Bounds and properties of the expected value of sample information for a project-selection problem

In this article we extend the work of Mehrez and Stulman [5] on the expected value of perfect information (EVPI) to the expected value of sample information (EVSI) for a class of economic problems dealing with the decision to reject or accept an investment project. It is shown that shifting the mean of the underlying a priori distribution of X, the project's monetary value from zero in either direction will decrease the associated EVSI of Y, the random sampled information. A theorem is then presented which gives an upper bound on the EVSI over all distributions of Y, as well as the structure of the posterior mean E[X|Y] for which this upper bound is achieved. Finally, the case where E[X|Y] is linear in Y is discussed and its performance compared with that of the optimal case.     

A note comparing glover's and young's simplified primal algorithms

Glover and Young, References [4] and [8], respectively, present convergent primal integer programming algorithms. The algorithm outlined in Young's paper (which was deliberately specialized) is shown to be a special case of the Glover algorithm under his acceptable source row selection, Rule 1.     

The uncertainty sensitivity index method (USIM) and its extension

This article deals with optimization problems that have some uncertain parameters with unknown probabilities. The article proposes a strategy of transferring the system's uncertainty associated with these optimization problems into a norm or a set of norms that is added to the original objective function(s) within a multiobjective framework. The uncertainty sensitivity index method (USIM) proposed by Haimes and Hall [1977] is extended to several general cases. A robust algorithm is developed to guarantee an ideal solution for cases where the nominal value of the uncertain parameter is itself an uncertain variable. A design problem is also addressed to identify the best-compromise values of the system's parameters by integrating the USIM with the envelope approach.     

Scheduling of depalletizing and truck loading operations in a food distribution system

This paper studies a scheduling problem arising in a beef distribution system where pallets of various types of beef products in the warehouse are first depalletized and then individual cases are loaded via conveyors to the trucks which deliver beef products to various customers. Given each customer's demand for each type of beef, the problem is to find a depalletizing and truck loading schedule that fills all the demands at a minimum total cost. We first show that the general problem where there are multiple trucks and each truck covers multiple customers is strongly NP‐hard. Then we propose polynomial‐time algorithms for the case where there are multiple trucks, each covering only one customer, and the case where there is only one truck covering multiple customers. We also develop an optimal dynamic programming algorithm and a heuristic for solving the general problem. By comparing to the optimal solutions generated by the dynamic programming algorithm, the heuristic is shown to be capable of generating near optimal solutions quickly. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

Vendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Optimal control policies for an inventory system with commitment lead time

We consider a firm which faces a Poisson customer demand and uses a base‐stock policy to replenish its inventories from an outside supplier with a fixed lead time. The firm can use a preorder strategy which allows the customers to place their orders before their actual need. The time from a customer's order until the date a product is actually needed is called commitment lead time. The firm pays a commitment cost which is strictly increasing and convex in the length of the commitment lead time. For such a system, we prove the optimality of bang‐bang and all‐or‐nothing policies for the commitment lead time and the base‐stock policy, respectively. We study the case where the commitment cost is linear in the length of the commitment lead time in detail. We show that there exists a unit commitment cost threshold which dictates the optimality of either a buy‐to‐order (BTO) or a buy‐to‐stock strategy. The unit commitment cost threshold is increasing in the unit holding and backordering costs and decreasing in the mean lead time demand. We determine the conditions on the unit commitment cost for profitability of the BTO strategy and study the case with a compound Poisson customer demand.     

Analysis of parameter estimation using the sampling-type algorithm of discrete fractional Fourier transform

Parameter estimation is analyzed using two kinds of common sampling-type DFRFT (discrete fractional Fourier transform) algorithm. A model of parameter estimation is established. The factors which influence estimation accuracy are analyzed. And the simulation is made to verify the conclusions. From the theoretic analysis and simulation verification, it can be drawn that, for the estimation of chirp-rate and initial frequency, Pei's method [10] is more suitable if the absolute value of chirp-rate is small relatively; Ozaktas' method [9] is more suitable if the absolute value of chirp-rate is large relatively; and the two methods are both workable if the absolute value of chirp-rate is moderate. The scope of moderate chirp-rate can be approximately determined as [40 Hz/s, 110 Hz/s].     

