model shows that the coordination of the reorder point together with order quantity can increase the overall chain profitability as well as each member s profitability

a review of trade credit literature opportunities for research in operations abstract trade credit arises when a buyer delays payment for purchased goods or services its nature has predominantly been an area of inquiry for researchers from the disciplines of finance marketing and economics but it has received relatively little attention in other domains in our article we provide an integrative review of the existing literature and discuss conflicting study outcomes we organize the relevant literature into seven areas of inquiry and analyze four in detail trade credit motives order quantity decisions credit term decisions and settlement period decisions additionally we derive a detailed agenda for future research in these areas

optimal ordering policy for stock dependent demand under progressive payment scheme abstract in this article a mathematical model is developed to formulate optimal ordering policies for retailer when demand is partially constant and partially dependent on the stock and the supplier offers progressive credit periods to settle the account the notion of progressive credit period is as follows if the retailer settles the outstanding amount by m the supplier does not charge any interest if the retailer pays after m but before second period n offered by the supplier then the supplier charges the retailer on the un paid balance at the rate ic 1 if the retailer settles the account after n then he will have to pay at interest rate ic 2 on the un paid balance ic 2 ic 1 the cost minimization is considered to be an objective function an algorithm is given to find the flow of optimal ordering policy a numerical illustration is given to study the effect of various parameters on ordering policy and total cost of an inventory system

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

on the failure of core convergence in economies with asymmetric information in interim economies with asymmetric information we show that the coarse core of wilson 1978 does not converge to price equilibrium allocations as the economy is replicated this failure of core convergence is a basic consequence of asymmetric information and extends to any reasonable notion of either interim core or price equilibrium

trade credit and informational asymmetry commonly used trade credit terms implicitly define a high interest rate that operates as an efficient screening device where information about buyer default risk is asymmetrically held by offering trade credit a seller can identify prospective defaults more quickly than if financial institutions were the sole providers of short term financing the information is valuable in cases where the seller has made nonsalvageable investments in buyers since it enables the seller to take actions to protect such investments traditional explanations for the widespread use of trade credit fall into two categories the financing motive holds that capital market imperfections enable sellers to finance buyer purchases at lower cost than financial institutions ferris 4 argues that trade credit provides payment flexibility and thus reduces the overall need for buyers and sellers to maintain precautionary balances emery 3 contends that noncompetitive rents of financial institutions can be circumvented by sellers and buyers through provision of trade credit however the financing motive is not sufficient to explain why small suppliers offer trade credit the wide cross sectional variation in terms or why large buyers often take the prompt payment discount late a second set of explanations is best described as pricing motivations for trade credit provision nadiri 10 argues that availability of alternative payment terms can increase product demand but does not indicate why the offered terms could not be duplicated by financial institutions schwartz and whitcomb 14 argue that trade credit is used to circumvent robinson patman and similar prohibitions on price discrimination the correctness of this position depends on the charge to users of trade credit exceeding the cost of provision by the seller although the explanation is possible in principle an empirical question remains as to why variations in actual credit terms appear to be based on product market rather than buyer characteristics the literature also contains analyses of the impact of changing macroeconomic conditions on trade credit terms and aggregate credit flows schwartz 13 for example employs a financing motive for trade credit to conclude that restrictive monetary policy can be partly mitigated by liberalization of trade credit terms by firms with relatively easy access to capital markets however a microeconomic

a discounted cash flow approach to the base stock inventory model abstract a widespread approach to inventory modelling is to associate costs with measures of system performance and determine the control policy which minimises the long run average cost per unit time this type of approach ignores the impact of a control policy on the timing of the cash flows associated with payments to suppliers and revenue streams from customers the approach in this paper is to concentrate on cash flows and determine the control policy which maximises the expected net present value of the cash flows associated with a demand valued at the time when that demand occurs there is a poisson demand process a fixed lead time unsatisfied demand is backordered and the system is controlled using a base stock policy a solution procedure is given and a comparison is made with an equivalent simple interest model and with the standard cost model with linear holding and shortage costs

