Resale price maintenance in supply chains with general multiplicative demand

We analyze a supply chain with a Resale Price Maintenance (RPM) contract in which the manufacturer sets the retail price with a general multiplicative price–demand function and prove the existence/uniqueness of an equilibrium. We also compare the equilibrium prices and quantities, consumer surplus and total system welfare for the RPM and wholesale price contracts. We conclude that a manufacturer may capture a smaller share of the total supply chain profit despite her ability to set the retail price.     

Electricity swing options: Behavioral models and pricing

Electricity swing options are supply contracts for power, which give the owner the right to change the required delivery on short time notice. It gives more flexibility than fixed base load or peak load contracts. The name “option” is a bit misleading, since it gives the owner multiple exercise rights at many different time horizons with exercise amounts on a continuous scale. We look at the problem to determine a rational ask price for such a contract from the viewpoint of the contract seller. The pricing of these contracts differs drastically from the pricing of financial options. First, peculiar properties arise from the non-storability of the underlying (the energy) and therefore the impossibility to hedge with the underlying, hedging is only possible with some future contracts. Second, the behavior of the owner plays an important role. Based on some behavioral model for the option holder, we develop a game-theoretic model, which allows to identify the equilibrium price. Besides some theoretical results, we present some numerical results which clarify the dependence of the asked price on the amount of flexibility offered in the swing option.     

零售商占优下的两部定价合同与通道费

本文考虑由单个占优的零售商和单个供应商组成的二级供应链模型.在价格相依的随机需求下,研究分散系统下的批发价格合同与两部定价合同.在一定的条件下得到两种合同中供应链成员的最优决策和利润以及供应链系统的利润.分析表明,当零售商占优时两部定价合同比批发价格合同更有效.这在一定程度上说明当前零售业中收取通道费的合理性.     

Horizontal coordinating contracts in the semiconductor industry

Integrated device manufacturers (IDMs) and foundries are two types of manufacturers in the semiconductor industry. IDMs integrate both design and manufacturing functions whereas foundries solely focus on manufacturing. Since foundries often have cost advantage over IDMs due to their specialization and economies of scale, IDMs have incentives to source from foundries for the purpose of avoiding excessive capacity investment risk. As the IDM is also a potential capacity source, the IDM and foundry are in a horizontal setting rather than a purely vertical setting. In the absence of sophisticated contracts, the benchmark contract for the IDM and foundry is a wholesale price contract. We define “coordinating” contracts as those that improve both the IDM’s and foundry’s expected profits over the benchmark wholesale price contract and also lead to the maximum system profit. This paper examines if there exist coordinating capacity reservation contracts. It is found that wholesale price contracts in the horizontal setting cannot achieve the maximum system profit due to either double marginalization effect, or “misalignment of capacity-usage-priority”. In contrast, if the IDM’s capacity investment risk is not too low, there always exist coordinating capacity reservation contracts. Furthermore, under coordinating contracts, the IDM’s sourcing structure, either sole sourcing from the foundry or dual sourcing, is contingent on the firms’ cost structures.     

Optimal procurement strategies for online spot markets

Spot markets have emerged for a broad range of commodities, and companies have started to use them in addition to their traditional, long-term procurement contracts (forward contracts). In comparison to forward contracts, spot markets offer products at essentially negligible lead time, but typically command a higher expected price for this added flexibility while also exhibiting substantial price uncertainty. In our research, we analyze the resulting procurement challenge and quantify the benefits of using spot markets from a supply chain perspective. We develop and solve mathematical models that determine the optimal order quantity to purchase via forward contracts and the optimal quantity to purchase via spot markets. We analyze the most general situation where commodities can be both bought and sold via a spot market and derive closed-form results for this case. We compare the obtained results to the reference scenario of pure contract sourcing and we include results for situations where the use of spot markets is restricted to either buying or selling only. Our approaches can be used by decision makers to determine optimal procurement strategies based on key parameters such as, demand and spot price volatilities, correlation between demand and spot prices, and risk aversion. The results of our analysis demonstrate that significant profit improvements can be achieved if a moderate fraction of the commodity demand is procured via spot markets. The results also show that companies who use spot markets can offer a higher expected service level, but that they might experience a higher variability in profits than companies who do not use spot markets. We illustrate our analytical results with numerical examples throughout the paper.     

