Optimal response against bioterror attack on airport terminal

We consider a potential bioterror attack on an airport. After the attack is identified, the government is faced with the problem of how to allocate limited emergency resources (human resources, vaccines, etc.) efficiently. The government is assumed to make a one-time resource allocation decision. The optimal allocation problem is discussed and it is shown how available information on the number of infected passengers can be incorporated into the model. Estimation for parameters of the cost function (number of deaths after the epidemic is over) is provided based on known epidemic models. The models proposed in the paper are demonstrated with a case study using real airport data.     

Uncertainty and value of information when allocating resources within and between healthcare programmes

A two-stage stochastic mathematical programming formulation has been developed to optimally allocate resources within and between healthcare programmes when there is an exogenous budget and the parameters of the healthcare models are variable and uncertain. This formulation solves the optimal resource allocation problem and calculates the expected value of acquiring additional information to resolve the uncertainties within the allocation. It is shown that the proposed formulation has several advantages over the chance constrained and robust mathematical programming methods.     

Minimizing the weighted number of tardy jobs and maximum tardiness in relocation problem with due date constraints

The relocation problem addressed in this paper is to determine a reconstruction sequence for a set of old buildings, under a limited budget, such that there is adequate temporary space to house the residents decanted during rehabilitation. It can be regarded as a resource-constrained scheduling problem where there is a set of jobs to be processed on a single machine. Each job demands a number of resources for processing and returns probably a different number of resources on its completion. Given a number of initial resources, the problem seeks to determine if there is a feasible sequence for the successful processing of all the jobs. Two generalizations of the relocation problem in the context of single machine scheduling with due date constraints are studied in this paper. The first problem is to minimize the weighted number of tardy jobs under a common due date. We show that it is NP-hard even when all the jobs have the same tardy weight and the same resource requirement. A dynamic programming algorithm with pseudo-polynomial computational time is proposed for the general case. In the second problem, the objective is to minimize the maximum tardiness when each job is associated with an individual due date. We prove that it is strongly NP-hard. We also propose a pseudo-polynomial time dynamic programming algorithm for the case where the number of possible due dates is predetermined.     

Hierarchical multi-objective decision systems for general resource allocation problems

We consider optimization methods for hierarchical power-decentralized systems composed of a coordinating central system and plural semi-autonomous local systems in the lower level, each of which possesses a decision making unit. Such a decentralized system where both central and local systems possess their own objective function and decision variables is a multi-objective system. The central system allocates resources so as to optimize its own objective, while the local systems optimize their own objectives using the given resources. The lower level composes a multi-objective programming problem, where local decision makers minimize a vector objective function in cooperation. Thus, the lower level generates a set of noninferior solutions, parametric with respect to the given resources. The central decision maker, then, parametric with respect to the given resources. The central decision maker, then, chooses an optimal resource allocation and the best corresponding noninferior solution from among a set of resource-parametric noninferior solutions. A computational method is obtained based on parametric nonlinear mathematical programming using directional derivatives. This paper is concerned with a combined theory for the multi-objective decision problem and the general resource allocation problem.The authors are indebted to Professor G. Leitmann for his valuable comments and suggestions.     

Structural properties of the optimal resource allocation policy for single-queue systems

This paper studies structural properties of the optimal resource allocation policy for single-queue systems. Jobs arrive at a service facility and are sent one by one to a pool of computing resources for parallel processing. The facility poses a constraint on the maximum expected sojourn time of a job. A central decision maker allocates the servers dynamically to the facility. We consider two models: a limited resource allocation model, where the allocation of resources can only be changed at the start of a new service, and a fully flexible allocation model, where the allocation of resources can also change during a service period. In these two models, the objective is to minimize the average utilization costs whilst satisfying the time constraint. To this end, we cast these optimization problems as Markov decision problems and derive structural properties of the relative value function. We show via dynamic programming that (1) the optimal allocation policy has a work-conservation property, and (2) the optimal number of servers follows a step function with as extreme policy the bang-bang control policy. Moreover, (3) we provide conditions under which the bang-bang control policy takes place. These properties give a full characterization of the optimal policy, which are illustrated by numerical experiments.     

Basin-wide cooperative water resources allocation

The Cooperative Water Allocation Model (CWAM) is designed within a general mathematical programming framework for modeling equitable and efficient water allocation among competing users at the basin level and applied to a large-scale water allocation problem in the South Saskatchewan River Basin located in southern Alberta, Canada. This comprehensive model consists of two main steps: initial water rights allocation and subsequent water and net benefits reallocation. Two mathematical programming approaches, called the priority-based maximal multiperiod network flow (PMMNF) method and the lexicographic minimax water shortage ratios (LMWSR) technique, are developed for use in the first step. Cooperative game theoretic approaches are utilized to investigate how the net benefits can be fairly reallocated to achieve optimal economic reallocation of water resources in the second step. The application of this methodology to the South Saskatchewan River Basin shows that CWAM can be utilized as a tool for promoting the understanding and cooperation of water users to achieve maximum welfare in a river basin and minimize the potential damage caused by water shortages, through water rights allocation, and water and net benefit transfers among water users under a regulated water market or administrative allocation mechanism.     

