装备采购线性合同优化研究

高额装备费支出使对招投标合同优化问题备受国防经济学界关注,对装备采办过程中招投标线性合同的优化进行了研究。采用招投标模型与委托-代理模型分析相结合的方法,先从道德风险与风险分担2个方面分析装备采购合同的优化问题,然后引入竞争效应,分析风险分担的问题。即使在双方为风险中性不需要风险分担时,DoD仍然需要在最初的投标竞争与中标后承包商降低成本行为之间进行权衡。一般的投标中,应使最终支付基于实际成本和投标值2个因素,并考虑最终支付基于道德风险损失。研究的基本结论是:固定价格合同应尽可能少地使用;若存在2个以上的投标人,成本加价合同也应禁止使用;在使用激励合同时,应慎重选择合同系数,提出了计算优化线性激励合同系数的方法。     

Sequential bid selection by stochastic approximation

Suppose that a contractor is faced with a sequence of “minimum bid wins contract” competitions. Assuming that a contractor knows his cost to fulfill the contract at each competition and that competitors are merely informed whether or not they have won, bids may be selected sequentially via a tailored stochastic approximation procedure. The efficacy of this approach in certain bidding environments is investigated.     

The impact of operational decisions on the design of salesforce incentives

When facing high levels of overstock inventories, firms often push their salesforce to work harder than usual to attract more demand, and one way to achieve that is to offer attractive incentives. However, most research on the optimal design of salesforce incentives ignores this dependency and assumes that operational decisions of production/inventory management are separable from design of salesforce incentives. We investigate this dependency in the problem of joint salesforce incentive design and inventory/production control. We develop a dynamic Principal‐Agent model with both Moral Hazard and Adverse Selection in which the principal is strategic and risk‐neutral but the agent is myopic and risk‐averse. We find the optimal joint incentive design and inventory control strategy, and demonstrate the impact of operational decisions on the design of a compensation package. The optimal strategy is characterized by a menu of inventory‐dependent salesforce compensation contracts. We show that the optimal compensation package depends highly on the operational decisions; when inventory levels are high, (a) the firm offers a more attractive contract and (b) the contract is effective in inducing the salesforce to work harder than usual. In contrast, when inventory levels are low, the firm can offer a less attractive compensation package, but still expect the salesforce to work hard enough. In addition, we show that although the inventory/production management and the design of salesforce compensation package are highly correlated, information acquisition through contract design allows the firm to implement traditional inventory control policies: a market‐based state‐dependent policy (with a constant base‐stock level when the inventory is low) that makes use of the extracted market condition from the agent is optimal. This work appears to be the first article on operations that addresses the important interplay between inventory/production control and salesforce compensation decisions in a dynamic setting. Our findings shed light on the effective integration of these two significant aspects for the successful operation of a firm. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 320–340, 2014     

Flexible capacity strategy in an asymmetric oligopoly market with competition and demand uncertainty

This article studies flexible capacity strategy (FCS) under oligopoly competition with uncertain demand. Each firm utilizes either the FCS or inflexible capacity strategy (IFCS). Flexible firms can postpone their productions until observing the actual demand, whereas inflexible firms cannot. We formulate a new asymmetrical oligopoly model for the problem, and obtain capacity and production decisions of the firms at Nash equilibrium. It is interesting to verify that cross‐group competition determines the capacity allocation between the two groups of firms, while intergroup competition determines the market share within each group. Moreover, we show that the two strategies coexist among firms only when cost differentiation is medium. Counterintuitively, flexible firms benefit from increasing production cost when the inflexible competition intensity is sufficiently high. This is because of retreat of inflexible firms, flexibility effect, and the corresponding high price. We identify conditions under which FCS is superior than IFCS. We also demonstrate that flexible firms benefit from increasing demand uncertainty. However, when demand variance is not very large, flexible firms may be disadvantaged. We further investigate the effects of cross‐group and intergroup competition on individual performance of the firms. We show that as flexible competition intensity increases, inflexible firms are mainly affected by the cross‐group competition first and then by the intergroup competition, whereas flexible firms are mainly affected by the intergroup competition. Finally, we examine endogenous flexibility and identify its three drivers: cost parameters, cross‐group competition, and intergroup competition. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 117–138, 2017     

Capacity games for partially complementary products under multivariate random demands

