A Game Theory Approach for Assessment of Risk and Deployment of Police Patrols in Response to Criminal Activity in San Francisco

An efficient police patrol schedule must ensure the allocation of an appropriate number of officers sufficient to respond to the danger of criminal incidents, particularly in an urban environment, even when the available number of personnel is limited. This study proposes a framework that incorporates two game theory models designed for the allocation of police officers to patrol shifts. In the first step, the interactions of three factors between the criminal and the operation captain are modeled as a zero-sum, noncooperative game, after which a mixed strategy Nash equilibrium method is used to derive the risk value for each district to be patrolled. In the second step, the risk values are used to compute the Shapley value for all 10 districts, for three different threat levels. A fair allocation of police personnel based on the Shapley value is made with a minimum set of personnel deployment costs. The efficacy of the proposed method is verified using openly available data from the San Francisco City Police detailing incidents from the year 2016. The experimental results show that police planners can use this framework to quantitatively evaluate the criminal threat in each district when deciding upon the deployment of patrol officers for three shifts per day.     

POLICE PATROL BEAT DESIGN: ALLOCATION OF EFFORT AND EVALUATION OF EXPECTED PERFORMANCE*

This paper describes an iterative process for deploying police patrol force manpower. An application of the process is described as a case study of the St. Louis County Police Department (Missouri). The application is based on the county geographic information system (COGIS) and uses the hypercube queuing model (HQM). The procedures presented illustrate the generation of performance characteristics associated with a specific beat deployment. The application results indicate that the iterative model presented is a reliable and valid instrument for allocating police patrols.     

Manpower planning for maintenance jobs in process industries

This paper describes a model for allocating the weekly requirement of manpower for maintenance jobs in the process units. We develop a simple procedure for the solution of the manpower allocation problem which has to deal with planned and unplanned jobs during a planning period. The solution procedure is illustrated by a numerical example. Possible extensions of this model are also discussed.     

中小呼叫中心月度排班优化模型与算法

国内中小呼叫中心制定坐席人员月度排班表时,通常考虑劳动法规合同约束和体现企业自身用工管理诉求。构建坐席人员月度排班优化问题的二次整数规划模型。鉴于问题模型难解性,依据调研企业需求和模型逻辑结构分析,把问题分解成三个子问题。通过构建整数规划模型和提出启发式算法来求出子问题解,从而生成排班问题优化解。问题实例计算表明,模型算法能够有效控制人力成本和兼顾员工同班次管理目标。与周排班方法比较,该方法能够充分体现月度排班人力灵活性来实现人力优化配置。     

Markov and renewal models for total manpower system

This study compares the predictive utility of three stochastic models for both total manpower system and cohort personnel movement. The models are all discrete time versions, including a first order Markov chain, a Markov chain with duration of stay (semi-Markov) and a vacancy model having both renewal and Markov properties. The analysis covers a continuous 20 year period: 1950–1970 for a state police (U.S.A.) internal labor market. The simple Markov chain model is inadequate for long term cohort forecasts, but reasonably adequate for long term organizational forecasts. The semi-Markov model outperforms the simple Markov model for cohorts, but is surprisingly less accurate for the total organization. The heuristic information it portrays for the cohort is, however, quite informative. The best model for intermediate (5 year) and long term (10 year) forecasts in both cohort and organizational tests is the renewal type vacancy model. This finding is viewed as particularly important both in terms of empirical performance, which we expect can be improved due to the initial simplifying assumptions used, and in terms of further theoretical explication of the underlying causal process since internal staff flows are conceptualized as contingent on the opportunities available.     

Simulation of a police patrol activity

This paper describes the use of the Patrol Car Allocation Model to structure the relationships which exist between the utilization of patrol resources and various measures of performance. The relationships depict the cost vs service trade-offs that are present in patrol allocation decisions. The results of an actual study are presented along with a discussion of their potential value to the police patrol allocation function.     