an incentive compatible solution for trade credit term incorporating default risk abstract this paper studies the optimal trade credit term decision in an extended economic ordering quantity eoq framework that incorporates a default risk component a principal agent bilevel programming model with costs minimization objectives is set up to derive the incentive compatible credit term the supplier determines the credit term as the leader in the first level programming by balancing her his financing capacity with the retailer s default risk order behavior and cost shifting at the second level the retailer makes decisions on ordering and payment time by reacting on the term offered by the supplier a first order condition solution procedure is derived for the bilevel programming when credit term is confined within the practically feasible interval two key results are obtained the condition to derive incentive compatible credit term and an equation system to derive threshold default risk criterion filtering retailers suitable for credit granting numerical experiments show that the capital cost of the supplier is the most important factor determining the credit term default risk acts like a filtering criterion for selecting retailers suitable for credit granting empirical evidence supporting our theoretical considerations is obtained by estimating three panel econometric models using a dataset from china s listed companies

production cost minimization versus consumer payment minimization in electricity pools algorithms that involve some kind of optimization have been adopted by several electricity pools as a tool to clear the market traditionally this kind of models were used on a cost minimizing basis but recent papers have pointed out that alternative dispatches may be obtained that even with higher production costs result in lower electricity prices for consumers this paper studies this new payment minimization approach including the long term economic signals that it provides and their impact on future investments the authors results show that minimizing consumer payment results in discriminatory scheduling for certain generation resources and may cause in the long run higher prices for consumers

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

on the core of an economy with differential information abstract we show that the fine core of an atomless exchange economy with differential information is a subset of the ex post core of the economy this inclusion may be proper and it does not hold for economies with a finite number of traders consequently every fine core allocation is a selection from the equilibrium corre spondence of the associated family of full information economies moreover when each trader knows his or her own utility function and his of her own endowment every fine core allocation is a rational expectations equilibrium allocation journal of economic literature classification numbers c72 d50

coordination and profit sharing between a manufacturer and a buyer with target profit under credit option several studies have focused on buyer vendor coordination through quantity discount credit option mechanism but few quantitative models and investigations are available that have explored the mechanism for transfer of surplus generated due to coordination in this paper we develop a coordination mechanism through credit option such that both the parties can divide the surplus equitably after satisfying their own profit targets two situations are explored here in the first situation both the parties have no individual profit target from the business whereas in the second situation there are individual profit target for both the parties the proposed mechanism for division of surplus is studied through a numerical study and the impact of different parameter values on the results are examined

optimal inventory policy with noninstantaneous receipt under trade credit abstract in the last two decades the models for inventory replenishment policies under trade credit have been widely studied by several researchers however the extant papers only consider the effects of permissible delay in payments in the inventory systems in some situations the supplier also may offer a cash discount to encourage retailer to pay for his purchases quickly on the other hand an inventory model with instantaneous receipt is not a common feature in actual practice for generality this study develops an inventory model with noninstantaneous receipt under trade credit in which the supplier provides not only a permissible delay but also a cash discount to the retailer we then characterize the optimal solution and provide an easy to use criterion to find the optimal order strategies finally several numerical examples are presented to illustrate the theoretical results

trade credit and credit rationing asymmetric information between banks and firms can preclude financing of valuable projects trade credit alleviates this problem by incorporating in the lending relation the private information held by suppliers about their customers incentive compatibility conditions prevent collusion between two of the agents e g the buyer and the seller against the third e g the bank consistent with the empirical findings of petersen and rajan 1995 firms without relationships with banks resort more to trade credit and sellers with greater ability to generate cash lows provide more trade credit finally small firms react to monetary contractions by using trade credit consistent with the empirical results of nilsen 1994 article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

optimal order quantity and selling price over a product life cycle with deterioration rate linked to expiration date it is evident that the lower the price the higher the demand therefore price is an important factor in a consumer s purchasing decision additionally for today s health conscious consumers product freshness is another important factor in purchasing decisions since product freshness declines over time today s health conscious consumers prefer a perishable product with a longer sell by date to a shorter one moreover a product s demand rate moving through its life cycle can be approximately represented by a trapezoid type pattern which includes constant demand increasing demand and decreasing demand as special cases in existing literature several researchers have developed inventory models for trapezoidal demand however they failed to consider pricing strategy product freshness linked to expiration date and purchasing cost in this study we enhance previous models by 1 taking pricing into consideration 2 exploring deterioration rate linked to expiration date and 3 adding an appropriate non constant purchasing cost we then derive theoretical results and run numerical examples to obtain managerial insights for instance the total profit without purchasing cost is significantly lower than that with purchasing cost included also if the cost of lost sales is improperly low then the total profit may become negative due to a large amount of lost sales

