Combined Pricing and Portfolio Option Procurement

In this paper, we study a single‐product periodic‐review inventory system that faces random and price‐dependent demand. The firm can purchase the product either from option contracts or from the spot market. Different option contracts are offered by a set of suppliers with a two‐part fee structure: a unit reservation cost and a unit exercising cost. The spot market price is random and its realization may affect the subsequent option contract prices. The firm decides the reservation quantity from each supplier and the product selling price at the beginning of each period and the number of options to exercise (inventory replenishment) at the end of the period to maximize the total expected profit over its planning horizon. We show that the optimal inventory replenishment policy is order‐up‐to type with a sequence of decreasing thresholds. We also investigate the optimal option‐reservation policy and the optimal pricing strategy. The optimal reservation quantities and selling price are shown to be both decreasing in the starting inventory level when demand function is additive. Building upon the analytical results, we conduct a numerical study to unveil additional managerial insights. Among other things, we quantify the values of the option contracts and dynamic pricing to the firm and show that they are more significant when the market demand becomes more volatile.     

Optimal procurement of long-term contracts in the presence of imperfect spot market

B2B spot market has grown rapidly and become an effective trading channel for commodity products. Besides long-term contract procurement from conventional suppliers (forward and option), a buyer can procure or sell commodities at any time in B2B spot market to adjust her inventory level. However, spot prices are generally volatile and the market is imperfect in the sense that spot trading may be realized with uncertainty in a given period of time and often comes with extra transaction cost. This paper considers a commodity buyer who can order forward and option contracts in advance and trade in a B2B spot market when spot price and demand are observed stochastically. Based on a single-period newsvendor model, we discuss three optimal order strategies and derive respective expected profits when the buyer is risk-neutral. The sensitivity of purchase costs, market liquidity and transaction cost is investigated. We also compare the optimal expected profits for different strategies to illustrate the effects of the two long-term contracts in the presence of the B2B spot market. We then extend our model to a multi-period setting and derive the optimal strategy. Finally, we numerically compute the optimal order strategy for a risk-averse buyer and analyze the impact of spot market, risk aversion, as well as the correlation between customer demand and spot price.     

相对业绩与投资组合思想在期权激励契约设计中的应用

传统股票期权激励契约以股票价格来度量经理人的业绩,但股票价格实际上受到经理人不可控因素(系统风险)的影响,从而导致用股票价格来衡量经理人业绩时会出现反向激励现象,错误惩罚有能力的经理人或慷慨奖励无能的经理人。针对传统股票期权激励契约的缺陷,一些学者把期权激励契约的执行价格和一些指数相联系起来,消除了部分市场水平噪音对期权激励契约的影响。但这种绝对指数股票期权也没有改变指数期权激励契约的结构性缺陷,即不能完全消除市场和行业噪音对期权激励契约的影响。因此,本文借鉴相对业绩和投资组合思想,重新对股票期权的执行价格进行设计,即改变期权到期时权益结构或把执行价格设计成基准绩效投资组合形式,从而达到完全消除市场和行业噪音对期权激励契约的影响,提高期权报酬契约的绩效。     

现货价格和需求关联时期权组合合约模式下采购风险管理策略

在现货价格和客户端需求关联的情形下,本文引用期权组合合约建立现货市场供应量有限时的两阶段采购风险管理模型,以期最大化零售商的期望收益。文中先用逆向归纳法列出零售商第二阶段的最优策略,采用标准扰动定理得出有效合约应满足的最优性条件,并将原模型转化为单调的最短路径问题,应用动态规划求解最优的采购策略。最后用算例分析了现货价格与需求的相关系数及现货市场的供应量对最优策略的影响,发现当供应量一定时,各有效合约的最优预订量及有效合约的总预订量都随着相关系数的增大而提高,并且有效合约受相关系数的影响大小取决于合约的灵活性;并且,当相关系数一定时,有效合约的总预订量及执行价格最低的有效合约的最优预订量都随着供应量的增加而单调减少。     

Promotion Planning and Supply Chain Contracting in a High–Low Pricing Environment

Demand forecast errors threaten the profitability of high–low price promotion strategies. This article shows how to match demand and supply effectively by means of two‐segment demand forecasting and supply contracts. We find that demand depends on the path of past retail prices, which leads to only a limited number of reachable demand states. However, forecast errors cannot be entirely eliminated because competitive promotions entail some degree of random (i.e., last‐minute) pricing. A hedging approach can be deployed to distribute demand risk efficiently over multiple promotional campaigns and within the supply chain. A retailer that employs a portfolio of forward, option, and spot contracts can avoid both stockouts and excess inventories while achieving the first‐best solution and Pareto improvements. We provide an improved forecasting method as well as stochastic programs to solve for optimal production and purchasing policies such that the right amount of inventory is available at the right time. By connecting a stockpiling model of demand with the supply side, we derive insights on optimal risk management strategies for both manufacturers and retailers in a market environment characterized by frequent price promotions and multiple discount levels. We employ a data set of the German retail market for a key generator of store traffic—namely, diapers.     