In this study, we consider n firms, each of which produces and sells a different product. The n firms face a common demand stream which requests all their products as a complete set. In addition to the common demand stream, each firm also faces a dedicated demand stream which requires only its own product. The common and dedicated demands are uncertain and follow a general, joint, continuous distribution. Before the demands are realized, each firm needs to determine its capacity or production quantity to maximize its own expected profit. We formulate the problem as a noncooperative game. The sales price per unit for the common demand could be higher or lower than the unit price for the dedicated demand, which affects the firm's inventory rationing policy. Hence, the outcome of the game varies. All of the prices are first assumed to be exogenous. We characterize Nash equilibrium(s) of the game. At the end of the article, we also provide some results for the endogenous pricing. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 59: 146–159, 2012     

On the timing of adoption of multiproduct technologies

This article examines a game of multiproduct technology adoption. We consider a duopoly model in which firms choose when to switch from a traditional single-product technology to a more flexible and more expensive multiproduct technology. The multiproduct technology allows a firm to invade the other firm's market, creating a more competitive environment and reducing profits. We analyze this investment decision as a game of timing using two different equilibrium concepts. First, we utilize the “silent” equilibrium concept, where firms commit at time zero to a switching time. This concept would be applicable to situations where firms cannot observe each other's actions, or when the implementation of the technology requires long lead times and the investment decision is private information. Using this notion we find that both firms adopt the multiproduct technology simultaneously within a certain time interval. We then characterize this time interval in terms of cost and demand conditions. We also derive conditions under which sequential adoption of the multiproduct technology occurs. The second concept used is that of noisy equilibrium, where firms cannot precommit themselves to an adoption time. This concept is appropriate when investment decisions are common knowledge. In this case a firm can credibly threaten to immediately follow suit if the other firm decides to adopt. This threat is sufficient to ensure the collusive outcome where neither firm adopts the flexible technology. © 1994 John Wiley & Sons, Inc.     

Stability in a general oligopoly model

We analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the “regular” extension of a base set of affine functions. The model specifies a product assortment, along with their prices and demand volumes, in contrast to most commonly used demand models. We identify a fully best response operator which is monotonically increasing so that the market converges to a Nash equilibrium, when firms dynamically adjust their prices, as best responses to their competitors' prices, at least when starting in one of two price regions. Moreover, geometrically fast convergence to a common equilibrium can be guaranteed for an arbitrary starting point, under an additional condition for the price sensitivity matrix.     

Purchase and retrieval competition for seasonal produce

We study the competition problem of purchase and multiretrieval of perishable seasonal produce, where wholesalers purchase and stock their products in the first period, and then retrieve and sell them in subsequent periods. We first consider the duopoly case and assume that the prices are exogenous and fluctuate. In each period, after the price realization, the wholesalers retrieve some stock from their warehouses to satisfy their demands. One wholesaler's unsatisfied customers can switch to another and be satisfied by its left retrieved products. Any unsold retrieved stock has no salvage value and any unsatisfied demand is lost. The unretrieved stock is carried to the next period at a perishable rate. The wholesalers compete for the substitute demand by determining their own purchase and retrieval quantities. We show the existence and uniqueness of a pure-strategy Nash equilibrium, and that the Nash equilibrium strategy has the simple “sell-down-to” structure. We also consider the general N-person game and show the existence of the Nash equilibrium, and characterize the structure of the equilibrium strategy for the symmetric case. In addition, we consider the case with endogenous prices, and show that the problem reduces to a repeated newsvendor game with price and inventory competition. We derive the conditions under which a unique Nash equilibrium exists and characterize the equilibrium strategy. Finally, we conduct numerical studies to examine the impacts of the model parameters on the equilibrium outcomes and to generate managerial insights.     

A sequential auction‐bargaining procurement model

One of the most important decisions that a firm faces in managing its supply chain is a procurement decision: selecting suitable suppliers among many potential competing sellers and reducing the purchase cost. While both auctions and bargaining have been extensively studied in the literature, the research that combines auctions and bargaining is limited. In this article, we consider a combined auction‐bargaining model in a setting where a single buyer procures an indivisible good from one of many competing sellers. The procurement model that we analyze is a sequential model consisting of the auction phase followed by the bargaining phase. In the auction phase, the sellers submit bids, and the seller with the lowest bid is selected as the winning bidder. In the bargaining phase, the buyer audits the cost of the winning seller and then negotiates with him to determine the final price. For this auction‐bargaining model, we find a symmetric equilibrium bidding strategy for the sellers in a closed form, which is simple to understand and closely related to the classical results in the auction and bargaining literature. We also show that the auction‐bargaining model generates at least as much profit to the buyer as the standard auction or sequential bargaining model. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