the viewpoint on optimal inventory policy with non instantaneous receipt under trade credit by ouyang teng chuang and chuang abstract ouyang et al 2005 international journal of production economics 98 290 300 develop an inventory model with non instantaneous receipt under trade credit in which the supplier provides not only a permissible delay but also a cash discount to the retailer they establish a criterion to find the optimal order cycle such that the total relevant cost per unit time is minimized although their inventory model is correct and interesting their solution procedure has shortcomings such that it cannot locate all optimal order cycles so the main purpose of this paper will remove the shortcoming of ouyang et al 2005 and present a solution procedure to search for the entirely optimal order cycles furthermore this paper reveals an example to show that ouyang et al s 2005 solution procedure does not work for locating the optimal order cycle to that example however our solution procedure does in sum this paper improves ouyang et al 2005

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

trade credit and productive efficiency in developing countries abstract in developing countries credit shortages are often so severe as to impact a firm s day to day production decisions using firm level data from five african countries i show supplier credit is positively correlated with capacity utilization the result continues to hold when credit access is instrumented using supplier characteristics i claim that this is because firms lacking credit likely face inventory shortages leading to lower rates of capacity utilization this explanation yields several further predictions that are supported by the data there is a positive relationship between supplier credit and inventory holdings moreover raw materials stockouts are positively correlated with capacity utilization particularly in inventory intensive industries

retailer s economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity abstract trade credit financing is increasingly recognized as an important strategy to increase profitability in inventory management we revisit an economic order quantity model under conditionally permissible delay in payments in which the supplier offers the retailer a fully permissible delay of m periods i e there is no interest charge until m if the retailer orders more than or equal to a predetermined quantity w however if the retailer s order quantity is less than w then the retailer must make a partial payment to the supplier and enjoy a permissible delay of m periods for the remaining balance in this paper we extend the mentioned eoq under conditionally permissible delay in payments to complement some shortcomings of the model by contrast to the differential calculus method we propose a simple arithmetic geometric method to solve the problem furthermore we establish some discrimination terms to identify the unique optimal solution among three alternatives and explain those theoretical results by simply economical interpretations finally we solve several numerical examples to illustrate the theoretical results and obtain some managerial implications

economic production quantity models for deteriorating items with up stream full trade credit and down stream partial trade credit abstract in practice in order to reduce default risks with credit risk customers a seller e g a manufacturer or a retailer frequently requests its credit risk customers to pay a fraction of the purchase amount at the time of placing an order as collateral deposit and then grants a permissible delay on the outstanding balance i e a down stream partial trade credit by contrast the seller usually receives a permissible delay on the entire purchase amount from the supplier i e an up stream full trade credit in this paper we propose an economic production quantity epq model for deteriorating items in a supply chain with both up stream and down stream trade credit financing by using fractional programming results we can prove that the optimal solution not only exists but also is unique moreover we propose three discrimination terms to identify the optimal solution among possible alternatives finally some numerical examples are presented to highlight the theoretical results and managerial insights

incomplete information incentive compatibility and the core abstract we consider an exchange economy in which agents possess private information at the time of engaging in state contingent contracts while communication of private information is permitted the true information state is not verifiable the enforcement of contracts is therefore limited by incentive compatibility constraints we formalize a notion of the core for such an economy our analysis can be viewed as an attempt to incorporate incentive compatibility in the coarse core of r wilson 1978 econometrica46 807 816 or as an attempt to introduce coalitional contracts in the notion of incentive efficiency of b holmstrom and r myerson 1983 econometrica51 1799 1819 while there are some special cases in which the incentive compatible core is non empty our main result shows that is not generally true journal of economic literatureclassification numbers c71 c72 d51

artificial power markets and unintended consequences administrative pricing rules that try to mimic economic equilibria often fail to capture the complexity of real markets and in that failure can distort incentives as much as or more than cost based pricing in this paper the authors provide three examples of the failure of administrative mechanisms meant to mimic a market two of those examples are very relevant to current debates over industry restructuring in each case the pricing rule fails to maximize social welfare even though in the last two examples production cost is minimized

