A Model for Evaluation of Transport Policies in Multimodal Networks with Road and Parking Capacity Constraints

This paper presents a model for evaluation of transport policies in multimodal networks with road and parking capacity constraints. The proposed model simultaneously considers choices of travelers on route, parking location and mode between auto and transit. In the proposed model, it is assumed that auto drivers make a simultaneous route and parking location choice in a user equilibrium manner, and the modal split between auto and transit follows a multinomial logit formulation. A mathematical programming model with capacity constraints on road link and parking facilities is proposed that generates optimality conditions equivalent to the requirements for multimodal network equilibrium. An augmented Lagrangian dual algorithm embedded by partial linearization approach is developed to solve the proposed model. Numerical results on two example networks are presented to illustrate the proposed methodology. The results show that the service level of transit, parking charges, road link and parking capacities, and addition of a new parking location may bring significant impacts on travelers’ behavior and network performance. In addition, transport policies may result in paradoxical phenomenon.     

Probabilistic programming models for traffic incident management operations planning

This paper proposes mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for the planning of traffic incident management operations. For the incident response planning, we use the concept of quality of service during a potential incident to give the decision-maker the flexibility to determine the optimal policy in response to various possible situations. An integer programming model with probabilistic constraints is also proposed to address the incident response problem with stochastic resource requirements at the sites of incidents. For the resource allocation planning, we introduce a mathematical model to determine the number of service vehicles allocated to each depot to meet the resource requirements of the incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities. A detailed case study for the incident resource allocation problem is included to demonstrate the use of proposed model in a real-world context. The paper concludes with a summary of results and recommendations for future research.     

Transient policies in discrete dynamic programming: Linear programming including suboptimality tests and additional constraints

This paper investigates the computation of transient-optimal policies in discrete dynamic programming. The model, is quite general: it may contain transient as well as nontransient policies. and the transition matrices are not necessarily substochastic. A functional equation for the so-called transient-value-vector is derived and the concept of superharmonicity is introduced. This concept provides the linear program to compute the transientvalue-vector and a transient-optimal policy. We also discuss the elimination of suboptimal actions, the solution of problems with additional constraints, and the computation of an efficient policy for a multiple objective dynamic programming problem.     

A Mathematical Model for Optimal Functional Disruption of Biochemical Networks

Biochemical networks are a particular kind of biological networks which describe the cell metabolism and regulate various biological functions, from biochemical pathways to cell growth. The relationship between structure, function and regulation in complex cellular networks is still a largely open question. This complexity calls for proper mathematical models and methods relating network structure and functional properties. In this paper we focus on the problem of drug targets’ identification by detecting network alteration strategies which lead to a cell functionality loss. We propose a mathematical model, based on a bi-level programming formulation, to obtain the minimum cost disruption policy through the identification of specific gene deletions. These deletions represent drug target identification of new drug treatments for hindering bacterial infections.     

Analytical solution of A dynamic transaction flow problem

We analyze a mathematical programming model of a fractional flow process which consists ofn sectors and all possible time-dependent streams of flow between, into and out of the sectors. Assuming specific constraints on flow, least cost policies are determined for control of the system transactions involved over a given finite time horizon and over an infinite horizon. Several applications of the model are presented and discussed.     

Monetary and Fiscal Policy Interaction in the EMU: A Dynamic Game Approach

The interaction of monetary and fiscal policies is a crucial issue in a highly integrated economic area as the European Union. We investigate to which extent the EMU, that introduced a common monetary policy and restrictions on fiscal policy at the national level, benefits from macroeconomic policy cooperation due to the various interactions, spillovers and externalities from national macroeconomic policies. To study the effects of policy cooperation we compare the impact of three alternative policy regimes in a stylized dynamic model of the EMU: (i) non-cooperative monetary and fiscal policies, (ii) partial cooperation, and (iii) full cooperation both in symmetric and asymmetric settings where countries differ in structural characteristics, policy preferences and/or bargaining power. The paper introduces an analysis of coalitional behaviour in a dynamic setting into the literature.     

The achievable region method in the optimal control of queueing systems; formulations,bounds and policies

We survey a new approach that the author and his co-workers have developed to formulate stochastic control problems (predominantly queueing systems) asmathematical programming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., find linear or nonlinear constraints on the performance vectors that all policies satisfy. We present linear and nonlinear relaxations of the performance space for the following problems: Indexable systems (multiclass single station queues and multiarmed bandit problems), restless bandit problems, polling systems, multiclass queueing and loss networks. These relaxations lead to bounds on the performance of an optimal policy. Using information from the relaxations we construct heuristic nearly optimal policies. The theme in the paper is the thesis that better formulations lead to deeper understanding and better solution methods. Overall the proposed approach for stochastic control problems parallels efforts of the mathematical programming community in the last twenty years to develop sharper formulations (polyhedral combinatorics and more recently nonlinear relaxations) and leads to new insights ranging from a complete characterization and new algorithms for indexable systems to tight lower bounds and nearly optimal algorithms for restless bandit problems, polling systems, multiclass queueing and loss networks.     