价格和服务双因素影响的供应链协调决策模型研究

以单个制造商和存在竞争的两个零售商组成的供应链结构模型为研究对象,建立价格和服务两个重要因素影响的市场需求函数,研究供应链协调决策模型。以销售价格、服务质量和制造商批发价格作为三个决策变量,分析集中决策和分散决策两种情景的最优策略,研究收益共享、服务成本分担、收益共享成本分担等三种不同契约的供应链协调问题,并使用数值仿真方法,分析了相关参数变化对系统协调的影响。仿真结果表明:收益共享契约和成本分担契约需满足一定条件才能达到供应链协调,但其效果不一定实现帕累托最优;收益共享和成本分担契约可实现供应链协调,但收入共享系数需在合理区间取值;改进的收益共享成本分担契约能够避免共享系数的盲区,更加有效地达到供应链协调,保持供应链良好运行。     

Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio

We develop a pricing rule for life insurance under stochastic mortality in an incomplete market by assuming that the insurance company requires compensation for its risk in the form of a pre-specified instantaneous Sharpe ratio. Our valuation formula satisfies a number of desirable properties, many of which it shares with the standard deviation premium principle. The major result of the paper is that the price per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting price as an expectation with respect to an equivalent martingale measure. Via this representation, one can interpret the instantaneous Sharpe ratio as a market price of mortality risk. Another important result is that if the hazard rate is stochastic, then the risk-adjusted premium is greater than the net premium, even as the number of contracts approaches infinity. Thus, the price reflects the fact that systematic mortality risk cannot be eliminated by selling more life insurance policies. We present a numerical example to illustrate our results, along with the corresponding algorithms.     

Customer differentiated end-of-life inventory problem

This paper deals with the service parts end-of-life inventory problem in a circumstance that demands for service parts are differentiated. Customer differentiation might be due to criticality of the demand or based on various service contracts. In both cases, we model the problem as a finite horizon stochastic dynamic program and characterize the structure of the optimal inventory policy. We show that when customers are differentiated based on the demand criticality then the optimal structure consists of time and state dependent threshold levels for inventory rationing. In case of differentiation based on service contracts, we show that in addition to rationing thresholds we also need contract extension thresholds by which the system decides whether to offer an extension to an expiring contract or not. By numerical experiments in both cases, we identify the value of incorporating such decisions in service parts end-of-life inventory management with customer differentiation. Moreover, we show that these decisions not only result in cost efficiency but also decrease the risk of part obsolescence drastically.     

Transferring and sharing exchange-rate risk in a risk-averse supply chain of a multinational firm

This paper analyzes risk management contracts used to handle currency risk in a decentralized supply chain that consists of risk-averse divisions in a multinational firm. Particular contracts of interest involve transferring risk to a third party by using risk-transfer contracts such as currency options and re-arranging risk between supply chain members using risk-sharing contracts. Due to decentralization, operational and risk management decisions are made locally; however, a headquarter who is interested in total supply chain profit has some controllability over those activities. We question if each kind of risk management contract can improve the utility of all supply chain members compared to the utility without any of those, and how the conditions to achieve such improvements are different. Further structural differences are investigated via sensitivity analysis with respect to the transfer price, the variability of exchange rates, and the location of the headquarter. We also find that using the two kinds of contracts jointly does not necessarily result in better outcomes.     

The uncertain mortality intensity framework: Pricing and hedging unit-linked life insurance contracts

We study the valuation and hedging of unit-linked life insurance contracts in a setting where mortality intensity is governed by a stochastic process. We focus on model risk arising from different specifications for the mortality intensity. To do so we assume that the mortality intensity is almost surely bounded under the statistical measure. Further, we restrict the equivalent martingale measures and apply the same bounds to the mortality intensity under these measures. For this setting we derive upper and lower price bounds for unit-linked life insurance contracts using stochastic control techniques. We also show that the induced hedging strategies indeed produce a dynamic superhedge and subhedge under the statistical measure in the limit when the number of contracts increases. This justifies the bounds for the mortality intensity under the pricing measures. We provide numerical examples investigating fixed-term, endowment insurance contracts and their combinations including various guarantee features. The pricing partial differential equation for the upper and lower price bounds is solved by finite difference methods. For our contracts and choice of parameters the pricing and hedging is fairly robust with respect to misspecification of the mortality intensity. The model risk resulting from the uncertain mortality intensity is of minor importance.     