on the solution of revenue and network constrained day ahead market clearing under marginal pricing part i an exact bilevel programming approach the first of this two paper series addresses a practical day ahead auction model where generation revenue constraints are explicitly incorporated in the problem formulation as routinely done in several national electricity markets across europe the revenue constrained market clearing procedure includes the effect of the transmission network inter temporal constraints associated with generation scheduling demand side bidding and marginal pricing this auction design is an instance of price based market clearing which features two major complicating factors first locational marginal prices become decision variables of the optimization process in addition producer revenues are formulated as bilinear and highly nonconvex products of power outputs and market clearing prices the resulting problem is formulated as a mixed integer nonlinear bilevel program with bilinear terms for which available solution techniques rely on heuristics approximations or modeling simplifications this paper presents a novel and exact methodology whereby the original problem is recast as an equivalent single level mixed integer linear program as a consequence finite convergence to optimality is guaranteed and the use of standard commercial software is allowed the proposed transformation is based on duality theory of linear programming karush kuhn tucker optimality conditions and integer algebra results in the second part of this two paper series numerical results from several case studies illustrate the effective performance of the proposed solution approach

an eoq model under retailer partial trade credit policy in supply chain abstract the main purpose of this paper is to investigate the retailer s inventory policy under two levels of trade credit to reflect the supply chain management situation in this paper we assume that the retailer has the powerful decision making right so we extend the assumption that the retailer can obtain the full trade credit offered by the supplier and the retailer just offers the partial trade credit to his her customer then we investigate the retailer s inventory system as a cost minimization problem to determine the retailer s optimal inventory policy under the supply chain management two easy to use theorems are developed to efficiently determine the optimal inventory policy for the retailer we deduce some previously published results of other researchers as special cases finally numerical examples are given to illustrate the theorems and obtain a lot of managerial phenomena

inventory models for deteriorating items with maximum lifetime under downstream partial trade credits to credit risk customers by discounted cash flow analysis abstract getting loans from banks are almost impossible after 2008 global financial crisis as a result about 80 of companies in united kingdom and united states offer their products on various short term free interest loans i e trade credit to customers numerous researchers and academicians apply discounted cash flow dcf analysis merely to compute the interest earned and charged during the credit period but not to the revenue and other costs which are considerably larger than the interest earned and charged for a rigorous analysis the dcf on all relevant costs is applied in addition many products deteriorate continuously and cannot be sold after their maximum lifetimes or expiration dates however very few researchers and investigators have implemented the product lifetime expectance into their models in this paper a supplier retailer customer chain system is developed in which the retailer gets an upstream full trade credit from the supplier whereas offers a downstream partial trade credit to credit risk customers the deterioration rate is non decreasing over time and near 100 particularly close to its expiration date and dcf analysis is applied to compute all relevant costs this paper demonstrates that the retailer s optimal replenishment cycle time not only exists but also is unique thus the search of the global optimal reduces to finding a local solution finally several numerical examples and sensitivity analysis are performed in order to illustrate the problem and obtain managerial insights

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

a note on seller s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime in 2014 wang et al 2014 extended the model of lou and wang 2012 to incorporate the credit period dependent demand and default risk for deteriorating items with maximum lifetime however the rates of demand default risk and deterioration in the model of wang et al 2014 are assumed to be specific functions of credit period which limits the contributions in this note we first generalize the theoretical results of wang et al 2014 under some certain conditions furthermore we also present some structural results instead of a numerical analysis on variation of optimal replenishment and trade credit strategies with respect to key parameters

sustainable newsvendor models under trade credit abstract governments and industry are actively seeking means of reducing global warming the management of supply chains while taking into account the effects on the environment is an important issue therefore we present newsvendor models that take into account carbon emissions trade credit and product recycling in which the credit period affects the risk of default and the demand is uncertain in this paper the objective of these models is to determine the optimal ordering quantity credit period and recycle price in order to maximize total profits three carbon emission incentives are taken into account 1 carbon tax 2 direct cap 3 carbon cap and trade we also incorporate risk management methods to limit risk of default providing a solution for each type of carbon emission incentive numerical analysis is used to illustrate the implementation of solutions and the degree to which system parameters affect profits and decision making the results show that higher carbon taxes reduce recycle prices order quantities and total profits increasing the carbon cap leads to increases in recycle price order quantity and total profit a higher carbon price drives down the recycle price order quantity and total profits