Managing High‐Tech Capacity Expansion via Reservation Contracts

We study capacity reservation contracts between a high‐tech manufacturer (supplier) and her OEM customer (buyer). The supplier and the buyer are partners who enter a ‘design‐win” agreement to develop the product, and who share the stochastic demand information. To encourage the supplier for more aggressive capacity expansion, the buyer reserves capacity upfront by paying a deductible fee. As capacity expansion demonstrates diseconomy of scale in this context, we assume convex capacity costs. We show that as the buyer's revenue margin decreases, the supplier faces a sequence of four profit scenarios with decreasing desirability. We examine the effects of market size and demand variability to the contract conditions. We propose two channel coordination contracts, and discuss how such contracts can be tailored for situations where the supplier has the option of not complying with the contract, and when the buyer's demand information is only partially updated during the supplier's capacity lead‐time.     

Multi‐Echelon Inventory Management under Short‐Term Take‐or‐Pay Contracts

We extend the Clark–Scarf serial multi‐echelon inventory model to include procuring production inputs under short‐term take‐or‐pay contracts at one or more stages. In each period, each such stage has the option to order/process at two different cost rates; the cheaper rate applies to units up to the contract quantity selected in the previous period. We prove that in each period and at each such stage, there are three base‐stock levels that characterize an optimal policy, two for the inventory policy and one for the contract quantity selection policy. The optimal cost function is additively separable in its state variables, leading to conquering the curse of dimensionality and the opportunity to manage the supply chain using independently acting managers. We develop conditions under which myopic policies are optimal and illustrate the results using numerical examples. We establish and use a generic one‐period result, which generalizes an important such result in the literature. Extensions to cover variants of take‐or‐pay contracts are included. Limitations are discussed.     

基于电子与契约市场的供应链协作的研究

通过期权机制,建立了电子市场与传统契约市场共存下的供应链各决策主体的决策模型,供应商通过设定合理的契约参数,增强其产品在电子市场的竞争力,而在契约市场获得相应的收益,同时激励零售商的产品购买量为最优,以实现供应链的协调,并求得了均衡状况下供应链的最优价格、产能和购买决策,最后,对上述各决策模型的影响因素进行了敏感性分析,进一步验证了结论的有效性.     

有限供应的现货市场与期权合约下的采购策略

在随机现货价格与随机需求相独立的情况下,当现货市场供应量有限时,本文采用期权组合合约建立两阶段采购风险管理模型,以期最大化零售商的期望利润.文中提供了甄别有效合约的算法,得到零售商的最优采购策略,并进一步用算例分析了现货市场的供应量、现货价格和客户需求的波动性对最优采购策略的影响,发现当现货市场的供应量增加时,零售商应...     

AMBIVALENT INVESTMENT AND THE HOLD‐UP PROBLEM

In this paper we add to the foundations of incomplete contracting literature. We study the hold‐up problem with ambivalent investment, where investment benefits the investing party if ex post the right decision is undertaken but harms the investing party if the wrong decision is made. In this context, we show that the power of contracts to provide investment incentives depends on three factors: the commitment value of contracts, the amount of quasirents that the investing party can expect in the case of out‐of‐contract renegotiation, and the degree of ambivalence of investment. First, contracts provide first‐best investment incentives when parties can commit to a contract regardless of the type of investment. Second, with sufficiently ambivalent investment, if parties cannot commit not to renegotiate a contract and if the investing party's bargaining power is intermediate, contracts cannot improve investment incentives above those provided by no contract. In contrast, a simple buyer or seller option contract is optimal when the investing party's bargaining power is extreme. (JEL: D23, K12, L22)     

Quantity Flexibility Contracts: Optimal Decisions with Information Updates*

We study single and multiperiod quantity flexibility contracts involving one demand forecast update in each period and a spot market. We obtain the optimal order quantity at the beginning of a period and order quantities on contract and from the spot market at the then prevailing price after the forecast revision and before the demand materialization. The amount that can be purchased on contract is bounded by a given flexibility limit. We discuss the impact of the forecast quality and the level of flexibility on the optimal decisions and managerial insights behind the results.     

