Sourcing decisions with capacity reservation contracts

By committing to long-term supply contracts, buyers seek to lower their purchasing costs, and have products delivered without interruption. When a long-term contract is available, suppliers are less pressured to find new customers, and can afford to charge a price lower than the prevailing spot market price. We examine sourcing decisions of a firm in the presence of a capacity reservation contract that this firm makes with its long-term supplier in addition to the spot market alternative. This contract entails delivery of any desired portion of a reserved fixed capacity in exchange for a guaranteed payment by the buyer. We investigate rational actions of the two parties under two different types of periodic review inventory control policies used by the buyer: the two-number policy, and the base stock policy. When typical demand probability distributions are considered, inclusion of the spot market source in the buyer’s procurement plan significantly reduces the capacity commitments from the long-term supplier.     

Robust Management and Pricing of Liquefied Natural Gas Contracts with Cancelation Options

Liquefied Natural Gas contracts offer cancelation options that make their pricing difficult, especially if many gas storages need to be taken into account. We develop a valuation mechanism from the buyer’s perspective, a large gas company whose main interest in these contracts is to provide to clients a reliable supply of gas. The approach combines valuation with hedging, taking into account that price-risk is driven by international markets, while volume-risk depends on local weather and is stage-wise dependent. The methodology is based on setting risk-averse stochastic mixed 0-1 programs, for different contract configurations. These difficult problems are solved with light computational effort, thanks to a robust rolling-horizon approach. The resulting pricing mechanism not only shows how a specific set of contracts will impact the company business, but also provides the manager with alternative contract configurations to counter-propose to the contract seller.     

Pareto-optimal insurance contracts with premium budget and minimum charge constraints

In view of the fact that minimum charge and premium budget constraints are natural economic considerations in any risk-transfer between the insurance buyer and seller, this paper revisits the optimal insurance contract design problem in terms of Pareto optimality with imposing these practical constraints. Pareto optimal insurance contracts, with indemnity schedule and premium payment, are solved in the cases when the risk preferences of the buyer and seller are given by Value-at-Risk or Tail Value-at-Risk. The effect of our constraints and the relative bargaining powers of the buyer and seller on the Pareto optimal insurance contracts are highlighted. Numerical experiments are employed to further examine these effects for some given risk preferences.     

Long-term and penalty contracts in a two-stage supply chain with stochastic demand

Recent applications of game-theoretic analysis to supply chain efficiency have focused on constructs between a buyer (the retailer or manufacturer) and a seller (the supplier) in successive stages of a supply chain. If demand for the final product is stochastic then the supplier has an incentive to keep its capacity relatively low to avoid creating unneeded capacity. The manufacturer, on the other hand, prefers the supplier’s capacity to be high to ensure that the final demand is satisfied. The manufacturer therefore constructs a contract to induce the supplier to increase its production capacity. Most research examines contracting when final demand is realized after the manufacturer places its order to the supplier. However, if final demand is realized before the manufacturer places its order to the supplier, these types of contracts can be ineffective. This paper examines two contracts under the latter timing scenario: long-term contracts in which the business relationship is repeated, and penalty contracts in which the supplier is penalized for too little capacity. Results indicate long-term contracts increase the profit potential of the supply chain. Furthermore, the penalty contracts can ensure that the supplier chooses a capacity level such that the full profit potential is achieved.     

Option and forward contracting with asymmetric information: Valuation issues in supply chains

We investigate the role of forward commitments and option contracts between a seller (supplier) and a buyer (retailer) in the presence of asymmetric information. In our case, both parties face price and demand uncertainty but the retailer, being closer to the market, has additional information about the true demand and price. The supplier, aware of this asymmetry, and acting as a Stackelberg leader, designs a contracting arrangement that best meet his interest. We contrast the role of forward and option contracts in this environment and identify cases where combinations of the two are dominant. Finally, we investigate how alternative contracting arrangements alter the expected value of obtaining information that eliminates asymmetric information.     