Cost optimal allocation of rail passenger lines

We consider the problem of cost optimal railway line allocation for passenger trains for the Dutch railway system. At present, the allocation of passenger lines by Dutch Railways is based on maximizing the number of direct travelers. This paper develops an alternative approach that takes operating costs into account. A mathematical programming model is developed which minimizes the operating costs subject to service constraints and capacity requirements. The model optimizes on lines, line types, routes, frequencies and train lengths. First, the line allocation model is formulated as an integer nonlinear programming model. This model is transformed into an integer linear programming model with binary decision variables. An algorithm is presented which solves the problem to optimality. The algorithm is based upon constraint satisfaction and a Branch and Bound procedure. The algorithm is applied to a subnetwork of the Dutch railway system for which it shows a substantial cost reduction. Further application and extension seem promising.     

Constraint propagation,relational arithmetic in AI systems and mathematical programs

This paper explores the interrelationships between methods developed in mathematical programming to discover the structure of constraint (feasibility) sets and constraint propagation over networks used by some AI systems to perform inferences about quantities. It is shown that some constraint set problems in mathematical programming are equivalent to inferencing problems for constraint networks with interval labels. This makes the inference and query capabilities associated with AI systems that use logic programming, directly accessible to mathematical programming systems. On the other hand, traditional and newer methods which mathematical programming uses to obtain information about its associated feasibility set can be used to determine the propagation of constraints in a network of nodes of an AI system. When viewed from this point of view, AI problems can access additional mathematical programming analytical tools including new ways to incorporate qualitative data into constraint sets via interval and fuzzy arithmetic.This work was partially supported by the Industrial Consortium to Develop an Intelligent Mathematical Programming System — Amoco Oil Company, General Research Corporation, Ketron Management Science, Shell Oil Company, MathPro, and US West Advanced Technologies.     

Calculating risk neutral probabilities and optimal portfolio policies in a dynamic investment model with downside risk control

This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio’s worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifying the optimal terminal wealth distribution and a stochastic linear programming model replicating the identified optimal portfolio wealth. The replicating portfolio coincides with the optimal solution to the investor’s problem if the market is frictionless. The multiperiod stochastic linear programming model tests for the absence of arbitrage opportunities and its dual feasible solutions generate all risk neutral probability measures. When there are constraints such as liquidity or position requirements, the method yields approximate portfolio policies by minimizing the initial cost of the replication portfolio. A numerical example illustrates the difference between the replicating result and the optimal unconstrained portfolio.     

A mixed-integer goal programming model for nursing service budgeting

This paper presents a mixed-integer goal programming model for expense budgeting in a hospital nursing department. The model incorporates several different objectives based upon such considerations as cost containment and providing appropriate nursing hours for delivering quality nursing care. Also considered are possible trade-offs among full-time, part-time and overtime nurses on weekdays as well as weekends. The budget includes vacation, sick leave, holiday, and seniority policies of a hospital and various constraints on a hospital nursing service imposed by nursing unions. The results are based upon data from a study hospital and indicate that the model is practical for budgeting in a hospital nursing department.     

Supporting rural telecommunications: A compromise solutions approach

Rural telecommunication networks can foster the development of needed infrastructures for rural residents in an economically viable way. Thanks to emerging broadband fiber optics technology, rural telecommunications can be established via hub cities that function as service centers for neighboring smaller rural areas. Determining hub locations typically requires trade-offs among conflicting criteria. Policy makers typically set their goals as target values. The main aim of this paper is to present a zero—one compromise programming model that reflects such policy makers' target-setting behavior under a multiple criteria environment. A case in which the model is applied to the location of hub telecommunication centers in an American state further illustrates the applicability of the method.     

Scenario optimization

Uncertainty in the parameters of a mathematical program may present a modeller with considerable difficulties. Most approaches in the stochastic programming literature place an apparent heavy data and computational burden on the user and as such are often intractable. Moreover, the models themselves are difficult to understand. This probably explains why one seldom sees a fundamentally stochastic model being solved using stochastic programming techniques. Instead, it is common practice to solve a deterministic model with different assumed scenarios for the random coefficients. In this paper we present a simple approach to solving a stochastic model, based on a particular method for combining such scenario solutions into a single, feasible policy. The approach is computationally simple and easy to understand. Because of its generality, it can handle multiple competing objectives, complex stochastic constraints and may be applied in contexts other than optimization. To illustrate our model, we consider two distinct, important applications: the optimal management of a hydro-thermal generating system and an application taken from portfolio optimization.     

