Suchergebnisse

Kyle Lin ; This study aims to develop a mathematical model to describe the interactions between defense contractors and the government, in order to estimate cost and schedule for developing a technologically advanced weapon system. The research goal is twofold: (1) Explain why the development of a new weapon system is often subject to cost overrun and schedule delay; and (2) Identify market mechanisms to improve the efficiency of the bidding and contracting process in order to better manage risk. ; Naval Research Program ; Prepared for: N98, Mr. Christopher Marsh

The government runs a program to develop a technologically advanced weapon system. In the competition phase, the government provides initial funding to several defense contractors to develop system prototypes. Based on the demonstration of these prototypes, the government selects one defense contractor as the sole source to produce the final product. We develop a mathematical model to describe this process. By analyzing the model and conducting a numerical study, we find three main reasons why such a program often suffers delay and cost overrun. First, the selected contractor tends to be luckier than usual in the competition phase, so the government tends to overestimate its capability. Second, once a contractor becomes the sole source, their goal is to complete the scheduled tasks within each fiscal year on time, but not to deliver the final product as soon as possible. Third, the contractor may be motivated to exert extra effort during the competition phase in order to improve their chance of getting selected as the sole source, which may result in an overly optimistic estimation on program completion time. Based on a cost structure, our model offers recommendations on the optimal length of the competition phase and the number of contractors to invite, in order to minimize the program completion time and total cost. ; OPNAV N98 2000 Navy Pentagon Rm 5C469 Washington DC, 20350 ; Approved for public release; distribution is unlimited.

The government runs a program to develop a technologically advanced weapon system. In the competition phase, the government provides initial funding to several defense contractors to develop system prototypes. Based on the demonstration of these prototypes, the government selects one defense contractor as the sole source to produce the final product. We develop a mathematical model to describe this process. By analyzing the model and conducting a numerical study, we find three main reasons why such a program often suffers delay and cost overrun. First, the selected contractor tends to be luckier than usual in the competition phase, so the government tends to overestimate its capability. Second, once a contractor becomes the sole source, their goal is to complete the scheduled tasks within each fiscal year on time, but not to deliver the final product as soon as possible. Third, the contractor may be motivated to exert extra effort during the competition phase in order to improve their chance of getting selected as the sole source, which may result in an overly optimistic estimation on program completion time. Based on a cost structure, our model offers recommendations on the optimal length of the competition phase and the number of contractors to invite, in order to minimize the program completion time and total cost. ; OPNAV N98. ; Approved for public release; distribution is unlimited.

Two forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force—knowing which units are still alive in real time—decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two‐person zero‐sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This article gives an iterative algorithm to compute the optimal strategy without having to enumerate the entire payoff matrix, and offers some insights into the special case, where one force has only one unit. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 56–65, 2014

Radio-controlled improvised explosive devices (RCIEDs) have been a major weapon of choice by the insurgents in Operation Iraqi Freedom since 2003. One effective way to prevent an RCIED attack is to use electronic jamming devices to interfere with the communication between the trigger and the bomb itself. Due to power constraints and other considerations, however, a jammer usually cannot jam all triggers simultaneously. In this paper, we develop game-theoretic models to study both active jamming and reactive jamming. For active jamming, we compute the optimal mixed strategy by linear programming; for reactive jamming, we use an iterative method. Finally, we demonstrate the applications of our models with numerical experiments. ; Approved for public release; distribution is unlimited.

AbstractConsider a sequential dynamic pricing model where a seller sells a given stock to a random number of customers. Arriving one at a time, each customer will purchase one item if the product price is lower than her personal reservation price. The seller's objective is to post a potentially different price for each customer in order to maximize the expected total revenue. We formulate the seller's problem as a stochastic dynamic programming model, and develop an algorithm to compute the optimal policy. We then apply the results from this sequential dynamic pricing model to the case where customers arrive according to a continuous‐time point process. In particular, we derive tight bounds for the optimal expected revenue, and develop an asymptotically optimal heuristic policy. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

AbstractConsider a distributed system where many gatekeepers share a single server. Customers arrive at each gatekeeper according to independent Poisson processes with different rates. Upon arrival of a new customer, the gatekeeper has to decide whether to admit the customer by sending it to the server, or to block it. Blocking costs nothing. The gatekeeper receives a reward after a customer completes the service, and incurs a cost if an admitted customer finds a busy server and therefore has to leave the system. Assuming an exponential service distribution, we formulate the problem as an n‐person non‐zero‐sum game in which each gatekeeper is interested in maximizing its own long‐run average reward. The key result is that each gatekeeper's optimal policy is that of a threshold type regardless what other gatekeepers do. We then derive Nash equilibria and discuss interesting insights. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 702–718, 2003.