Buyer-supplier currency exchange rate flexibility contracts in global supply chains

This paper analyzes a decentralized global supply chain under a newsvendor setting, where a supplier delivers a certain quantity of a single product to a buyer in accordance with the terms of a mutually agreed upon contract. This contract is signed prior to the delivery of the product and subsequent payment, thus, exposing the supply chain to the risk of currency exchange rate fluctuations. We propose two types of currency exchange rate flexibility contracts to explore the characteristics of exchange rate risk mitigation policies for the buyer and the supplier. Furthermore, we investigate the effects of the contract structures on the optimal order quantity, as well as the expected profits of both supply chain members. Our results show that the optimal order quantity of the buyer decreases when the wholesale price is uncertain due to exchange rate volatility. Also, both our proposed contracts tend to improve the expected profits of both the buyer and the supplier, when the payment is made in the supplier’s currency, indicating the desirability of adopting such contractual agreements from the perspective of both parties. On the other hand, when the payment is made in the buyer’s currency, our suggested contracts do not yield such win-win scenarios. Finally, we examine the effectiveness of availing the services of a local vendor, which is capable of satisfying any demand in excess of the quantity ordered from the foreign source with short notice, in order to mitigate the risks associated with an overseas order.     

Supply chain coordination for newsvendor-type products with two ordering opportunities and demand information update

This paper studies a coordination issue with two ordering opportunities in a two-echelon supply chain, where one manufacturer sells a single newsvendor-type product through one buyer. The manufacturer does not hold inventory and activates production or order with an infinite capacity and a fixed setup cost in response to the buyer’s order. The buyer places two orderings during the selling period of the product: one happens at the beginning of the period and the other at some specified time within the selling period. The whole selling period is divided into two stages or sub-periods by the buyer’s second order. The stochastic demands in the two sub-periods are assumed to be auto-correlated. The excess demand before the second order is partially backordered, whereas the excess demand at the end of the selling season is utterly lost. Under both the centralized and decentralized settings, we develop the models of how the buyer determines his two-ordering policies. We analyse the existence and uniqueness of the optimal solutions to the models and present the corresponding analytical solutions. Furthermore, we propose an improved revenue-sharing contract that can realize the perfect coordination of the supply chain and study how the revenue-sharing policies affect the supply chain members’ decisions. Finally, we show the superiority of the presented two-ordering strategy through numerical examples.     

Electricity swing option pricing by stochastic bilevel optimization: A survey and new approaches

We demonstrate how the problem of determining the ask price for electricity swing options can be considered as a stochastic bilevel program with asymmetric information. Unlike as for financial options, there is no way for basing the pricing method on no-arbitrage arguments. Two main situations are analyzed: if the seller has strong market power he/she might be able to maximize his/her utility, while in fully competitive situations he/she will just look for a price which makes profit and has acceptable risk. In both cases the seller has to consider the decision problem of a potential buyer – the valuation problem of determining a fair value for a specific option contract – and anticipate the buyer’s optimal reaction to any proposed strike price. We also discuss some methods for finding numerical solutions of stochastic bilevel problems with a special emphasis on using duality gap penalizations.     

Analysis of supply contracts with quantity flexibility

This paper explores a class of supply contracts under which a buyer receives discounts for committing to purchases in advance. The further in advance the commitment is made, the larger the discount. As time rolls forward, the buyer can increase the order quantities for future periods of the rolling horizon based on updated demand forecast information and inventory status. However, the buyer pays a higher per-unit cost for the incremental units. Such contracts are used by automobile and contract manufacturers, and are quite common in fuel oil and natural gas delivery markets. We develop a finite-horizon dynamic programming model to characterize the structure of the optimal replenishment strategy for the buyer. We present heuristic approaches to calculate the order volume in each period of the rolling horizon. Finally, we numerically evaluate the heuristic approaches and draw some managerial insights based on the findings.     

平台型企业定价影响因素研究:以银行卡为例

本文运用双边市场理论,构建了平台型企业的定价模型及回归方程,并运用国内14家商业银行2001~2017年的实际运营数据,对构建的模型和方程进行了实证检验。研究结论表明,平台对买方价格决定的主要影响因素有:平台向消费者(买方)提供产品或服务的成本、买方边的需求价格弹性,产品(服务)差异化程度,以及相对方(商户)接入平台的数量;而平台对卖方价格决定的主要影响因素有:卖方给买方产生的网络外部性强度,卖方边的需求价格弹性,以及市场份额。     