基于排队系统的偏好差异性顾客服务策略分析

在服务商为不同偏好顾客提供差异性服务的排队系统中,其收益受到需求规模、顾客类型等因素影响,如何制定策略才能达到服务特定类型顾客并获取最大收益的目的？本文以服务时间与效果正相关的顾客密集型服务为背景,基于M/M/1模型对服务商为两种偏好顾客提供两种服务的情景进行研究,并将从偏好服务所获基准效用相对较低、较高的顾客分别定义为1类、2类顾客。结果表明,①随着潜在顾客规模的增加,最优策略所适用的3种基本策略依次为公平策略、优先服务2类顾客的策略以及仅服务2类顾客的排他性策略;②3种基本策略的适用范围仅与1类顾客的服务选择标准相关;③在优先服务某类顾客的策略中,有效到达速率及服务速度由另一类顾客的特征决定。     

Multi-parallel work centers scheduling optimization with shared or dedicated resources in low-volume low-variety production systems

A new methodology for modeling large-scale scheduling problems in low-volume low-variety production systems is proposed through this paper. Such scheduling problems are constrained by limited time and resources, where each work center is assigned a unique statement of work, to be completed on-time with the budgeted number of resources. Products assembled in low-volume low-variety production systems are processed through a series of stations referred to as work centers, where varying levels and classifications of resources are deployed onto the product. Aircraft, heavy aero-structures, and heavy military equipment are examples of products assembled in low-volume low-variety production systems. To ensure products are delivered on-time and on-budget, it is crucial to execute to a detailed schedule, such that all precedence, resource, zonal, and other constraints and characteristics inherent in such production systems are successfully satisfied. Despite the criticality of detailed schedules in delivering products on-time and on-budget, limited research is reported on mixed-integer programming approaches for scheduling optimization of activities in low-volume low-variety production systems. The discrete-time linear mixed-integer mathematical programming model developed in this paper fills the gap in the current literature with a direct impact on the organizations’ service levels and bottom line. The proposed mathematical programming models are validated through a real-world case-study of the assembly process of a narrow body aircraft to ensure compatibility in the modeling of large-scale industrial problems.     

面向供应恢复时效性的弹性分销网络研究

关于供应链的弹性,供应能力恢复时效性的重要程度丝毫不亚于供应能力的恢复程度。本文研究了面向供应恢复时效性的弹性分销网络设计问题。考虑一个三级分销网络,其中各分销中心互为各自的备用分销中心。当一个分销中心因发生失效事件而不能接受制造商的供货时,制造商通过其他分销中心向失效的分销中心供货。分销中心需要保持一定量的应急库存以满足在应急供应到达之前的顾客需求。针对该问题建立了混合整数规划模型。该模型包含的大M约束使得直接使用优化软件求解需要很长的计算时间,并对计算平台的硬件配置有较高要求。为了更高效地求解该模型,提出了改进的MILP分解算法。通过对比实验,证明了所提算法的效率和有效性。进行了模型的敏感性分析,研究了各项参数对分销网络结构和成本的影响。     

Integration of Markov and Linear Programming Models to Assess the Farmgate and National Consequences of Adopting New Bovine Reproductive Technologies in the United Kingdom Agriculture

Despite many advances in biotechnology being futuristic, in some industries such technological improvements are now becoming generally available for absorption into commercial practice. The new reproductive technologies for bovine animals are such an example. For a regulated industry like agriculture, an ex ante evaluation of the impact of their adoption is the concern of policy makers. This paper describes a modelling strategy devised to assess these impacts, using a sequence of stochastic, financial and linear programming models. A set of individual farm type models were developed and later extended to a national model to simulate the interactions that occur between dairy and beef enterprises and the competition between them for resources on individual farms. Restraints reflecting national policies such as quotas on milk production and industry support through subsidies are built into the model to explore several scenarios. These models are used to assess the impact of new technologies on dairy and beef production nationally and for regions which have been identified by the Ministry of Agriculture, Fisheries and Food.     

A mixed-integer programming approach to a class timetabling problem: A case study with gender policies and traffic considerations

This paper considers the class scheduling and timetabling problem faced at Kuwait University (KU). The principal focus is to design efficient class offering patterns while taking into consideration newly imposed gender policies. We formulate a mathematical programming model that assigns offered classes to time-slots and addresses gender issues by defining appropriate surrogate constraints along with objective penalty terms. The model aims to enhance existing manual scheduling and timetabling approaches that are often accompanied with arduous combinatorial tasks such as resolving class conflicts, dealing with parking and traffic congestion, and ensuring an efficient utilization of facility and human resources. This modeling approach emphasizes the generation of flexible class timetables for students, and the efficient utilization of available facility resources. Computational results based on a number of case studies related to Kuwait University reveal that this approach yields improved schedules in terms of offering patterns and class conflicts.     

A Non-linear Multi-criteria Programming Approach for Determining County Emergency Medical Service Ambulance Allocations

In this paper an integer, non-linear mathematical programming model is developed to allocate emergency medical service (EMS) ambulances to sectors within a county in order to meet a government-mandated response-time criterion. However, in addition to the response-time criterion, the model also reflects criteria for budget and work-load, and, since ambulance response is best described within the context of a queueing system, several of the model system constraints are based on queueing formulations adapted to a mathematical programming format. The model is developed and demonstrated within the context of an example of a county encompassing rural, urban and mixed sectors which exhibit different demand and geographic characteristics. The example model is solved using an integer, non-linear goal-programming technique. The solution results provide ambulance allocations to sectors within the county, the probability of an ambulance exceeding a prespecified response time, and the utilization factor for ambulances per sector.