Transfer of risk in the newsvendor model with discrete demand

In this paper we consider the transfer of risk in a newsvendor model with discrete demand. We view the newsvendor model as a leader/follower problem where the manufacturer (leader) decides the wholesale price and the retailer (follower) decides the quantity ordered. Taking a Pareto-optimal contract as a starting point, the manufacturer wishes to design a real option contract to enhance profits. A new real option contract is said to be feasible if both parties' expected profit is at least as great as in the original contract. When demand is discrete, there are usually infinite feasible contracts that yield maximum expected profits to the manufacturer. In the paper we show that either all, some or none of these real option contracts offer an improved position for the retailer.     

Supply Chain Coordination in the Presence of Gray Markets and Strategic Consumers

The practice of diverting genuine products to unauthorized gray markets continues to challenge companies in various industries and creates intense competition for authorized channels. Recent industry surveys report that the abuse of channel incentives is a primary reason for the growth of gray market activities. Therefore, it is crucial that companies take the presence of gray markets into consideration when they design contracts to distribute products through authorized retailers. This issue has received little attention in the extensive literature on contracting and supply chain coordination. In this study, we analyze the impacts of gray markets on two classic contracts, wholesale price and quantity discount, in a supply chain with one manufacturer and one retailer when the retailer has the opportunity to sell to a domestic gray market. Our analysis provides interesting and counterintuitive results. First, a classic quantity‐discount contract that normally coordinates the supply chain can perform so poorly in the presence of a gray market that the supply chain would be better off using a wholesale price contract instead. Second, the presence of gray market can also degrade the performance of the wholesale price contract; therefore, a more sophisticated contract is needed for coordinating the supply chain. We show that contracts that solely depend on retailer's order quantity cannot coordinate the supply chain, and provide the conditions for coordinating the supply chain with price‐dependent quantity discount contracts. We also provide comparative statics and show that when there is a gray market, coordinating the supply chain enhances total consumer welfare.     

供应链单向及双向期权柔性契约比较分析

在随机市场需求环境下,对于易逝品供应链合作契约的数量柔性问题,建立了两种不同期权模式的柔性契约模型。通过对模型的求解与分析,得出了不同契约下销售商的订货策略,而且销售商在双向期权契约下比在单向看涨期权契约时的期权购买量要小,初始订货量要大,但总的预期订货量要小。销售商在两种期权契约模式下的总的最优订货量均大于传统订货方式下总的最优订货量。两种期权契约均可以提高销售商总的订货量,但在具体契约参数下,两者在接近供应链最优订货量上存在差异。     

基于B2B电子交易市场的零售商最优订购策略

B2B电子交易市场能够为企业提供现货交易、远期合约交易以及产能期权合约交易等交易服务.B2B电子交易市场中交易的期权合约在签订后至到期日之前可再次交易.以此为背景研究了零售商最优采购策略.研究结果表明,期权合约可再次交易为供应链中的零售商提供新的投机渠道,显著地提高了零售商对期仅合约的采购数量,而对与固定供应商签订的长...     

Workload Balancing Through Recurrent Subcontracting

We model a situation where a firm wishes to balance workload requirements by creating a portfolio of recurrent insourcing and outsourcing contracts. We use harmonic analysis to decompose an input workload profile into a portfolio of insourcing and outsourcing contracts using rectangular‐wave basis functions to better achieve some desired constant workload level. However, this initial selection of contracts may result in impractical options. Therefore, we also develop mathematical programs using principles from goal programming and integer programming to refine the portfolio of contracts to more accurately reflect a realistic environment by placing constraints on the available contracts and explicitly considering operational costs. We consider several modeling extensions including the ability to hold limited amounts of inventory and the use of one‐shot contracts to supplement our portfolio of recurrent contracts.     

Asymmetric Competition in B2B Spot Markets

We model strategic behavior of two types of suppliers in B2B spot markets: a supplier that has forward contracts and uses the spot market only for inventory liquidation, and a supplier that uses the spot market as its sole selling channel. We find that when the spot market demand is small, the supplier that has forward contracts has a higher incentive to invest in expanding the spot market. When the spot market demand exceeds a threshold size, this situation is reversed, and the supplier with no contracts benefits more from making the spot market more prevalent. We show that a supplier with forward contracts benefits from the existence of the spot market more than a supplier with no contracts and that this result holds with both negative and positive correlation between spot market demand and contracted demand. We find that suppliers producing only for the spot market gain from working in industries where contracted demand and spot market demand are positively correlated, whereas suppliers that have forward contracts benefit from working in industries with a negative correlation between demands, since it allows them to better manage risk. In addition, both total industry supply and spot market supply are higher in industries where demands are negatively correlated.     

