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     

Scheduling recurrent construction

A problem we call recurrent construction involves manufacturing large, complex, expensive products such as airplanes, houses, and ships. Customers order configurations of these products well in advance of due dates for delivery. Early delivery may not be permitted. How should the manufacturer determine when to purchase and release materials before fabrication, assembly, and delivery? Major material expenses, significant penalties for deliveries beyond due dates, and long product makespans in recurrent construction motivate choosing a release timetable that maximizes the net present value of cash flows. Our heuristic first projects an initial schedule that dispatches worker teams to tasks for the backlogged products, and then solves a series of maximal closure problems to find material release times that maximize NPV. This method compares favorably with other well‐known work release heuristics in solution quality for large problems over a wide range of operating conditions, including order strength, cost structure, utilization level, batch policy, and uncertainty level. Computation times exhibit near linear growth in problem size. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

基于改进信息熵的抢修操作过程复杂性测度模型

抢修操作过程复杂性既是抢修人员准确衡量抢修操作难易程度及不确定性的重要指标,又是辅助指挥员进行抢修任务分配及抢修资源调度的重要参考,还是进行抢修时间估计的重要依据。然而,目前没有合适的抢修操作过程复杂性测度方法。考虑到普通信息熵极大值公理与抢修操作过程复杂性的特征不相符,利用改进的信息熵建立抢修操作过程的复杂性测度模型,并利用回归分析法通过实例验证,模型测度结果可以客观地反映抢修操作过程的复杂性。     

An approach to the allocation of common costs of multi-mission systems

Many Naval systems, as well as other military and civilian systems, generate multiple missions. An outstanding problem in cost analysis is how to allocate the costs of such missions so that their true costs can be determined and resource allocation optimized. This paper presents a simple approach to handling this problem for single systems. The approach is based on the theory of peak-load pricing as developed by Marcel Boiteux. The basic principle is that the long-run marginal cost of a mission must be equal to its “price.” The implication of this is that if missions can cover their own marginal costs, they should also be allocated some of the marginal common costs. The proportion of costs to be allocated is shown to a function of not only the mission-specific marginal costs and the common marginal costs, but also of the “mission price.” Thus, it is shown that measures of effectiveness must be developed for rational cost allocation. The measurement of effectiveness has long been an intractable problem, however. Therefore, several possible means of getting around this problem are presented in the development of the concept of relative mission prices.     

基于战备完好率的军用飞机维修费用需求确定方法

军用飞机维修费用需求与战备完好率要求密切相关,为保持飞机一定的战备完好率水平,必须投入一定的维修费用。维修费用投入多,则维修设备齐全,维修人员维修能力高,维修备件充足,飞机故障修复时间短,战备完好率高;维修费用投入少,会造成维修设备短缺,设施破旧,维修人员培训不到位,维修备件供应不足等各种问题,直接影响战备完好率水平。     

On the manipulation of transfer prices in a static environment

In a static environment, J. Hirschleifer's marginal cost solution to the transfer pricing problem is commonly accepted as analytically correct. However, actual pricing practice within Western corporations and socialist-planned economies generally deviates from marginal cost pricing. Some form of average cost pricing is more commonly chosen. Recently in this journal, H. Enzer has claimed to show that some form of average cost pricing is indeed the analytically correct solution to the transfer pricing problem when choice of technique and manipulation are allowed. Enzer claims that optimal decisions made by each of two divisions according to their individual self-interests are made compatible with overall firm optimization when the transfer price assigned to the internally-transferred commodity is any form of average cost. We show that the marginal cost solution is correct for Enzer's problem in the absence of manipulation by either division. Indeed, this was all that Hirschleifer claimed. In the process, we uncover a fundamental mathematical error in Enzer's argument. When manipulation of the transfer price by divisions is allowed, we demonstrate the faults with Enzer's average cost solution and conclude Hirschleifer's original statements on manipulation to be correct even in Enzer's environment. A final section briefly indicates the importance to the transfer pricing problem of a growing body of economic literature on incentive structures.     