Optimal corrective maintenance contract planning for aging multi‐state system

This paper considers an aging multi‐state system, where the system failure rate varies with time. After any failure, maintenance is performed by an external repair team. Repair rate and cost of each repair are determined by a corresponding corrective maintenance contract with a repair team. The service market can provide different kinds of maintenance contracts to the system owner, which also can be changed after each specified time period. The owner of the system would like to determine a series of repair contracts during the system life cycle in order to minimize the total expected cost while satisfying the system availability. Operating cost, repair cost and penalty cost for system failures should be taken into account. The paper proposes a method for determining such optimal series of maintenance contracts. The method is based on the piecewise constant approximation for an increasing failure rate function in order to assess lower and upper bounds of the total expected cost and system availability by using Markov models. The genetic algorithm is used as the optimization technique. Numerical example is presented to illustrate the approach. Copyright © 2009 John Wiley & Sons, Ltd.     

First- and second-price sealed-bid auctions applied to push and pull supply contracts

We investigate a newsvendor-type retailer sourcing problem under demand uncertainty who has the option to source from multiple suppliers. The suppliers’ manufacturing costs are private information. A widely used mechanism to find the least costly supplier under asymmetric information is to use a sealed-bid reverse auction. We compare the combinations of different simple auction formats (first- and second-price) and risk sharing supply contracts (push and pull) under full contract compliance, both for risk-neutral and risk-averse retailer and suppliers. We show the superiority of a first-price push auction for a risk-neutral retailer. However, only the pull contracts lead to supply chain coordination. If the retailer is sufficiently risk-averse, the pull is preferred over the push contract. If suppliers are risk-averse, the first-price push auction remains the choice for the retailer. Numerical examples illustrate the allocation of benefits between the retailer and the (winning) supplier for different number of bidders, demand uncertainty, cost uncertainty, and degree of risk-aversion.     

基于批发价契约的多零售商横向转载的供应链协调

研究了多零售商横向转载的供应链批发价契约协调问题。以包含一个制造商和多个零售商的供应链系统为研究对象,基于批发价契约研究了零售商转载下的供应链协调问题,获取了批发价契约可以协调零售商存在横向转载的供应链的理论证据,并给出了相应的产生供应链协调的条件,详细分析了协调情形下供应链系统最优订货量与多零售商无转载及单报童等情形下的最优订货量之间的关系。进一步研究了制造商与零售商在Stackelberg博弈下,零售商横向转载对制造商收益的影响,并提出了在Stackelberg博弈模型中,批发价契约也有可能促使制造商选择供应链系统最优订货量所对应的批发价格,使得供应链协调,且给出了此种协调产生的具体条件。数值算例则对两种供应链协调情形下的订货量、批发价格及期望收益进行了计算与仿真。研究表明,批发价契约可能会使得多零售商存在转载的供应链实现协调,传统的双重边际化效应将会由于制造商和零售商的理性而被弱化。     

Optimizing maintenance service contracts under imperfect maintenance and a finite time horizon

When a company decides to outsource a service, the most important reasons for doing so usually are to focus on core business, to be able to access high‐quality services at lower costs, or to benefit from risk sharing. However, service contracts typically follow a structure whereby both owner and contractor attempt to maximize expected profits in a noncoordinated way. Previous research has considered supply chain coordination by means of contracts but is based on unrealistic assumptions such as perfect maintenance and infinite time‐span contracts. In this work, these limitations are overcome by defining the supply chain through a preventive maintenance strategy that maximizes the total expected profit for both parties in a finite time‐span contract. This paper presents a model to establish such conditions when maintenance is imperfect, and the contract duration is fixed through a number of preventive maintenance actions along a significant part of the asset life cycle under consideration. This formulation leads to a win–win coordination under a set of restrictions that can be evaluated a priori. The proposed contract conditions motivate stakeholders to continually improve their maintenance services to reach channel coordination in which both parties obtain higher rewards. Copyright © 2012 John Wiley & Sons, Ltd.     

A stochastic programming model for scheduling call centers with global Service Level Agreements

We consider the issue of call center scheduling in an environment where arrivals rates are highly variable, aggregate volumes are uncertain, and the call center is subject to a global service level constraint. This paper is motivated by work with a provider of outsourced technical support services where call volumes exhibit significant variability and uncertainty. The outsourcing contract specifies a Service Level Agreement that must be satisfied over an extended period of a week or month. We formulate the problem as a mixed-integer stochastic program. Our model has two distinctive features. Firstly, we combine the server sizing and staff scheduling steps into a single optimization program. Secondly, we explicitly recognize the uncertainty in period-by-period arrival rates. We show that the stochastic formulation, in general, calculates a higher cost optimal schedule than a model which ignores variability, but that the expected cost of this schedule is lower. We conduct extensive experimentation to compare the solutions of the stochastic program with the deterministic programs, based on mean valued arrivals. We find that, in general, the stochastic model provides a significant reduction in the expected cost of operation. The stochastic model also allows the manager to make informed risk management decisions by evaluating the probability that the Service Level Agreement will be achieved.     