COMPARISON OF NURSE ALLOCATION POLICIES-A MONTE CARLO MODEL*

Many hospitals have historically used a fixed staffing policy for allocating nursing personnel, in which the daily demand in each ward is met by nurses who are permanently assigned to the specific wards. In recent years, the concept of variable staffing has been proposed as a means of increasing manpower efficiency. A variable staffing policy is one which provides for staffing adjustments to meet work load through the use of a common pool of cross-trained nurses. In this paper, a model is formulated to evaluate the relative benefits of variable and fixed staffing policies. Results from a Monte Carlo evaluation of the model demonstrate how the hospital administrator can assess the sensitivity of savings to changes in policy and operating parameters. Several criteria which an administrator might adopt for equating levels of patient care under alternative staffing schemes are suggested and studied. The proposed method of analyzing benefits of alternative allocation procedures shows promise for evaluating policy choices in hospitals, as well as other service organizations with similar characteristics.     

RESOURCE PLANNING FOR MULTIPLE PROJECTS *

This paper is concerned with the estimation of the resource requirements to service multiple projects that use many types of resources. It reports on a systematic procedure to determine the low cost levels of these resources, focusing on the two following characteristics: (1) the comparative cost of standard time to overtime in the utilization of these resources for the economical completion of the projects, and (2) the impact of highly expensive equipment in the determination of the economic levels of the manpower resources that combine with the equipment to form a crew. A numerical example is also presented to illustrate the method. Resource planning is of particular interest in the area of multiproject scheduling, since most of the commonly utilized heuristic solution approaches focus on the allocation of a limited set of available resources. In the corporate strategic planning functions, resource planning is particularly important for capital investment, training and development, and procurement scheduling.     

Some statistical aspects of manpower planning in the civil service

A special feature of modern manpower planning methods is the use of computer-based statistical models, and the Civil Service Department is taking the lead in their development and use for manpower planning in the non-industrial Civil Service. Account is being taken of related data requirements in the development of a new Personnel Record Information System which will replace a range of existing records.Development work in hand covers both the “demand” and “supply” aspects of manpower planning and a bank of generalized “supply” models is in operation. Stationary population, renewal and Markovian principles are involved, and the particular statistical problems of modelling small manpower groups are being met in the development of a “small group” simulation model.     

A Simulation Metamodel for Response-Time Planning*

Field service management continues to be a major challenge for many service organizations as companies are required to provide more service with less resources. Especially in information intense environments, short response times for service calls are essential to avoid disruptions to a business office or production facility. Managers must regularly assess their manpower needs, and ensure that their allocation and operational decisions lead to the best service at the lowest cost. Xerox Corporation provides copiers, duplicators, and printing systems to an international market. Xerox operates a service network consisting of over 30,000 trained service personnel, each allocated to service regions by the service planning staff. Response-time planning involves many challenging problems: requirements planning at the national level, allocation planning at the district level, and operational planning at the team level. Customer service is critical and is commonly measured by response time—the time that elapses from when a service call is placed to when a service engineer begins service. This paper discusses how Xerox Corporation has used simulation models and metamodels to improve response-time planning and field service operations.     

A quantitative model for manpower decision making

Today's society is continually influenced by various changes, requiring managers to plan for manpower requirements. An approach that can be used by firms to solve one of the most pressing of today's employment problems is examined. In effect, the problem becomes one of determining an optimal work force composition based on both sociological and skill components. The problem is viewed as one of establishing rank ordered priorities among multiple conflicting manpower objectives. This study discusses some of the internal and external constraints faced by the firm and suggests a particular technique, goal programming, to facilitate the manpower decision-making process. The technique is examined under two different circumstances to provide some indication of the model's flexibility.     

Some social implications of personnel planning

It would appear that most discussions on manpower or personnel planning are concerned with highlighting the dichotomy between organizational needs and personal needs. The assumption that these two separate need areas can be successfully harmonized through personnel planning is implicit. In this paper the intention is to discuss this relationship in terms of the consequences for employees of attempts to achieve the aims of organizational manpower plans through the establishment of personnel control mechanisms.     