Quality control chart design under Jidoka

We consider design of control charts in the presence of machine stoppages that are exogenously imposed (as under jidoka practices). Each stoppage creates an opportunity for inspection/repair at reduced cost. We first model a single machine facing opportunities arriving according to a Poisson process, develop the expressions for its operating characteristics and construct the optimization problem for economic design of a control chart. We, then, consider the multiple machine setting where individual machine stoppages may create inspection/repair opportunities for other machines. We develop exact expressions for the cases when all machines are either opportunity‐takers or not. On the basis of an approximation for the all‐taker case, we then propose an approximate model for the mixed case. In a numerical study, we examine the opportunity taking behavior of machines in both single and multiple machine settings and the impact of such practices on the design of an X – Q C chart. Our findings indicate that incorporating inspection/repair opportunities into QC chart design may provide considerable cost savings. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Warranty policies and burn-in

Warranty is an important factor for consumer durable products in the marketplace. However, the warranty cost may drastically reduce profitability. Burn in is a common procedure to improve the quality of products after they have been produced, but it is also costly. By taking both the burn-in procedure and warranty policy into consideration, several cost functions can be formulated and optimized. Assuming that the failure-rate function of the product has a bathtub shape, it is shown that the optimal burn-in times that minimize the considered cost functions never exceed the first change point of the failure-rate function. The continuous dependence of the optimal burn-in times on the model parameters and the underlying distribution is also established. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 199–209, 1997     

Optimal replacement under additive damage and other failure models

A machine or production system is subject to random failure. Upon failure the system is replaced by a new one, and the process repeats. A cost is associated with each replacement, and an additional cost is incurred at each failure in service. Thus, there is an incentive for a controller to attempt to replace before failure occurs. The problem is to find an optimal control strategy that balances the cost of replacement with the cost of failure and results in a minimum total long-run average cost per unit time. We attack this problem under the cumulative damage model for system failure. In this failure model, shocks occur to the system in accordance with a Poisson process. Each shock causes a random amount of damage or wear and these damages accumulate additively. At any given shock, the system fails with a known probability that depends on the total damage accumulated to date. We assume that the cumulative damage is observable by the controller and that his decisions may be based on its current value. Supposing that the shock failure probability is an increasing function of the cumulative damage, we show that an optimal policy is to replace either upon failure or when this damage first exceeds a critical control level, and we give an equation which implicitly defines the optimal control level in terms of the cost and other system parameters. Also treated are some more general models that allow for income lost during repair time and other extensions.     

A Markovian model for process setup and improvement

We examine the setup and improvement policies for a production process with multiple performance states. Assume that the production process deteriorates randomly over time, following a Markovian process with known transition probabilities. In order to reduce the production cost incurred because of process deterioration, the process is inspected at the end of each period. Then one of three actions may be taken: do nothing, perform routine process setup, or perform routine setup and process improvement. The routine setup operation returns the process to its best performance state, whereas the process improvement action may reduce future production and setup costs and improve the process-state transition probabilities. A discounted Markovian model is formulated to find the strategy that minimizes the total cost of operating the production process. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 383–400, 1997     

Requirements planning for modular products

The focus of this paper is on determining the requirements of different component options of a modular end‐product in an uncertain environment. We explicitly model two distinct sources of uncertainty: stochastic end‐product demand and unknown market proportions for the different product options available. Our cost minimizing model focuses on determining the optimal requirements policies for component options that meet a pre‐set service level. We show that simple common‐sense requirements policies are not generally optimal; there is a non‐linear connection between service level and component requirements that is hard to characterize without a detailed analysis. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Periodic replacement when minimal repair costs vary with time

A policy of periodic replacement with minimal repair at failure is considered for a complex system. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening system failures. The cost of a minimal repair to the system is assumed to be a nonde-creasing function of its age. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the system. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited in the case where the system life distribution is strictly increasing failure rate (IFR).     

Oligopolistic contracting: Channel coordination under competition

We study contracts between a single retailer and multiple suppliers of two substitutable products, where suppliers have fixed capacities and present the retailer cost contracts for their supplies. After observing the contracts, the retailer decides how much capacity to purchase from each supplier, to maximize profits from the purchased capacity from the suppliers plus his possessed inventory (endowment). This is modeled as a noncooperative, nonzero‐sum game, where suppliers, or principals, move simultaneously as leaders and the retailer, the common agent, is the sole follower. We are interested in the form of the contracts in equilibrium, their effect on the total supply chain profit, and how the profit is split between the suppliers and the retailer. Under mild assumptions, we characterize the set of all equilibrium contracts and discuss all‐unit and marginal‐unit quantity discounts as special cases. We also show that the supply chain is coordinated in equilibrium with a unique profit split between the retailer and the suppliers. Each supplier's profit is equal to the marginal contribution of her capacity to supply chain profits in equilibrium. The retailer's profit is equal to the total revenue collected from the market minus the payments to the suppliers and the associated sales costs.     