payment cost minimization auction for deregulated electricity markets using surrogate optimization deregulated electricity markets use an auction mechanism to select offers and their power levels for energy and ancillary services a settlement mechanism is then used to determine the payments resulting from the selected offers currently most independent system operators isos in the united states use an auction mechanism that minimizes the total offer costs but determine payment costs using a settlement mechanism that pays uniform market clearing prices mcps to all selected offers under this setup the auction and settlement mechanisms are inconsistent since minimized costs are different from payment costs illustrative examples in the literature have shown that for a given set of offers if an auction mechanism that directly minimizes the payment costs is used then payment costs can be significantly reduced as compared to minimizing offer costs this observation has led to discussions among stakeholders and policymakers in the electricity markets as to which of the two auction mechanisms is more appropriate for isos to use while methods for minimizing offer costs abound limited approaches for minimization of payment costs have been reported this paper presents an effective method for directly minimizing payment costs in view of the specific features of the problem including the nonseparability of its objective function the discontinuity of offer curves and the maximum term in defining mcps our key idea is to use augmented lagrangian relaxation and to form and solve offer and mcp subproblems by using the surrogate optimization framework numerical testing results demonstrate that the method is effective and the resulting payment costs are significantly lower than what are obtained by minimizing the offer costs for a given set of offers

perfect competition in asymmetric information economies compatibility of efficiency and incentives the idea of perfect competition for an economy with asymmetric information is formalized via an idiosyncratic signal process in which the private signals of almost every individual agent can influence only a negligible group of agents and the individual agents relevant signals are essentially pairwise independent conditioned on the true states of nature thus there is no incentive for an individual agent to manipulate her private information the existence of incentive compatible ex post walrasian allocations is shown for such a perfectly competitive asymmetric information economy with or without common values consequently the conflict between incentive compatibility and pareto eciency is resolved exactly and its asymptotic version is derived for a sequence of large but finite private information economies

a transactions theory of trade credit use this paper derives a transactions theory of trade credit use from the motives of trading partners to economize on the joint costs of exchange in the formal analysis uncertain delivery time is used to generate a demand by firms to hold inventories of both goods and money trade credit is viewed as a mechanism that separates the exchange of money from the uncertainty present in the exchange of goods by forewarning both trading partners of the timing of money flows credit permits a reduction in precautionary money holdings and the more effective management of net money accumulations

pareto optima and competitive equilibria with adverse selection and moral hazard this paper explores the extent to which standard general equilibrium analysis of pareto optima and of competitive equilibria can be applied to environments with moral hazard and adverse selection problems allowing for lotteries contracts with random components we first establish that an adverse selection insurance economy a moral hazard insurance economy a signaling economy and a private information labor market economy are all special cases of a simple general structure we then show that techniques for characterizing pareto optimal contracts as solutions to concave programming problems are useful and nice and appear to be broadly applicable allowing for lotteries we show how to characterize the optimal allocations for the adverse selection insurance and labor market economies we then show that standard existence and optimality theorems for competitive equilibria apply in the linear space containing lotteries if agents with characteristics which are distinct and privately observed at the time of initial trading enter the economy wide resource constraints in a homogeneous way other kinds of diversity are not critical for economies with moral hazard which satisfy the homogeneity condition competitive contract markets single out a subset of the optima and thus can be consistent with apparent unemployment and with a random allocation of labor supplied though all households are averse to risk the adverse selection insurance and signaling economies however do not satisfy the homogeneity condition and are difficult to decentralize efficiently with a price system

equilibria and incentives in private information economies abstract this paper considers three solution concepts in a large private information economy namely walrasian expectations equilibrium private core and insurance equilibrium it shows that these three concepts coincide with each other when the agents are informationally negligible in such an economy in contrast to the finite agent setting one can construct a large private information economy in which incentive compatibility fails completely in the sense that almost every agent in any walrasian expectations equilibrium private core insurance equilibrium allocation has the incentive to misreport her type

joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two level partial trade credits in supply chain abstract this paper develops an inventory model for deteriorating items under a two level partial trade credit with allowable shortages this paper considers a supplier retailer customer supply chain in which a for settling the cost of purchasing the retailer receives a partial trade credit from the supplier and at the same time the retailer offers a separate partial trade credit to the customer b the downstream credit period not only increases demand but also opportunity cost c the deterioration rate is non decreasing over time and the product is fully deteriorated close to its expiration date and d shortages are allowed the objective of the problem is to determine the optimal selling price the optimal replenishment cycle time and the time taken for the inventory to reach zero at the same time such that the total profit per unit is maximized theoretical results are established a numerical example is provided to illustrate the theoretical results and yield some managerial insights