Because developing a new weapon system involves advanced technology pertinent to national security, the pricing of such systems primarily relies on cost estimation, as opposed to basic economic principles such as supply and demand. During the R&D period—which can take up to several years—however, the research may hit a roadblock and the various costs may change. As a consequence, such projects are often subject to substantial delays and cost overrun. This project will develop a mathematical model for the interaction among stakeholders in the defense industry, including the government and major defense contractors. The goal is to identify market mechanism to improve the efficiency of the contracting process. These mechanisms could improve the cost estimation process or contracting structure to better manage risk. ; Naval Research Program ; Prepared for: N9 Sponsor, POC: Mr. Chris Marsh

The article of record as published may be found at https://doi.org/10.1016/j.tcs.2020.03.011 ; A set of n boxes, located on the vertices of a hypergraph G, contain known but different rewards. A Searcher opens all the boxes in some hyperedge of G with the objective of collecting the maximum possible total reward. Some of the boxes, however, are booby trapped. If the Searcher opens a booby trapped box, the search ends and she loses all her collected rewards. We assume the number k of booby traps is known, and we model the problem as a zero-sum game between the maximizing Searcher and a minimizing Hider, where the Hider chooses k boxes to booby trap and the Searcher opens all the boxes in some hyperedge. The payoff is the total reward collected by the Searcher. This model could reflect a military operation in which a drone gathers intelligence from guarded locations, and a booby trapped box being opened corresponds to the drone being destroyed or incapacitated. It could also model a machine scheduling problem, in which rewards are obtained from successfully processing jobs but the machine may crash. We solve the game when G is a 1-uniform hypergraph (the hyperedges are all singletons), so the Searcher can open just 1 box. When G is the complete hypergraph (containing all possible hyperedges), we solve the game in a few cases: (1) same reward in each box, (2) k=1, and (3) n=4 and k = 2. The solutions to these few cases indicate that a general simple, closed form solution to the game appears unlikely. ; This material is based upon work supported by the National Science Foundation under Grant No. IIS-1909446. ; This material is based upon work supported by the National Science Foundation under Grant No. IIS-1909446.

This report examines two forms of decoy that may arise in warfare involving improvised explosive devices (IEDs). The first is a fake IED, which costs less than a real IED and wastes the time of route-clearing patrols that investigate it. The second is an understaffed surveillance tower, which may provide some deterrence to insurgent activities, as from the outside the tower appears to be fully operational. For each form of decoy, we formulate mathematical models to study the optimal strategies for both the insurgents and the government forces. We use numerical examples to demonstrate our models, and to point out the situations when these decoys may play a significant role in IED warfare. ; Approved for public release; distribution is unlimited.

AbstractThis article concerns scheduling policies in a surveillance system aimed at detecting a terrorist attack in time. Terrorist suspects arriving at a public area are subject to continuous monitoring, while a surveillance team takes their biometric signatures and compares them with records stored in a terrorist database. Because the surveillance team can screen only one terrorist suspect at a time, the team faces a dynamic scheduling problem among the suspects. We build a model consisting of an M/G/1 queue with two types of customers—red and white—to study this problem. Both types of customers are impatient but the reneging time distributions are different. The server only receives a reward by serving a red customer and can use the time a customer has spent in the queue to deduce its likely type. In a few special cases, a simple service rule—such as first‐come‐first‐serve—is optimal. We explain why the problem is in general difficult and we develop a heuristic policy motivated by the fact that terrorist attacks tend to be rare events. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

Mathematical Methods of Operations Research, V. 68, pp 539-549. ; A target is hidden in one of several possible locations, and the objective is to find the target as fast as possible. One common measure of effectiveness for the search process is the expected time of the search. This type of search optimization problem has been addressed and solved in the literature of the case where the searcher has imperfect sensitivity (possible false negative results), but perfect specificity (no false positive detections). In this paper, which is motivated by recent military and homeland security search situations, we extend the results to the case where the search is subject to false positive detections.

AbstractThis 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

AbstractConsider a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. An attack takes a random amount of time to complete. The patroller takes one time unit to move to and inspect an adjacent node, and will detect an ongoing attack with some probability. If an attack completes before it is detected, a cost is incurred. The attack time distribution, the cost due to a successful attack, and the detection probability all depend on the attack node. The patroller seeks a patrol policy that minimizes the expected cost incurred when, and if, an attack eventually happens. We consider two cases. A random attacker chooses where to attack according to predetermined probabilities, while a strategic attacker chooses where to attack to incur the maximal expected cost. In each case, computing the optimal solution, although possible, quickly becomes intractable for problems of practical sizes. Our main contribution is to develop efficient index policies—based on Lagrangian relaxation methodology, and also on approximate dynamic programming—which typically achieve within 1% of optimality with computation time orders of magnitude less than what is required to compute the optimal policy for problems of practical sizes. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 557–576, 2014