Manpower studies for industrial sectors

The author has been head of the Engineering Industry Training Board's Research, Planning and Statistics Division since the Board was established. This paper deals with developments over the past 10 years in manpower studies for industrial sectors. The term manpower studies is a portmanteau one which covers a complex of interrelated activities: monitoring trends manpower forecasting, devising in manpower supply and demand, training policies to meet anticipated manpower needs, or otherwise seeking to optimise the utilisation of existing and future manpower resources. The development of these studies is briefly described and the work of the Engineering Industry Training Board—which covers both methodological studies and data collection—is dealth with in more detail.     

Personnel policy and manpower planning in banking

Forces of rapid change and strong competition are now operating in the world. Banking with its rapidly changing technology must keep pace with these forces but it must at the same time provide secure and continuous employment for staff. Personnel policy now encompasses manpower planning which is defined as ‘A strategy to acquire, utilize, retain and develop people by formulating and implementing sound manpower policies agreed with employees and their unions’.     

A simulation-based dynamic operator assignment strategy considering machine interference - a case study on integrated circuit chip moulding operations

A simulation-based dynamic operator assignment strategy is proposed considering machine interference in solving an integrated circuit moulding operation problem. The strategy iteratively solves a floating manpower operator-assignment problem between simulation-based diagnostic study and operator assignment decision. Given current-state information, it provides a means for system performance evaluation. It searches a satisfactory solution for both cycle time and service level performances by using floating manpower method. A structured experimental design is used to illustrate the effectiveness of the proposed methodology. Empirical results show promise for the proposed methodology in solving a practical application. Finally, the system implementation constraints from both hardware and management problems are addressed.     

Developing a manpower strategy for an industry

This paper considers the following issues for developing an industry manpower strategy. An idea of the national system that exists for implementing a manpower strategy. The main questions arising from the strategy, and a definition of manpower planning. From this, the information and analysis techniques used to identify the strategy. The first application produces a manpower picture of the foundry industry. For company manpower planning the paper describes a manpower model of a company, and how the relationship between the activity and employment patterns of boundries was investigated. The industry findings are verified by company manpower planning investigations using the same information and techniques. The conclusions discuss some of the strengths and weaknesses of using this approach.     

Discrete simulation modelling for corporate manpower planning

Manpower planners within South African companies have very few, if any, decision support tools at their disposal to assist them in the formulation of their manpower strategies. Such quantitative tools as do exist are mathematically too sophisticated to be easily understood and implemented by manpower managers who are, on the whole, non numerate. The approach proposed in this paper, namely simulation modelling, discusses and demonstrates a powerful quantitative method which is conceptually easy to understand and whose results are easily interpreted. This particular simulation model examines the impact on organisational staffing levels over time as a result of specific present/proposed manpower policies in the areas of procurement and promotion. Through manipulating the inputs, the manpower planner can, with relative ease, examine the consequences of a range of alternative policies within a very short period of time.     

内部资本市场存在性、有效性及其公平性的理论演绎

文章构建了大股东控制下的企业集团内部资金借贷优化模型,推导并演绎了内部资本市场的存在性、有效性和公平性。研究发现,理想型内部资本市场实现了资本配置的最优化,形成参与博弈各方"共赢"的局面;附加冲突成本的效率型内部资本市场在一定条件下存在和有效,可以持续维持参与博弈各方的持续合作,实现社会福利的增加;利益输送型内部资本市场资本配置扭曲,有损效率性和公平性,并且不可持续。本文的结论可以为实证研究提供理论依据。     

Hospital productivity measurement: An engineering approach

A model for measuring hospital productivity is proposed, based on the determination of standard inputs per case. From these standards and the number of cases passing through a hospital, total standard inputs can be determined. Division of the standard inputs by the actual inputs provides productivity figures for each kind of input. Standard inputs per class of cases are calculated, through a chain of matrices, from standard inputs per elementary operation. Classification of cases into diagnostic categories, and the validity of assuming a typical average set of treatments for each class, are discussed. A numerical example is presented which demonstrates the proposed approach for calculating manpower productivity in a maternity ward.