Inspection and crime prevention : an evolutionary perspective

In this paper, we analyse inspection games with an evolutionary perspective. In our evolutionary inspection game with a large population, each individual is not a rational payoff maximiser, but periodically updates his strategy if he perceives that other individuals' strategies are more successful than his own, namely strategies are subject to the evolutionary pressure. We develop this game into a few directions. Firstly, social norms are incorporated into the game and we analyse how social norms may influence individuals' propensity to engage in criminal behaviour. Secondly, a forward-looking inspector is considered, namely, the inspector chooses the level of law enforcement whilst taking into account the effect that this choice will have on future crime rates. Finally, the game is extended to the one with continuous strategy spaces

Quasi-regular sequences and optimal schedules for security games

We study security games in which a defender commits to a mixed strategy for protecting a finite set of targets of different values. An attacker, knowing the defender's strategy, chooses which target to attack and for how long. If the attacker spends time $t$ at a target $i$ of value $\alpha_i$, and if he leaves before the defender visits the target, his utility is $t \cdot \alpha_i$; if the defender visits before he leaves, his utility is 0. The defender's goal is to minimize the attacker's utility. The defender's strategy consists of a schedule for visiting the targets; it takes her unit time to switch between targets. Such games are a simplified model of a number of real-world scenarios such as protecting computer networks from intruders, crops from thieves, etc. We show that optimal defender play for this continuous time security games reduces to the solution of a combinatorial question regarding the existence of infinite sequences over a finite alphabet, with the following properties for each symbol $i$: (1) $i$ constitutes a prescribed fraction $p_i$ of the sequence. (2) The occurrences of $i$ are spread apart close to evenly, in that the ratio of the longest to shortest interval between consecutive occurrences is bounded by a parameter $K$. We call such sequences $K$-quasi-regular. We show that, surprisingly, $2$-quasi-regular sequences suffice for optimal defender play. What is more, even randomized $2$-quasi-regular sequences suffice for optimality. We show that such sequences always exist, and can be calculated efficiently. The question of the least $K$ for which deterministic $K$-quasi-regular sequences exist is fascinating. Using an ergodic theoretical approach, we show that deterministic $3$-quasi-regular sequences always exist. For $2 \leq K < 3$ we do not know whether deterministic $K$-quasi-regular sequences always exist.Comment: to appear in Proc. of SODA 201

Unit-Contingent Power Purchase Agreement and Asymmetric Information about Plant Outage

This paper analyzes a unit-contingent power purchase agreement between an electricity distributor and a power plant. Under such a contract the distributor pays the plant a fixed price if the plant is operational and nothing if plant outage occurs. Pricing a unit-contingent contract is complicated by the fact that the plant’s true status is its private information. The difference between the electricity spot price and the unit-contingent contract price provides an incentive for the plant to misreport its status and earn profit at the distributor’s expense. To prevent misreporting, the distributor may inspect the plant and levy penalties if misreporting is discovered. We find that some type of misreporting under certain circumstances can benefit both the plant and the distributor, because it serves as a risk-allocation mechanism between the two parties. We show that such a risk-allocation mechanism is equivalent to using state-contingent options and prohibiting misreporting.http://deepblue.lib.umich.edu/bitstream/2027.42/61470/1/1120_OWu.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/61470/4/1120_may09_OWu.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/61470/6/1120_Aug11_Wu.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/61470/8/1120_Wu_Oct11.pd

Decision Making with Coupled Learning: Applications in Inventory Management and Auctions