Ensuring responsive capacity: How to contract with backup suppliers

Firms that source from offshore plants frequently perceive the lack of reliability and flexibility to be among the major drawbacks of their strategy. To mitigate against imminent mismatches of uncertain supply and demand, establishing capacity hedges in the form of responsive backup suppliers is a way out that many firms follow. This article analyzes how firms should contract with backup suppliers, inducing the latter to install responsive capacity. We show that supply options are appropriate to achieve sourcing channel coordination under forced compliance, whereas any firm commitment contract imposes a deadweight loss on the system. Whereas price-only contracts are unable to coordinate the sourcing channel under voluntary compliance, utilization-dependent price-only contracts are. Under the former contract, a price-focused strategy on the part of the manufacturer turns out to diminish the system’s service level and possibly has negative implications on installed backup capacity, and not least on the manufacturer’s profit.     

Optimal service contract under cost information symmetry/asymmetry

Service outsourcing has become a hot topic in both industry and academy. This paper studies the contract design problems for a service seller who consigns the service to a vendor. The vendor’s service cost parameter may or may not completely be known by the seller, which constitutes the cases of information symmetry or asymmetry. In both cases, the optimal contracts are developed to maximize the seller’s expected profit, with the consideration of contractible and non-contractible service qualities. The properties of the contract parameters are explored, along with the analysis of information rent and value of cost information. Moreover, we find that non-contractible service quality is not an issue for the service seller under cost information symmetry since a revenue-sharing type of contract can guarantee the seller’s profit. However, this result does not hold under cost information asymmetry and thus non-contractibility of the service quality indeed costs the seller.     

Coordination mechanism for capacity reservation by considering production time,production rate and order quantity

In this paper we study the coordination of a dyadic supply chain producing a high-tech product by contracts. The product has a short life cycle and the buyer faces stochastic demands during the selling period. We consider the production time, which causes the inventory costs on supplier’s side. As the supplier builds production capacity in advance, the production rate is limited to the capacity created during the production time. In addition, we take into account the inventory cost and operational cost for the buyer. We examine the model under both full information and partial information updating situations, and propose a coordinating contract for each case. Our analysis includes the study of members’ decisions under both forced and voluntary compliance regimes. Numerical results are presented to provide more insights into the models developed and the mechanisms proposed.     

Prevention efforts,insurance demand and price incentives under coherent risk measures

This paper studies an equilibrium model between an insurance buyer and an insurance seller, where both parties’ risk preferences are given by convex risk measures. The interaction is modeled through a Stackelberg type game, where the insurance seller plays first by offering prices, in the form of safety loadings. Then the insurance buyer chooses his optimal proportional insurance share and his optimal prevention effort in order to minimize his risk measure. The loss distribution is given by a family of stochastically ordered probability measures, indexed by the prevention effort. We give special attention to the problems of self-insurance and self-protection, and show that if the buyer’s risk measure decreases faster in effort than his expected loss, optimal effort is non-decreasing in the safety loading with a potential discontinuity when optimal coverage switches from full to zero. On the contrary, if the decrease of the buyer’s risk measure is slower than the expected loss, optimal effort may or may not be non-decreasing in the safety loading. In case of Pareto distributed losses, the seller sets the highest possible price under which the buyer still prefers full insurance over no insurance. We also analyze the case of discrete distributions: on the one hand, for self-protection, under the assumption that the marginal impact of the effort is higher on small losses than it is on catastrophic losses, the optimal effort is non-decreasing in the safety loading. On the other hand, in the case of self-protection, more conditions are needed, in particular, we obtain sufficient conditions for the optimal effort to be non-decreasing or non-monotone in the safety loading.     

Inequity aversion in a joint economic lot sizing environment with asymmetric holding cost information