装备采办中一级密封招标的博弈均衡分析

针对装备采办中的一级密封招标问题，分析了招标过程中的博弈特点，给出了一维贝叶斯均衡的求解方法和解析表达式，论证了在军工企业的最优战略是选择博弈的贝叶斯均衡，军方的选择是增加竞标者的人数。然后，重点分析了招标过程中的多维博弈问题，给出了多维贝叶斯均衡的一般求解方法，并针对特定的事例进行了多维均衡分析。最后，在多维博弈的框架下对一维博弈和多维博弈的均衡结果进行比较分析，结果表明：在一级密封招标过程中，多维博弈均衡是军工企业的最优战略。     

Supply contracts in manufacturer‐retailer interactions with manufacturer‐quality and retailer effort‐induced demand

We consider a decentralized distribution channel where demand depends on the manufacturer‐chosen quality of the product and the selling effort chosen by the retailer. The cost of selling effort is private information for the retailer. We consider three different types of supply contracts in this article: price‐only contract where the manufacturer sets a wholesale price; fixed‐fee contract where manufacturer sells at marginal cost but charges a fixed (transfer) fee; and, general franchise contract where manufacturer sets a wholesale price and charges a fixed fee as well. The fixed‐fee and general franchise contracts are referred to as two‐part tariff contracts. For each contract type, we study different contract forms including individual, menu, and pooling contracts. In the analysis of the different types and forms of contracts, we show that the price only contract is dominated by the general franchise menu contract. However, the manufacturer may prefer to offer the fixed‐fee individual contract as compared to the general franchise contract when the retailer's reservation utility and degree of information asymmetry in costs are high. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Competitive location and capacity decisions for firms serving time‐sensitive customers

In this article we explore how two competing firms locate and set capacities to serve time‐sensitive customers. Because customers are time‐sensitive, they may decline to place an order from either competitor if their expected waiting time is large. We develop a two‐stage game where firms set capacities and then locations, and show that three types of subgame perfect equilibria are possible: local monopoly (in which each customer is served by a single firm, but some customers may be left unserved), constrained local monopoly (in which firms serve the entire interval of customers but do not compete with each other), and constrained competition (in which firms also serve the entire interval of customers, but now compete for some customers). We perform a comparative statics analysis to illustrate differences in the equilibrium behavior of a duopolist and a coordinated monopolist. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Capacity allocation with traditional and Internet channels

In this paper we study a capacity allocation problem for two firms, each of which has a local store and an online store. Customers may shift among the stores upon encountering a stockout. One question facing each firm is how to allocate its finite capacity (i.e., inventory) between its local and online stores. One firm's allocation affects the decision of the rival, thereby creating a strategic interaction. We consider two scenarios of a single‐product single‐period model and derive corresponding existence and stability conditions for a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We also prove the existence of a Nash equilibrium for a generalized model in which each firm has multiple local stores and a single online store. Finally, we extend the results to a multi‐period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding “sequential game.” © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Optimal redesign decisions through failure rate estimates

To reduce the time-to-market of newly developed systems, manufacturers increasingly adopt strategies where systems are brought to market while system field reliability is still uncertain. These systems are typically sold under performance-based contracts, which incentivizes potential customers to invest in them despite reliability uncertainty. Such contracts make the manufacturer (partly) responsible for the availability of the system. Subsequently, when field reliability is lower than anticipated, the manufacturer may choose to redesign the system to avoid high contract penalties. Redesign is a costly effort which may substantially increase field reliability. Deciding when to redesign is challenging, especially because the initial failure rate estimate by the system's engineers is refined over time as failure data accrues. We propose a model that endogenizes the failure rate updating to analyze this tactical redesign decision. We study additive and multiplicative redesigns and show that the optimal policy has a control limit structure. We benchmark our optimal policy against a static counterpart numerically, and conclude that basing redesign decisions on the updated estimate of the failure rate can substantially reduce costs.     

Competition under time‐varying demands and dynamic lot sizing costs

We develop a competitive pricing model which combines the complexity of time‐varying demand and cost functions and that of scale economies arising from dynamic lot sizing costs. Each firm can replenish inventory in each of the T periods into which the planning horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carrying costs. Each firm adopts, at the beginning of the planning horizon, a (single) price to be employed throughout the horizon. On the basis of each period's system of demand equations, these prices determine a time series of demands for each firm, which needs to service them with an optimal corresponding dynamic lot sizing plan. We establish the existence of a price equilibrium and associated optimal dynamic lotsizing plans, under mild conditions. We also design efficient procedures to compute the equilibrium prices and dynamic lotsizing plans.© 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Optimal interdiction policy for a flow network

This paper analyzes the problem faced by a field commander who, confronted by an enemy on N battlefields, must determine an interdiction policy for the enemy's logistics system which minimizes the amount of war material flowing through this system per unit time. The resource utilized to achieve this interdiction is subject to constraint. It can be shown that this problem is equivalent to determining the set of arcs Z* to remove subject to constraint from a directed graph G such that the resulting maximal flow is minimized. A branch and bound algorithm for the solution to this problem is described, and a numerical example is provided.     