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.     

A nonparametric Bayes approach to decide system burn-in time

Burn-in is the preconditioning of assemblies and the accelerated power-on tests performed on equipment subject to temperature, vibration, voltage, radiation, load, corrosion, and humidity. Burn-in techniques are widely applied to integrated circuits (IC) to enhance the component and system reliability. However, reliability prediction by burn-in at the component level, such as the one using the military (e.g., MIL-STD-280A, 756B, 217E [23–25]) and the industrial standards (e.g., the JEDEC standards), is usually not consistent with the field observations. Here, we propose system burn-in, which can remove many of the residual defects left from component and subsystem burn-in (Chien and Kuo [6]). A nonparametric model is considered because 1) the system configuration is usually very complicated, 2) the components in the system have different failure mechanisms, and 3) there is no good model for modeling incompatibility among components and subsystems (Chien and Kuo [5]; Kuo [16]). Since the cost of testing a system is high and, thus, only small samples are available, a Bayesian nonparametric approach is proposed to determine the system burn-in time. A case study using the proposed approach on MCM ASIC's shows that our model can be applied in the cases where 1) the tests and the samples are expensive, and 2) the records of previous generation of the products can provide information on the failure rate of the system under investigation. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 655–671, 1997     

The (s,Q) inventory model with Erlang lead time and deterministic demand

We develop a simple, approximately optimal solution to a model with Erlang lead time and deterministic demand. The method is robust to misspecification of the lead time and has good accuracy. We compare our approximate solution to the optimal for the case where we have prior information on the lead‐time distribution, and another where we have no information, except for computer‐generated sample data. It turns out that our solution is as easy as the EOQ's, with an accuracy rate of 99.41% when prior information on the lead‐time distribution is available and 97.54–99.09% when only computer‐generated sample information is available. Apart from supplying the inventory practitioner with an easy heuristic, we gain insights into the efficacy of stochastic lead time models and how these could be used to find the cost and a near‐optimal policy for the general model, where both demand rate and lead time are stochastic. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Revenue sharing contracts in a supply chain with uncontractible actions

We consider a supplier–customer relationship where the customer faces a typical Newsvendor problem of determining perishable capacity to meet uncertain demand. The customer outsources a critical, demand‐enhancing service to an outside supplier, who receives a fixed share of the revenue from the customer. Given such a linear sharing contract, the customer chooses capacity and the service supplier chooses service effort level before demand is realized. We consider the two cases when these decisions are made simultaneously (simultaneous game) or sequentially (sequential game). For each game, we analyze how the equilibrium solutions vary with the parameters of the problem. We show that in the equilibrium, it is possible that either the customer's capacity increases or the service supplier's effort level decreases when the supplier receives a larger share of the revenue. We also show that given the same sharing contract, the sequential game always induces a higher capacity and more effort. For the case of additive effort effect and uniform demand distribution, we consider the customer's problem of designing the optimal contract with or without a fixed payment in the contract, and obtain sensitivity results on how the optimal contract depends on the problem parameters. For the case of fixed payment, it is optimal to allocate more revenue to the supplier to induce more service effort when the profit margin is higher, the cost of effort is lower, effort is more effective in stimulating demand, the variability of demand is smaller or the supplier makes the first move in the sequential game. For the case of no fixed payment, however, it is optimal to allocate more revenue to the supplier when the variability of demand is larger or its mean is smaller. Numerical examples are analyzed to validate the sensitivity results for the case of normal demand distribution and to provide more managerial insights. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost

In the last decade, there has been much progress in understanding scheduling problems in which selfish jobs aim to minimize their individual completion time. Most of this work has focused on makespan minimization as social objective. In contrast, we consider as social cost the total weighted completion time, that is, the sum of the agent costs, a standard definition of welfare in economics. In our setting, jobs are processed on restricted uniform parallel machines, where each machine has a speed and is only capable of processing a subset of jobs; a job's cost is its weighted completion time; and each machine sequences its jobs in weighted shortest processing time (WSPT) order. Whereas for the makespan social cost the price of anarchy is not bounded by a constant in most environments, we show that for our minsum social objective the price of anarchy is bounded above by a small constant, independent of the instance. Specifically, we show that the price of anarchy is exactly 2 for the class of unit jobs, unit speed instances where the finite processing time values define the edge set of a forest with the machines as nodes. For the general case of mixed job strategies and restricted uniform machines, we prove that the price of anarchy equals 4. From a classical machine scheduling perspective, our results establish the same constant performance guarantees for WSPT list scheduling. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Distributions of manufacturer's and user's replacement costs under warranty

We derive and compute time-dependent distributions of replacement costs under warranty over the product life cycle, both for the manufacturer and the user, under conditional pro-rata and nonrenewing free-replacement warranty policies. For pro-rata warranties, the analysis is based on the joint distribution of the number of replacements and the user's cost over time. For free-replacement warranties, distribution of the user's cost follows from the observation that replacement points outside warranty periods form a renewal process. This property is also exploited to determine the distribution of the manufacturer's cost. We apply our findings to measure the impact of product conformance quality on warranty cost distributions and find that manufacturer's cost measures are more sensitive to changes in quality than user's cost measures. © 1995 John Wiley & Sons, Inc.     

An application of the MTP2 property on bounds on system reliability

This paper is concerned with the joint prior distribution of the dependent reliabilities of the components of a binary system. When this distribution is MTP₂ (Multivariate Totally Positive of Order 2), it is shown in general that this actually makes the machinery of Natvig and Eide [7] available to arrive at the posterior distribution of the system's reliability, based on data both at the component and system level. As an illustration in a common environmental stress case, the joint prior distribution of the reliabilities is shown to have the MTP₂ property. We also show, similarly to Gåsemyr and Natvig [3], for the case of independent components given component reliabilities how this joint prior distribution may be based on the combination of expert opinions. A specific system is finally treated numerically. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 741–755, 1997     

Estimation from binomial data with classifiers of known and unknown imperfections

Observations from inspection by a “test” method and a standard method are combined to provide estimators of population proportion, and of probabilities of misclassification for the test method. Results of Hochberg and Tenenbein [3] and of Albers and Veldman [1] are extended to the case where the standard method is not perfect, but its misclassification probabilities have known values. Both moment and maximum-likelihood estimators are considered and some asymptotic properties of the resulting estimators are compared.     

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     

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.     

Excess procurement strategies by a dominant buyer under constrained supply

Supply chains are often characterized by the presence of a dominant buyer purchasing from a supplier with limited capacity. We study such a situation where a single supplier sells capacity to an established and more powerful buyer and also to a relatively less powerful buyer. The more powerful buyer enjoys the first right to book her capacity requirements at supplier's end, and then the common supplier fulfills the requirement of the less powerful buyer. We find that when the supplier's capacity is either too low (below the lower threshold) or too high (above the higher threshold), there is no excess procurement as compared to the case when supplier has infinite capacity. When the supplier's capacity is between these two thresholds, the more powerful buyer purchases an excess amount in comparison to the infinite capacity case.     

Scheduling to minimize the weighted sum of completion times with secondary criteria

A result of Smith previously published in this journal [3], on the use of secondary criteria in scheduling problems, is shown to be incorrect and a counter example is presented. Heck and Roberts [2] suggested that their paper would be extended in the same way Smith's algorithm was. A new algorithm is given that converges to a local optimum for both problems.     

On the inspection game

The Inspection Game is a multistage game between a customs inspector and a smuggler, first studied by Melvin Dresher and Michael Maschler in the 1960s. An extension allowing the smuggler to act more than once, treated by Sakaguchi in a special case, is solved. Also, a more natural version of Sakaguchi's problem is solved in the special case where the smuggler may act at each stage. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 327–334, 1998