Revenue-sharing versus wholesale price mechanisms under different channel power structures

We consider a supply chain channel with two manufacturers and one retailer. Each manufacturer can choose either a wholesale price contract or a revenue-sharing contract with the retailer. We discuss and compare the results of two different types of contracts under different channel power structures, to check whether it is beneficial for manufacturers to use revenue-sharing contracts under different scenarios. Then we consider a supply chain channel with one manufacturer and two retailers. Each retailer can choose either a wholesale price contract or a revenue-sharing contract with the manufacturer. We analyze the likely outcomes under different scenarios to discover whether it is beneficial to use revenue-sharing contracts.     

Pareto-optimal contracts for a supply chain with satisficing objectives

We analyse a decentralized supply chain consisting of a supplier and a retailer, each with a satisficing objective, that is, to maximize the probability of achieving a predetermined target profit. The supply chain is examined under two types of commonly used contracts: linear tariff contracts (including wholesale price contracts as special cases) and buy-back contracts. First, we identify the Pareto-optimal contract(s) for each contractual form. In particular, it is shown that there is a unique wholesale price that is Pareto optimal for both contractual types. Second, we evaluate the performance of the Pareto-optimal contracts. In contrast to the well-known results for a supply chain with the traditional expected profit objectives, we show that wholesale price contracts can coordinate the supply chain whereas buy-back contracts cannot. This provides an additional justification for the popularity of wholesale price contracts besides their simplicities and lower administration costs.     

碳减排外包下的契约优化与选择研究

在政府碳配额、碳交易市场机制和消费者低碳偏好背景下,研究了制造商与低碳服务提供商合作下的碳减排外包问题。对技术交易型契约和合作共享型契约两种契约进行了优化,分别得到了两种契约下的最优决策和契约可达成条件,并进一步分析了制造商和低碳服务提供商对两种契约的偏好,最后利用转移支付的方式对契约偏好冲突问题进行了协调。研究结果表明,单位减排成本和碳排放权市场价格均是影响技术交易型契约和合作共享型契约可行性的关键因素;当单位最小碳排放量、单位减排成本和碳排放权市场价格同时满足一定条件时,两种契约可同时达成;制造商总是偏好技术交易型契约,但低碳服务提供商对于契约类型的偏好并不是确定的;利用转移支付协调的方式可以解决合作双方的契约偏好冲突问题,并使得双方最终达成技术交易型契约。     

基于时间可控和随机损失的生鲜农产品供应链协调

生鲜农产品不仅是易腐的,其寿命还具有随机性,在订货和由产地运往远方销地的过程中,面临随机供给与需求的匹配、变质损失与物流成本的平衡这两重难题。基于现代物流条件下物流时间的可控性,分别建立了分散控制和集中控制供应链的决策模型,分析得到了它们的最优订货量和最优物流时间。在此基础上,设计了一组联合契约,推导出了实现生鲜农产品供应链协调时契约参数取值范围的计算公式。研究结果表明:通过选择合理的契约参数φ,联合契约能够完美协调生鲜农产品供应链、实现供需双方帕累托最优。进一步,对变质率参数和需求价格弹性系数进行了敏感性分析,为生鲜农产品供应链实践提供了一些管理启示。     

Quantity discounts based on the previous order in a two-period inventory model with demand uncertainty

We examine quantity discount contracts between a manufacturer and a retailer in a stochastic, two-period inventory model. The retailer places an order in each of the two periods to meet stochastic demands. The manufacturer gives the retailer a price discount on purchases in the second period in excess of the first-period order quantity (incremental QDP) or a price discount for all units ordered in the second period if the retailer orders more in the second period than in the first period (all-units QDP). We show that the retailer's optimal ordering decision in the second period depends on the sum of initial inventory and previous order quantity. Our computational study suggests that the QDP contract induces the retailer to buy more in the second period but less in the first period, while the increase of the total order quantity may not be significant; and that it increases the manufacturer's profit only when the wholesale margin is large relative to the retail margin.