Collaboration in contingent capacities with information asymmetry

We study the optimal contracting problem between two firms collaborating on capacity investment with information asymmetry. Without a contract, system efficiency is lost due to the profit‐margin differentials among the firms, demand uncertainty, and information asymmetry. With information asymmetry, we demonstrate that the optimal capacity level is characterized by a newsvendor formula with an upward‐adjusted capacity investment cost, and no first‐best solution can be achieved. Our analysis shows that system efficiency can always be improved by the optimal contract and the improvement in system efficience is due to two factors. While the optimal contract may bring the system's capacity level closer to the first‐best capacity level, it prevents the higher‐margin firm from overinvesting and aligns the capacity‐investment decisions of the two firms. Our analysis of a special case demonstrates that, under some circumstances, both firms can benefit from the principal having better information about the agent's costs. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 54:, 2007     

Supplier‐buyer contracting: Asymmetric cost information and cutoff level policy for buyer participation

We consider the problem of designing a contract to maximize the supplier's profit in a one‐supplier–one‐buyer relationship for a short‐life‐cycle product. Demand for the finished product is stochastic and price‐sensitive, and only its probability distribution is known when the supply contract is written. When the supplier has complete information on the marginal cost of the buyer, we show that several simple contracts can induce the buyer to choose order quantity that attains the single firm profit maximizing solution, resulting in the maximum possible profit for the supplier. When the marginal cost of the buyer is private information, we show that it is no longer possible to achieve the single firm solution. In this case, the optimal order quantity is always smaller while the optimal sale price of the finished product is higher than the single firm solution. The supplier's profit is lowered while that of the buyer is improved. Moreover, a buyer who has a lower marginal cost will extract more profit from the supplier. Under the optimal contract, the supplier employs a cutoff level policy on the buyer's marginal cost to determine whether the buyer should be induced to sign the contract. We characterize the optimal cutoff level and show how it depends on the parameters of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 41–64, 2001     

A three‐stage procurement optimization problem under uncertainty

This article examines a problem faced by a firm procuring a material input or good from a set of suppliers. The cost to procure the material from any given supplier is concave in the amount ordered from the supplier, up to a supplier‐specific capacity limit. This NP‐hard problem is further complicated by the observation that capacities are often uncertain in practice, due for instance to production shortages at the suppliers, or competition from other firms. We accommodate this uncertainty in a worst‐case (robust) fashion by modeling an adversarial entity (which we call the “follower”) with a limited procurement budget. The follower reduces supplier capacity to maximize the minimum cost required for our firm to procure its required goods. To guard against uncertainty, the firm can “protect” any supplier at a cost (e.g., by signing a contract with the supplier that guarantees supply availability, or investing in machine upgrades that guarantee the supplier's ability to produce goods at a desired level), ensuring that the anticipated capacity of that supplier will indeed be available. The problem we consider is thus a three‐stage game in which the firm first chooses which suppliers' capacities to protect, the follower acts next to reduce capacity from unprotected suppliers, and the firm then satisfies its demand using the remaining capacity. We formulate a three‐stage mixed‐integer program that is well‐suited to decomposition techniques and develop an effective cutting‐plane algorithm for its solution. The corresponding algorithmic approach solves a sequence of scaled and relaxed problem instances, which enables solving problems having much larger data values when compared to standard techniques. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

军队工程招标激励模型研究

运用激励理论研究了军队工程招标采购过程中军方与承包商之间的关系,建立了军队工程招标激励模型。在不完全信息和竞争性招标中,投标人的行为是追求最大的效用,军方则需要建立一种机制诱使投标人按真实成本信息报价,以达到预期支付最小的目的。这种招标博弈的结果是军方与投标人之间达成贝叶斯纳什均衡(Bayesian Nash equilib- rium),即军方利用激励合同诱使投标人报出其真实成本,而投标人为达到中标目的则必须采取讲真话的占优策略,最终在双方均可接受的条件下达成协议。在此基础上,结合实际研究提出了改进的综合评标模型。