consumer payment minimization in power pool auctions this paper presents a new methodology within the framework of centralized optimization for calculating optimal generation schedules that minimize energy payments by power pool consumers this paper addresses issues related to market structure and the operation of power pools such as bid evaluation generator no load and start up cost recovery generator unit operating constraints and market clearing price determination unlike conventional unit commitment algorithms that minimize total energy production costs the method presented here minimizes payments by power pool consumers a payment minimization objective leads to a different unit commitment and dispatch solution and lower market clearing prices additionally optimal allocation of generator no load and start up costs over the scheduling period is integrated in the bid evaluation process leading to a further reduction in consumer payments

auction design in day ahead electricity markets competition in day ahead electricity markets has been established through auctions where generators and loads bid prices and quantities different approaches have been discussed regarding the market auction design multi round auctions despite its implementation complexity allow market participants to adapt their successive bids to market prices considering their operational and economic constraints however most of the day ahead electricity market implementations use noniterative single round auctions this paper presents a market simulator to compare both auction models different auction alternatives such as the spanish single round auction that takes into account special conditions included in the generator bids and multi round auctions with different stopping rules are analyzed the results and acquired experience in the simulation of the spanish market started in january 1998 are presented hourly market prices average daily price price demand correlation and several economic efficiency indicators such as generator surplus consumer surplus and social welfare are compared to derive conclusions regarding the performance of the auction alternatives

on optimal payment time for a retailer under permitted delay of payment by the wholesaler abstract jamal et al 2000 optimal payment time for a retailer under permitted delay of payment by the wholesaler international journal of production economics 66 59 66 study a wholesaler retailer supply chain where the retailer is given a permissible credit period to pay back the dues without paying any interest to the wholesaler the problem is modeled as a cost minimization problem with two decision variables the payment time p of the retailer and the length of the inventory cycle t while the model represents in general an interesting problem we show in this note that there are a number of nontrivial flaws contained in the development of their model and therefore the solution they derived is not correct we give the correct model and derive the corresponding optimal solution

convergence of volatile power markets with price based demand response price based demand response dr program is a mechanism for encouraging electricity consumers to dynamically manage their energy consumptions in response to time varying electricity prices and thereby reduce peak electricity demands and alleviate the pressure to power systems however it brings additional dynamics and new challenges to the real time supply and demand balance specifically if real time price based dr programs are widely deployed in the future price sensitive dr load levels would constantly change in response to dynamic real time prices which will impact the economic dispatch ed schedule and in turn affect electricity market clearing prices this paper adopts two methods for examining the impacts of different dr price elasticity characteristics and dr participation levels on the convergence of volatile power market a closed loop iterative simulation method and a non iterative method based on the contraction mapping theorem in this paper convergence refers to the fact that load and or price values will finally converge to a fixed point after a finite number of iterations between the ed problem and the price sensitive dr load adjustment five price sensitive dr performance function categories are used to simulate different nonlinear price elasticity characteristics of dr loads numerical studies illustrate how the convergence status of power markets will be affected by the nonlinear price elasticity dr curves the dr penetration levels and the capacity limits of generating units

informational size and incentive compatibility with aggregate uncertainty in mclean and postlewaite econometrica 56 1992 p 2421 we analyzed pure exchange economies with asymmetrically informed agents we defined a notion of informational size and showed that when the aggregate information of all agents resolves nearly all the uncertainty regarding the state of nature the conflict between incentive compatibility and ex post efficiency can be made small if agents have sufficiently small informational size this paper investigates the relationship between informational size and efficiency for the case in which nontrivial aggregate uncertainty is present i e when significant uncertainty about the world persists even when the information of all agents is known