Operational decisions can be complicated by the presence of uncertainty. In many cases, there exist means to reduce uncertainty, though these may come at a cost. Decision makers then face the dilemma of acting based on current, incomplete information versus investing in trying to minimize uncertainty. Understanding the impact of this trade-off on decisions and performance is the central topic of this thesis. When attempting to construct probabilistic models based on data, operational decisions often affect the amount and quality of data that is collected. This introduces an exploration-exploitation trade-off between decisions and information collection. Much of the literature has sought to understand how operational decisions should be modified to incorporate this trade-off. While studying two well-known operational problems, we ask an even more basic question: does the exploration-exploitation trade-off matter in the first place? In the first two parts of this thesis we focus on this question in the context of the newsvendor problem and sequential auctions with incomplete private information. We first analyze the well-studied stationary multi-period newsvendor problem, in which a retailer sells perishable items and unmet demand is lost and unobserved. This latter limitation, referred to as demand censoring, is what introduces the exploration-exploitation trade-off in this problem. We focus on two questions: i.) what is the value of accounting for the exploration-exploitation trade-off; and, ii.) what is the cost imposed by having access only to sales data as opposed to underlying demand samples? Quite remarkably, we show that, for a broad family of tractable cases, there is essentially no exploration-exploitation trade-off; i.e., there is almost no value of accounting for the impact of decisions on information collection. Moreover, we establish that losses due to demand censoring (as compared to having full access to demand samples) are limited, but these are of higher order than those due to ignoring the exploration-exploitation trade-off. In other words, efforts aimed at improving information collection concerning lost sales are more valuable than analytic or computational efforts to pin down the optimal policy in the presence of censoring. In the second part of this thesis we examine the problem of an agent bidding on a sequence of repeated auctions for an item. The agent does not fully know his own valuation of the object and he can only collect information if he wins an auction. This coupling introduces the exploration-exploitation trade-off in this problem. We study the value of accounting for information collection on decisions and find that: i.) in general the exploration-exploitation trade-off cannot be ignored (that is, in some cases ignoring exploration can substantially affect rewards), but ii.) for a broad class of instances, ignoring exploration can indeed produce nearly optimal results. We characterize this class through a set of conditions on the problem primitives, and we demonstrate with examples that these are satisfied for common settings found in the literature. In the third part of this thesis we study the impact of uncertainty in the context of inventory record inaccuracies in inventory management systems. Record inaccuracies, mismatches between physical and recorded inventory, are frequently encountered in practice and can markedly affect revenues. Most of the literature is devoted to analyzing the cost-benefit relationship between investing in means to reduce inaccuracies and accounting for them in operational decisions. We focus on the less explored approach of using available data to reduce the uncertainty in inventory. In practice, collecting Point Of Sale (POS) data is substantially simpler than collecting stock information. We propose a model in which inventory is regarded as a virtually unobservable quantity and POS data is used to infer its state over time. Additionally, our method also works as an effective estimator of censored demand in the presence of inaccurate records. We test our methodology with extensive numerical experiments based on both simulated and actual retailing data. The results show that it is remarkably effective in inferring unobservable past statistics and predicting future stock status, even in the presence of severe data misspecifications

Applications of delay time theory to maintenance practice of complex plant

This thesis is concerned with investigating and understanding the role andconsequence of different modelling options and parameter estimation options formodelling a complex plant. As systems become more complicated and required newtechnologies and methodologies, more sophisticated maintenance models and controlpolicies are need to solve the maintenance problems. The initial chapter introduces thereview of previous work on a single component system and multi-component system.Although in recent years there has been a shift in the maintenance literature fromconsideration of single items to systems composed of several components, so far only afew papers have tackled the modelling of actual multi-component plant. In the thirdchapter, delay time concept and analysis technique have been presented. Ofparticularly importance are parameter estimation methods, namely the objective methodand the subjective methods. In the fourth chapter the component PM model and thesystem PM model for downtimes and costs based upon various PM policies arediscussed. The key options within maintenance modelling are to determine regularMinspection periods for the system modelled as a whole, and to determine the periodsfor the plant as a set of separate component models. An extension to the downtimemodel is presented for the case when the downtime due to failures within system is notsmall, and impacts upon the estimate of the number of failures arising over a specifiedtime zone. In the following chapter, we address parameter estimation methods usingsimulated data, and assess the ability of estimation techniques to capture the trueparameter values. Particular attention is paid to the problem arising during theparameter estimating process because of the inadequate recording of PM data andimplied correlation between model parameters. Finally, a case study is presented ofmaintenance modelling of production plant in a local company with view to improvingcurrent practice. The model developed is based upon the delay time concept wherebecause of an absence of PM data, using the results of earlier chapters, the processparameters and the delay time distribution were estimated from failure data only using the method of maximum likelihood. The modelling was repeated based uponsubjective assessmentosf parameter,a nd considerablec onsistencyw ith the objectivelybased case obtained. For the plant study, modelling indicated the current PMinspection program was ineffective. A snap-shot approach is then applied to assessother ways of reducing the downtime, and the possibility of improving the PMinspection practice. This leads to readily adapted improvements