Estimation of more than one parameters in stratified sampling with fixed budget

In a multivariate stratified sampling more than one characteristic are defined on every unit of the population. An optimum allocation which is optimum for one characteristic will generally be far from optimum for others. A compromise criterion is needed to work out a usable allocation which is optimum, in some sense, for all the characteristics. When auxiliary information is also available the precision of the estimates of the parameters can be increased by using it. Furthermore, if the travel cost within the strata to approach the units selected in the sample is significant the cost function remains no more linear. In this paper an attempt has been made to obtain a compromise allocation based on minimization of individual coefficients of variation of the estimates of various characteristics, using auxiliary information and a nonlinear cost function with fixed budget. A new compromise criterion is suggested. The problem is formulated as a multiobjective all integer nonlinear programming problem. A solution procedure is also developed using goal programming technique.     

A dual bin-packing approach to scheduling surgical cases at a publicly-funded hospital

Publicly-funded hospitals are typically allocated an annual budget by the government based on the number of enrollees in the region. Given tight budget constraints, the capacity of resources is fairly fixed. Such hospitals strive to maximize the utilization of their resources through continuous improvement and optimization techniques. We address a surgical case scheduling problem experienced at a publicly-funded hospital and conceptualize this multi-period, multi-resource, priority-based case scheduling problem as an unequal-sized, multi-bin, multi-dimensional dual bin-packing problem. A mixed integer programming model and a heuristic based on the first fit decreasing algorithm are presented. Resource availability, case priorities, and variation in surgery times are key features included in our model. Our proposed approach led to substantial savings, 20% reduction in number of days and up to 20% increase in operating room utilization, when compared to real schedules obtained from the surgical department at a publicly-funded hospital.     

A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin’s irrigation areas, Gansu Province, China. In this study, the irrigation areas’ economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties.     

On the Optimal Allocation of Resources in the Production of Human Capital

The problem considered here is the allocation of limited school resources over the school-life of students so as to maximize their human capital stock at the end of the schooling period. The constraints faced by school authorities in maximizing the terminal human capital stock include the production technology, a limited budget per pupil, and the constraint that the level of knowledge exceed some minimum level before the pupil can pass to the succeeding grade. The problem is solved using optimal control theory. Both the results obtained generally and those derived for specific examples indicate the optimal allocation is one where the level of expenditure per pupil increases with the grade level of the pupil.     

Decision support approach based on multiple objectives and resources for assessing the relocation plan of dangerous hillside aggregations

The overdevelopment of hillside areas, coupled with the effects of global climate change, has increased the likelihood of disasters with severe consequences, such as material damages and loss of lives. Thus, there is a great urgency to create relocation plans for dangerous hillside aggregations that are not suitable for human settlement. The government of Taipei City in Taiwan has not properly addressed the assessment needs for decisions involving priority and budget allocation for these relocation projects. This study proposes a hybrid approach combining the Delphi method, fuzzy-logic inference system (FLIS), and the multi-objective programming (MOP) method to assist the city government in dealing with complex aggregation relocation decision problems. Twenty-four projects are tested by the proposed approach. Compared to the original relocation plan, results from this study reveal that the proposed approach is more objective and effective in relocation prioritization, project selection, budget utilization, and resource planning. These results will provide the city government with useful information for improving the relocation plan, thereby reducing the potential for human and material losses due to inadequate decision-making.     

Optimization and mechanism design

Mechanism design is about optimizing the allocation of resources when the parameters needed to determine an optimal allocation are privately held by the agents who will consume the resources. An agent’s report of her information will influence the resulting allocation which in turn will affect her utility. In such a situation, how can one simultaneously elicit the information that is privately held and choose the optimal allocation? This paper illustrates how standard results in linear programming play a role in the analysis of mechanism design problems. It is not a comprehensive survey. Rather, it focuses on two variations of a particular problem: the allocation of a single object.     

The budget constrained r-interdiction median problem with capacity expansion

In this article, we elaborate on a budget constrained extension of the r-interdiction median problem with fortification (RIMF). The objective in the RIMF is to find the optimal allocation of protection resources to a given service system consisting of p facilities so that the disruptive effects of r possible attacks to the system are minimized. The defender of the system needs to fortify q facilities of the present system to offset the worst-case loss of r non-fortified facilities due to an interdiction in which the attacker’s objective is to cause the maximum possible disruption in the service level of the system. The defender-attacker relationship fits a bilevel integer programming (BIP) formulation where the defender and attacker take on the respective roles of the leader and the follower. We adopt this BIP formulation and augment it with a budget constraint instead of a predetermined number of facilities to be fortified. In addition, we also assume that each facility has a flexible service capacity, which can be expanded at a unit cost to accommodate the demand of customers who were serviced by some other interdicted facility before the attack. First, we provide a discrete optimization model for this new facility protection planning scenario with a novel set of closest assignment constraints. Then, to tackle this BIP problem we use an implicit enumeration algorithm performed on a binary tree. For each node representing a different fortification scheme, the attacker’s problem is solved to optimality using Cplex 11. We report computational results obtained on a test bed of 96 randomly generated instances. The article concludes with suggestions for future research.     