network constrained day ahead auction for consumer payment minimization this paper presents an alternative day ahead auction based on consumer payment minimization for pool based electricity markets this auction is an instance of price based market clearing wherein market clearing prices are explicitly modeled as decision variables of the optimization the auction design includes network constraints inter temporal constraints associated with generation scheduling and marginal pricing hence consumer payment is expressed in terms of locational marginal prices the proposed solution approach is based on bilevel programming in the upper level optimization generation is scheduled with the goal of minimizing the total consumer payment while taking into account that locational marginal prices are determined by a multiperiod optimal power flow in the lower level in this bilevel programming setting locational marginal prices are the lagrange multipliers or dual variables associated with the nodal power balance equations of the lower level problem the resulting mixed integer linear bilevel program is transformed into an equivalent single level mixed integer linear program suitable for efficient off the shelf software this transformation relies on the application of results from duality theory of linear programming and integer algebra the proposed methodology has been successfully applied to several test systems including the ieee 118 bus system numerical results have been compared with those obtained from declared social welfare maximization

stackelberg solution in a vendor buyer supply chain model with permissible delay in payments abstract in practice vendors or sellers often offer their buyers a fixed credit period to settle the account the benefits of trade credit are not only to attract new buyers but also to avoid lasting price competition on the other hand the policy of granting a permissible delay adds not only an additional cost but also an additional dimension of default risk to vendors in this paper we will incorporate the fact that granting a permissible delay has a positive impact on demand but negative impacts on both costs and default risks to establish vendor buyer supply chain models then we will derive the necessary and sufficient conditions to obtain the optimal solution for both the vendor and the buyer under non cooperative stackelberg equilibrium finally we will use two numerical examples to show that 1 granting a permissible delay may significantly improve profits for both the vendor and the buyer 2 the sensitivity analysis on the optimal solution with respect to each parameter and 3 the comparisons between nash and stackelberg solutions

core convergence with asymmetric information we analyze the ex ante incentive compatible core for replicated private information economies we show that any allocation in the core when the economy is replicated sufficiently often is approximately walrasian for the associated arrow debreu economy

an integrated vendor buyer inventory model with order processing cost reduction and permissible delay in payments trade credit plays an important role in financing for many businesses and industries for the buyers purchased inventory can be considered to be financed in whole or in part with permissible delay in payments during the purchasing process on the other hand both the vendor and buyer take part in order processing cost reduction by applying information technologies such as edi electronic data interchange the order processing cost can also be reduced by adding certain capital investments and this will affect the lot size decisions this article develops an integrated inventory model to determine the optimal inventory policy under conditions of order processing cost reduction and permissible delay in payments and shows that the total annual variable cost function possesses some kinds of convexities a solution procedure is provided to determine the optimal order policy finally a numerical example is presented to illustrate the solution procedure

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

lot sizing policies for deteriorating items with expiration dates and partial trade credit to credit risk customers abstract in practice a credit worthy retailer frequently receives a permissible delay on the entire purchase amount without collateral deposits from his her supplier i e an up stream full trade credit by contrast a retailer usually requests his her credit risk customers to pay a fraction of the purchase amount at the time of placing an order and then grants a permissible delay on the remaining balance i e a down stream partial trade credit in addition many products such as blood banks pharmaceuticals fruits vegetables volatile liquids and others deteriorate constantly and have their expiration dates however not many researchers have taken the expiration date of a deteriorating item into consideration the purpose of this paper is to establish optimal lot sizing policies for a retailer who sells a deteriorating item to credit risk customers by offering partial trade credit to reduce his her risk the proposed model is a generalized case of many previous models by applying theorems in pseudo convex fractional functions we can easily prove that the optimal solution not only exists but is also unique moreover we propose three discrimination terms which can easily identify the optimal solution among all possible alternatives finally some numerical examples are presented to highlight the theoretical results and managerial insights

informational size and incentive compatibility we examine a general equilibrium model with asymmetrically informed agents the presence of asymmetric information generally presents a conflict between incentive com patibility and pareto efficiency we present a notion of informational size and show that the conflict between incentive compatibility and efficiency can be made arbitrarily small if agents are of sufficiently small informational size the incompatibility of pareto efficiency and incentive compatibility is a central theme in economics and game theory the issues associated with this incompatibility are particularly important in the design of resource allocation mechanisms in the presence of asymmetrically informed agents where the need to acquire information from agents in order to compute efficient outcomes and the incentives agents have to misrepresent that information for personal gain come into conflict despite a large literature that focuses on these issues there has been little work aimed at understanding those situations in which informational asymmetries are quantitatively important virtually every transaction is characterized by some asymmetry of information any investor who buys or sells a share of stock generally knows something rel evant to the value of the share that is not known to the person on the other side of the transaction in order to focus on more salient aspects of the problem many models rightly ignore the incentive problems associated with informa tional asymmetries in the belief that for the problem at hand agents are infor mationally small however few researchers have investigated the circumstances under which an analysis that ignores these incentive problems will yield results similar to those obtained when these problems are fully accounted for in this paper we study a class of mechanism design problems our goal is to formalize informational size in a way that when agents are informationally small 1 early versions of this paper circulated under the titles informational smallness and pareto effi ciency and informational smallness and incentive compatibility we thank jacques cremer dean foster andreu mas colell stephen morris david schmeidler and particularly faruk gul for help ful conversations and rajiv vohra for a very careful reading we also thank the numerous partici pants in seminars at which this paper was presented for helpful comments we also thank an editor and the referees for very helpful comments and thank ichiro obara for pointing out an error in an earlier version postlewaite gratefully acknowledges support from the national science foundation