Screening contracts (or ‘menu of contracts’) are frequently used for aligning the incentives in supply chains with private information. In this context, it is assumed that all supply chain parties are strictly (expected) profit-maximizing. However, previous empirical work shows that this is a critical assumption. In fact, it seems that inequity adverse subjects are willing to invest money for achieving higher relative payoffs. Interestingly, the classical approach to design incentive compatible mechanisms gives the agent cheap leeway to increase relative pecuniary payoffs and thereby achieving more equitable profit allocations, because the agent is left (almost) indifferent between two contract alternatives. In other words, we argue (and actually observe in laboratory experiments) that this classical approach of contract design allows the agent to achieve more equitable outcomes at low cost. Since the agent’s better relative performance solely stems from reducing the principal’s payoffs, we observe a substantial negative impact on the overall supply chain performance. The present work relaxes the assumption of the profit-maximizing buyer (agent) in a serial supply chain for a lot sizing framework with asymmetrically distributed holding cost information and deterministic end-customer demand. The study provides researchers and managers an approach on how to account for disadvantageous inequity aversion (ie, the agent suffers from profits being lower than the principals profits) by designing a contract that anticipates such behaviour while providing a solution method for the resulting non-linear mathematical program. We denote the resulting contract as ‘behavioural robust’, since it limits the inefficiency losses that result if agents exhibit disadvantageous inequity aversion instead of being strictly profit-maximizing. A numerical study compares the advantages of the ‘behavioural robust’ contract against the classical screening contract. The results highlight that supply chain performance losses can be substantially reduced under the behavioural robust contract.     

Channel incentives in sharing new product demand information and robust contracts

Demand for a new product is often highly uncertain. As the developer of a new product, the manufacturer may reduce the uncertainty of the product’s demand through observing progress in his product development process or receiving demand signals directly from customers. This paper first shows that a centralized channel always benefits from improved demand information. Yet, to realize this benefit in a decentralized manufacturer–retailer channel, the manufacturer needs to disclose his private demand information to the retailer. We show that the manufacturer’s incentive to share his improved demand information depends on the supply contract signed with the retailer. Furthermore, mandating the manufacturer to disclose his improved demand information can actually reduce the total channel profit. We provide managerial insights by analyzing three widely used contract forms. We investigate whether these contracts are robust under an unanticipated demand information update observed by the manufacturer. We show that the quantity flexibility contract with a high return rate is not robust. The buyback contract, however, is robust and always achieves information sharing while preserving channel performance.     

A portfolio approach to managing procurement risk using multi-stage stochastic programming

Procurement is a critical supply chain management function that is susceptible to risk, due mainly to uncertain customer demand and purchase price volatility. A procurement approach in the form of a portfolio that incorporates the common procurement means is proposed. Such means include long-term contracts, spot procurements and option-based supply contracts. The objective is to explore possible synergies among the various procurement means, and so be able to produce optimal or near optimal results in profit while mitigating risk. The implementation of the portfolio approach is based on a multi-stage stochastic programming model in which replenishment decisions are made at various stages along a time horizon, with replenishment quantities being determined by simultaneously considering the stochastic demand and the price volatility of the spot market. The model attempts to minimise the risk exposure of procurement decisions measured as conditional value-at-risk. Numerical experiments to test the effectiveness of the proposed model are performed using demand data from a large air conditioner manufacturer in China and price volatility data from the Shanghai steel market. The results indicate that the proposed model can fairly reliably outperform other approaches, especially when either the demand and/or prices exhibit significant variability.     

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.     

Economic lot sizing: The capacity reservation model

Capacity reservation contracts allow a consumer to purchase up to a certain capacity at a unit price lower than that of the spot market, while the consumer’s excess orders are realized at the spot price. In this paper, we consider a lot sizing problem where the consumer places orders following a capacity reservation contract. In particular, we study the general problem and the polynomial time solvable special cases of the problem and propose corresponding algorithms for them.     

Optimal multi-period insurance contracts

In multi-period insurance contracts (such as automobile insurance contracts), unlike single-period ones, the premiums that the insured must pay increase whenever he files a claim. Hence, the buyer faces a problem that is absent in one-period models, namely: he must determine for which damages he should file a claim and for which he should not.The optimal claims policy of the buyer is presented for a large class of insurance contracts. It is shown that the buyer will file a claim only if it is larger than some critical value. Based on this it is shown that the buyer prefers a contract that provides full coverage above a deductible for damages that exceed his critical value. In this case the optimal contract is not unique since the buyer is indifferent to the form of the contract for damages below his critical value. It is shown, however, that as in one-period models (Arrow (1963, 1974)) there exists an optimal contract that provides full coverage above a deductible. In multi-period setting, however, the buyer will file a claim only if the damage is sufficiently higher than the deductible.It is also shown that the buyer prefers a strictly positive deductible. Unlike the one-period case (Mossin (1968)), this result holds true even if the premium rates equal the expected payments.