A mixed integer linear programming model for reliability optimisation in the component deployment problem

Component deployment is a combinatorial optimisation problem in software engineering that aims at finding the best allocation of software components to hardware resources in order to optimise quality attributes, such as reliability. The problem is often constrained because of the limited hardware resources, and the communication network, which may connect only certain resources. Owing to the non-linear nature of the reliability function, current optimisation methods have focused mainly on heuristic or metaheuristic algorithms. These are approximate methods, which find near-optimal solutions in a reasonable amount of time. In this paper, we present a mixed integer linear programming (MILP) formulation of the component deployment problem. We design a set of experiments where we compare the MILP solver to methods previously used to solve this problem. Results show that the MILP solver is efficient in finding feasible solutions even where other methods fail, or prove infeasibility where feasible solutions do not exist.     

Branch and bound based solution algorithms for the budget constrained discrete time/cost trade-off problem

The time/cost trade-off models in project management aim to reduce the project completion time by putting extra resources on activity durations. The budget problem in discrete time/cost trade-off scheduling selects a time/cost mode for each activity so as to minimize the project completion time without exceeding the available budget. There may be alternative modes that solve the budget problem optimally and each solution may have a different total cost value. In this study we consider the budget problem and aim to find the minimum cost solution among the minimum project completion time solutions. We analyse the structure of the problem together with its linear programming relaxation and derive some mechanisms for reducing the problem size. We solve the reduced problem by branch and bound based optimization and heuristic algorithms. We find that our branch and bound algorithm finds optimal solutions for medium-sized problem instances in reasonable times and the heuristic algorithms produce high quality solutions very quickly.     

An Iterated Local Search for the Budget Constrained Generalized Maximal Covering Location Problem

Capacitated covering models aim at covering the maximum amount of customers’ demand using a set of capacitated facilities. Based on the assumptions made in such models, there is a unique scenario to open a facility in which each facility has a pre-specified capacity and an operating budget. In this paper, we propose a generalization of the maximal covering location problem, in which facilities have different scenarios for being constructed. Essentially, based on the budget invested to construct a given facility, it can provide different service levels to the surrounded customers. Having a limited budget to open the facilities, the goal is locating a subset of facilities with the optimal opening scenario, in order to maximize the total covered demand and subject to the service level constraint. Integer linear programming formulations are proposed and tested using ILOG CPLEX. An iterated local search algorithm is also developed to solve the introduced problem.     

Optimal allocation and backup of computer resources under asymmetric information and incentive incompatibility

This paper presents the optimal allocation and backup of computing resources in a multidivisional firm in the presence of asymmetric information and incentive incompatibility. A game-theoretic model is developed and transformed to a linear programming problem. The solution to this linear programming problem enables the corporate headquarters to design a resource allocation scheme such that the revelation principle prevails and all divisions tell the truth. To cope with the combinatorial explosion of complexity caused by the resource constraint, a greedy-type algorithm and an averaged version of the original linear programming problem are developed to provide the upper and lower bounds. The greedy-type algorithm generates exact solutions for a wide range of instances. The lower bounds coincide with the exact solutions for the cases where the computer resource is either scarce or abundant. The averaged-version resource allocation model with slight modifications solves the optimal computer backup capacity problem. It determines how much back up capacity the firm should purchase when the firm's computer breaks down.     

政府干预与资源配置:传统产业和战略性新兴产业的对比

鉴于传统产业和战略性新兴产业所受政府干预程度不同,本文对比分析了政府干预导致两个产业资源配置扭曲的作用机理.实证分析以钢铁产业(传统产业)和光伏产业(战略性新兴产业)为例,利用2007-2015年沪深两市上市公司数据,量化测算了土地供给价格扭曲、财政补贴和预算软约束这三个因素对资源配置效率的影响程度.结果表明:钢铁产业和光伏产业均受到政府不同程度的干预,光伏产业中土地供给价格扭曲和财政补贴程度明显高于钢铁产业;土地供给价格扭曲、财政补贴、预算软约束显著降低了钢铁产业和光伏产业的资源配置效率;政府干预程度越大资源配置效率越低,因此光伏产业的资源配置扭曲现象比钢铁产业更严重.     

A fuzzy inexact two-phase programming approach to solving optimal allocation problems in water resources management

Inappropriate agricultural activities are the main reasons of water shortage and environmental pollution in many rural areas. How to generate preferred decision schemes for agricultural activities is a critical issue for decision makers. In this study, a two-phase programming approach is advanced for regional water resources allocation in a rural region of China. The approach shows applicability when the uncertain inputs are provided as intervals and such uncertainty is desired to be delivered to the corresponding solutions. Multiple control variables are introduced both in the objective function and constraints of the programming model, which make it possible for the constraints being relaxed under respective levels. A more satisfactory objective value can thus be expected as well as the impact of each constraint on the modeling outputs can be clarified effectively. The decision variables are useful for decision makers to justify and/or adjust the decision schemes for agricultural activities through incorporation of their implicit knowledge on water allocation management.