A multilevel passenger screening problem for aviation security

Passenger prescreening is a critical component of aviation security systems. This paper introduces the Multilevel Allocation Problem (MAP), which models the screening of passengers and baggage in a multilevel aviation security system. A passenger is screened by one of several classes, each of which corresponds to a set of procedures using security screening devices, where passengers are differentiated by their perceived risk levels. Each class is defined in terms of its fixed cost (the overhead costs), its marginal cost (the additional cost to screen a passenger), and its security level. The objective of MAP is to assign each passenger to a class such that the total security is maximized subject to passenger assignments and budget constraints. This paper shows that MAP is NP‐hard and introduces a Greedy heuristic that obtains approximate solutions to MAP that use no more than two classes. Examples are constructed using data extracted from the Official Airline Guide. Analysis of the examples suggests that fewer security classes for passenger screening may be more effective and that using passenger risk information can lead to more effective security screening strategies. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Optimal reject allowance with constant marginal production efficiency

A job shop must fulfill an order for N good items. Production is conducted in “lots,” and the number of good items in a lot can be accurately determined only after production of that lot is completed. If the number of good items falls short of the outstanding order, the shop must produce further lots, as necessary. Processes with “constant marginal production efficiency” are investigated. The revealed structure allows efficient exact computation of optimal policy. The resulting minimal cost exhibits a consistent (but not universal) pattern whereby higher quality of production is advantageous even at proportionately higher marginal cost.     

The long term effects of an aging fleet on operational availability and cost: evidence from the U.S. coast guard

This paper empirically examines whether the aging of a fleet affects operational availability and operating cost using a unique data-set on the 117 47-foot Motor Lifeboats (MLBs) of the United States Coast Guard (USCG). Procured from 1997 to 2003, the 47-foot MLB is the standard lifeboat of the USCG and all 117 MLBs remain in service. The aging of the MLB fleet has resulted in higher annual operating costs and lower operational availability, although the nature of this relationship remains unclear. Our estimation strategy utilizes an error components estimator to examine these issues. We employ three variants of the dependent variables (i.e. the standard logarithmic transformation as is most commonly seen in the literature, inverse hyperbolic sine [IHS], and level outcomes). The point estimates from the standard logarithmic model finds operational availability for the MLBs decreases at a rate between 0.83 and 1.8% per year and cost increases at a rate between 0.33 and 7.81% per year. Similar effects are shown with the IHS and level outcome specifications. In terms of nonlinearity effects, we find the most pronounced changes in operational availability and cost occur for MLBs aged 15 years or more (in comparison to younger MLBs).     

How not to pay for the war

As a result of allied subsidy and the influence of sunk costs, the marginal cost of the Gulf War to the US was reduced to negligible size. This result is at variance with the Olson‐Zeckhauser thesis that in an alliance “the small exploit the large.” A game theoretic alternative explanation suggests that the relation between allies resembles the game of Chicken, successfully played by the US. The ability to shift the marginal costs of war in the short term raises questions about the possible underestimation of long term effects.     

Return policies for an inventory system with positive and negative demands

We consider a single item inventory system with positive and negative stock fluctuations. Items can be purchased from a central stock, n items can be returned for a cost R + rn, and a linear inventory carrying cost is charged. It is shown that for minimizing the asymptotic cost rate when returns are a significant fraction of stock usage, a two-critical-number policy (a,b) is optimal, where b is the trigger level for returns and b – a is the return quantity. The values for a and b are found, as well as the operating characteristics of the system. We also consider the optimal return decision to make at time zero and show that it is partially determined by a and b.     

Dynamic routing of prioritized warranty repairs

Recent years have seen a strong trend toward outsourcing warranty repair services to outside vendors. In this article we consider the problem of dynamically routing warranty repairs to service vendors when warranties have priority levels. Each time an item under warranty fails, it is sent to one of the vendors for repair. Items covered by higher priority warranty receive higher priority in repair service. The manufacturer pays a fixed fee per repair and incurs a linear holding cost while an item is undergoing or waiting for repair. The objective is to minimize the manufacturer's long‐run average cost. Because of the complexity of the problem, it is very unlikely that there exist tractable ways to find the optimal routing strategies. Therefore, we propose five heuristic routing procedures that are applicable to real‐life problems. We evaluate the heuristics using simulation. The simulation results show that the index‐based “generalized join the shortest queue” policy, which applies a single policy improvement step to an initial state‐independent policy, performs the best among all five heuristics. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

基于逆向分层的工作流时间-费用优化方法

针对效用网格下基于优先级因子的工作流时间-费用优化问题,基于工作流的同步完成特征对任务进行分层并提出三种实时调度算法:基于逆向分层的sufferage(BLSuff)、基于逆向分层的min-min(BLMin)及基于逆向分层的min-max(BLMax)。算法设计基于优先级因子的衡量标准对时间与费用同时进行优化,并为任务设置期望完成时间以达到充分利用费用优化空间进行费用优化的目标。实验结果表明这三种算法在各种优先级因子下都能对工作流的执行时间与执行费用进行较好的优化。