optimal joint dynamic pricing advertising and inventory control model for perishable items with psychic stock effect abstract in this study a joint pricing advertising and inventory control problem will be investigated for a firm selling perishable products with psychic stock effect the proposed problem is analyzed in the deterministic multi period setting in which demand at each period depends on not only the amount of inventory displayed and advertising goodwill affected by the firm s current and past advertising efforts but also selling price and freshness index the objective is to determine the optimal pricing advertising and psychic stock strategies maximizing the discount total profit over the infinite planning horizon our theoretical results prove that the firm would adopt a static pricing strategy and then demonstrate that the optimal paths of the advertising goodwill and psychic stock can be determined uniquely we also show that the convergence of the advertising goodwill towards its equilibrium is from above or below depending on the relative location of the initial stock of advertising goodwill with respect to the unique equilibrium stock of advertising goodwill moreover a set of structural properties is developed to explore the relationships among the optimal decisions finally the concluding remarks and suggestions will be provided for future studies

retailer s optimal replenishment decisions with credit linked demand under permissible delay in payments abstract usually it is assumed that the supplier would offer a fixed credit period to the retailer but the retailer in turn would not offer any credit period to its customers which is unrealistic because in real practice retailer might offer a credit period to its customers in order to stimulate his own demand moreover it is observed that credit period offered by the retailer to its customers has a positive impact on demand of an item but the impact of credit period on demand has received a very little attention by the researchers to incorporate this phenomenon we assume that demand is linked to credit period offered by the retailer to the customers this paper incorporates the concept of credit linked demand and develops a new inventory model under two levels of trade credit policy to reflect the real life situations an easy to use algorithm is developed to determine the optimal credit as well as replenishment policy jointly for the retailer finally numerical example is presented to illustrate the theoretical results followed by the sensitivity of various parameters on the optimal solution

a joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive this paper considers the seller buyer channel in which the end demand is price sensitive and the seller may offer trade credit to the buyer the unit price seller charged by the seller and the length of the credit period offered by the seller to the buyer both influence the final demand for the product hence we consider both to be policy variables for the seller we use the case of no credit as a benchmark in our analysis the paper provides procedures for determiningthe seller s and the buyer s policies under non cooperative as well as cooperative relationships in the non cooperative case we determine for the seller the optimal unit price and the length of the credit period for the cooperative structure we provide a procedure for characterizingpareto efficient solutions r 2002 elsevier science b v all rights reserved

an economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity abstract to attract more sales suppliers frequently offer a permissible delay in payments if the retailer orders more than or equal to a predetermined quantity w in this paper we generalize goyal s k 1985 eoq under conditions of permissible delay in payments journal of the operational research society 36 335 338 economic order quantity eoq model with permissible delay in payment to reflect the following real world situations 1 the retailer s selling price per unit is significantly higher than unit purchase price 2 the interest rate charged by a bank is not necessarily higher than the retailer s investment return rate 3 many items such as fruits and vegetables deteriorate continuously and 4 the supplier may offer a partial permissible delay in payments even if the order quantity is less than w we then establish the proper mathematical model and derive several theoretical results to determine the optimal solution under various situations and use two approaches to solve this complex inventory problem finally a numerical example is given to illustrate the theoretical results

informational size incentive compatibility and the core of a game with incomplete information we study the ex ante incentive compatible core and provide conditions under which the ex ante incentive compatible core is nonempty when agents are informationally small in the sense of mclean and postlewaite 2002a econometrica 70 2421 2453