An extreme-point approach for obtaining weighted ratings in qualitative multicriteria decision making

Many attempts have been made in the past to obtain estimates for the weights and ratings values of a multicriteria linear utility function. In particular, the problem arises when both criteria importance and alternatives' ratings are expressed in a qualitative ordinal manner. This article proposes an extreme-point approach for obtaining the overall ratings in the presence of ordinal preferences both for the criteria importance and the alternatives' rankings. In particular it is shown that Borda's method of scores is obtained as a special case. © 1996 John Wiley & Sons, Inc.     

To catch an intruder: Part A—uncluttered scenario

We analyze an interdiction scenario where an interceptor attempts to catch an intruder as the intruder moves through the area of interest. A motivating example is the detection and interdiction of drug smuggling vessels in the Eastern Pacific and Caribbean. We study two models in this article. The first considers a nonstrategic target that moves through the area without taking evasive action to avoid the interdictor. We determine the optimal location the interceptor should position itself to best respond when a target arrives. The second model analyzes the strategic interaction between the interceptor and intruder using a Blotto approach. The intruder chooses a route to travel on and the interceptor chooses a route to patrol. We model the interaction as a two‐player game with a bilinear payoff function. We compute the optimal strategy for both players and examine several extensions. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 29–40, 2017     

Resource allocation in an asymmetric technology race with temporary advantages

We consider two opponents that compete in developing asymmetric technologies where each party's technology is aimed at damaging (or neutralizing) the other's technology. The situation we consider is different than the classical problem of commercial R&D races in two ways: First, while in commercial R&D races the competitors compete over the control of market share, in our case the competition is about the effectiveness of technologies with respect to certain capabilities. Second, in contrast with the “winner‐takes‐all” assumption that characterizes much of the literature on this field in the commercial world, we assume that the party that wins the race gains a temporary advantage that expires when the other party develops a superior technology. We formulate a variety of models that apply to a one‐sided situation, where one of the two parties has to determine how much to invest in developing a technology to counter another technology employed by the other party. The decision problems are expressed as (convex) nonlinear optimization problems. We present an application that provides some operational insights regarding optimal resource allocation. We also consider a two‐sided situation and develop a Nash equilibrium solution that sets investment values, so that both parties have no incentive to change their investments. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 128–145, 2012     

Failure profiles of coherent systems

In this paper we first introduce and study the notion of failure profiles which is based on the concepts of paths and cuts in system reliability. The relationship of failure profiles to two notions of component importance is highlighted, and an expression for the density function of the lifetime of a coherent system, with independent and not necessarily identical component lifetimes, is derived. We then demonstrate the way that failure profiles can be used to establish likelihood ratio orderings of lifetimes of two systems. Finally we use failure profiles to obtain bounds, in the likelihood ratio sense, on the lifetimes of coherent systems with independent and not necessarily identical component lifetimes. The bounds are relatively easy to compute and use. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Discrete repairable reliability systems

Consider a reliability system consisting of n components. The failures and the repair completions of the components can occur only at positive integer-valued times k ϵ N₊₊ ϵ (1, 2, …). At any time k ϵ N₊₊ each component can be in one of two states: up (i.e., working) or down (i.e., failed and in repair). The system state is also either up or down and it depends on the states of the components through a coherent structure function τ. In this article we formulate mathematically the above model and we derive some of its properties. In particular, we identify conditions under which the first failure times of two such systems can be stochastically ordered. A variety of special cases is used in order to illustrate the applications of the derived properties of the model. Some instances in which the times of first failure have the NBU (new better than used) property are pointed out. © 1993 John Wiley & Sons, Inc.     

An interactive optimization system for bulk-cargo ship scheduling

This article considers the efficient scheduling of a fleet of ships engaged in pickup and delivery of bulk cargoes. Our optimization system begins by generating a menu of candidate schedules for each ship. This menu can contain all feasible solutions, which guarantees we will find an optimal solution or can be heuristically limited to contain only those schedules likely to be in an optimal solution. The problem of choosing from this menu an optimal schedule for the fleet is formulated as a set-packing problem and solved with a dual algorithm. Computational experience is presented based on real data obtained from the Military Sealift Command of the U. S. Navy. Run times for this data were reasonable and solutions were generated with the potential of saving up to about $30 million per year over the manual system currently in place. We also describe a color-graphics interface developed to facilitate interaction with the optimization system.     

Models of sensor operations for border surveillance

This article is motivated by the diverse array of border threats, ranging from terrorists to arms dealers and human traffickers. We consider a moving sensor that patrols a certain section of a border with the objective to detect infiltrators who attempt to penetrate that section. Infiltrators arrive according to a Poisson process along the border with a specified distribution of arrival location, and disappear a random amount of time after their arrival. The measures of effectiveness are the target (infiltrator) detection rate and the time elapsed from target arrival to target detection. We study two types of sensor trajectories that have constant endpoints, are periodic, and maintain constant speed: (1) a sensor that jumps instantaneously from the endpoint back to the starting‐point, and (2) a sensor that moves continuously back and forth. The controlled parameters (decision variables) are the starting and end points of the patrolled sector and the velocity of the sensor. General properties of these trajectories are investigated. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Split delivery routing

This article examines a relaxed version of the generic vehicle routing problem. In this version, a delivery to a demand point can be split between any number of vehicles. In spite of this relaxation the problem remains computationally hard. Since only small instances of the vehicle routing problem are known to be solved using exact methods, the vehicle route construction for this problem version is approached using heuristic rules. The main contribution of this article to the existing body of literature on vehicle routing issues in (a) is presenting a new vehicle routing problem amenable to practical applications, and (b) demonstrating the potential for cost savings over similar “traditional” vehicle routing when implementing the model and solutions presented here. The solution scheme allowing for split deliveries is compared with a solution in which no split deliveries are allowed. The comparison is conducted on six sets of 30 problems each for problems of size 75, 115, and 150 demand points (all together 540 problems). For very small demands (up to 10% of vehicle's capacity) no significant difference in solutions is evident for both solution schemes. For the other five problem sets for which point demand exceeds 10% of vehicle's capacity, very significant cost savings are realized when allowing split deliveries. The savings are significant both in the total distance and the number of vehicles required. The vehicles' routes constructed by our procedure tend to cover cohesive geographical zones and retain some properties of optimal solutions.     

The effect of crowd density on the expected number of casualties in a suicide attack

Utilizing elementary geometric and probability considerations, we estimate the effect of crowd blocking in suicide bombing events. It is shown that the effect is quite significant. Beyond a certain threshold, the expected number of casualties decreases with the number of people in the arena. The numerical results of our model are consistent with casualty data from suicide bombing events in Israel. Some operational insights are discussed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Optimality of the greedy shooting strategy in the presence of incomplete damage information

Consider a situation where a single shooter engages, sequentially, a cluster of targets that may vary in terms of vulnerability and value or worth. Following the shooting of a round of fire at a certain target, the latter may either be killed or remain alive. We assume neither partial nor cumulative damage. If the target is killed, there is a possibility that the shooter is not aware of that fact and may keep on engaging that target. If the shooter recognizes a killed target as such, then this target is considered to be evidently killed. If the objective is to maximize the weighted expected number of killed targets, where the weight reflects the value of a target, then it is shown that a certain type of a shooting strategy, called a Greedy Strategy, is optimal under the general assumption that the more a target is engaged, but still not evidently killed, the less is the probability that the next round will be effective. If all weights are equal, then the greedy shooting strategy calls to engage, at each round, the least previously engaged target that is not evidently killed. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 613–622, 1997