基于看跌期权契约的应急物资采购储备模型

应急物资具有峰值需求量大,需求不确定性强,缺货成本高等特点,这使得政府必须在事前进行一定数量的物资储备。然而,由于应急物资需求的发生概率较低,针对食品药品等一类具有保质期限的物资,一旦在保质期限内需求未发生,则会造成大量的浪费与损失,加重政府的财政负担。虽然传统供应链中的回购契约可使政府将剩余物资回售给供应方,能够在一定程度上降低政府成本,但是供应方并没有因承担多余风险而获取到额外收益。基于此,本文设计了一种基于看跌期权契约的应急物资采购储备模型,用于解决保质期风险而引发的损失问题,并分析了实现政企供应链协调的机制,探讨了双方实现共赢协调的具体条件。此外,本文进一步表明与回购契约相比,基于看跌期权契约所建立的采购储备模式能够在降低政府成本的同时,合理地补偿供应方因承担多余风险而造成的损失,更好地保障了供应方的利益,达到了政府和供应方双赢的目的。     

Riester-Vertr?ge: Zur Bedeutung von Kosten und Garantien aus Anlegersicht

The article discusses insurance- and mutual fund-based Riester contracts with respect to the different cost structures and the nominal capital guarantee. A mutual fund-based contract is represented by a plan with a high equity exposure and a nominal capital guarantee, while an insurance-based contract is approximated by a contract with a lower equity exposure and a guaranteed annual rate of return of 2.25%. Both approaches are implemented using a constant proportion portfolio insurance (CPPI) strategy to ensure the relevant capital guarantee. Without taking cost into account, mutual fund-based contracts seem to be the preferred choice for large segments of the population. However, insurance-based Riester contracts become more attractive once the differences in the cost structures are taken into account. The cost disadvantage of mutual fund-based Riester contracts, which occurs whenever the active managers cannot beat the market, is especially important for weakly risk-averse investors, i.e. for the classic clientele of risky investments. Similarly, these savers suffer most from the nominal capital guarantee of mutual fund-based contracts because these individuals would prefer a constant-mix strategy over a CPPI strategy. Thus, the differences in cost structure and the nominal capital guarantee can be identified as possible reasons for the persistently high market shares of insurance-based contracts in the Riester market. However, mutual fund-based Riester contracts are still the first choice for many savers. For example, people with relatively secure private property outside a Riester contract would prefer mutual fund-based contracts, despite cost and capital guarantee issues. The results suggest that mutual fund-based Riester contracts that use Exchange Traded Funds are an attractive product innovation in the Riester market.     

Channel Coordination for a Supply Chain with a Risk‐Neutral Manufacturer and a Loss‐Averse Retailer*

This articles considers a decentralized supply chain in which a single manufacturer is selling a perishable product to a single retailer facing uncertain demand. It differs from traditional supply chain contract models in two ways. First, while traditional supply chain models are based on risk neutrality, this article takes the viewpoint of behavioral principal–agency theory and assumes the manufacturer is risk neutral and the retailer is loss averse. Second, while gain/loss (GL) sharing is common in practice, there is a lack of analysis of GL‐sharing contracts in the supply chain contract literature. This article investigates the role of a GL‐sharing provision for mitigating the loss‐aversion effect, which drives down the retailer order quantity and total supply chain profit. We analyze contracts that include GL‐sharing‐and‐buyback (GLB) credit provisions as well as the special cases of GL contracts and buyback contracts. Our analytical and numerical results lend insight into how a manufacturer can design a contract to improve total supply chain, manufacturer, and retailer performance. In particular, we show that there exists a special class of distribution‐free GLB contracts that can coordinate the supply chain and arbitrarily allocate the expected supply chain profit between the manufacturer and retailer; in contrast with other contracts, the parameter values for contracts in this class do not depend on the probability distribution of market demand. This feature is meaningful in practice because (i) the probability distribution of demand faced by a retailer is typically unknown by the manufacturer and (ii) a manufacturer can offer the same contract to multiple noncompeting retailers that differ by demand distribution and still coordinate the supply chains.