A simulation model for emergency evacuation

This paper describes the development of a prototype spatial decision support system for use by emergency planners in developing contingency plans for evacuations from disaster areas. It links together a geographical information system (ARC/INFO) with a specially written object-oriented micro-simulator via a windowing computer operating system. The details of the system are described, its limitations are discussed and potential enhancements are identified.     

Combining simulation and goal programming for healthcare planning in a medical assessment unit

This paper describes a detailed simulation model for healthcare planning in a medical assessment unit (MAU) of a general hospital belonging to the national health service (NHS), UK. The MAU is established to improve the quality of care given to acute medical patients on admission, and to provide the organisational means of rapid assessment and investigation in order to avoid unnecessary admissions. The simulation model enables different scenarios to be tested to eliminate bottlenecks in order to achieve optimal clinical workflow. The link between goal programming (GP) and simulation for efficient resource planning is explored. A GP model is developed for trade-off analysis of the results obtained from the simulation. The implications of MAU management preferences to various objectives are presented.     

Single observation adaptive search for discrete and continuous stochastic optimization

Solving a stochastic optimization problem often involves performing repeated noisy function evaluations at points encountered during the algorithm. Recently, a continuous optimization framework for executing a single observation per search point was shown to exhibit a martingale property so that associated estimation errors are guaranteed to converge to zero. We generalize this martingale single observation approach to problems with mixed discrete–continuous variables. We establish mild regularity conditions for this class of algorithms to converge to a global optimum.     

Simulation modelling for contracting hospital emergency services at the regional level

Hospital emergency services are closely connected to demographic issues and population changes. The methodology presented here helps to assess the effects of the forecasted demand changes on the next-year emergency unit workloads. The objective of the study is to estimate the expected volume of emergency hospital services, as measured by the number and costs of medical procedures provided to patients, to be contracted by the Polish National Health Fund (NFZ) branch at the regional level to cover the forecasted demand. A discrete-event simulation model was developed to elaborate the credible forecasts of the function components, the fundamental elements of the contract values granted by the NFZ for emergency departments for the following year. Emergency department-level data were drawn from the NFZ regional branch registry to perform a statistical analysis of emergency services provided to patients in 17 admission units and emergency wards in 2010. The model results indicate that the predicted increase in two age groups, i.e., the youngest children and the older population, will have different effects on the number and value of hospital emergency services to be considered in the contracting policy. There is potential for a discrete-event simulation to support strategic health policy decision making at the regional level. The value of this approach lies in providing estimates for the what-if scenarios related to the prognosis of changing acute demand.     

A knowledge-based multi-role decision support system for ore blending cost optimization of blast furnaces

Literature illustrates the difficulties in obtaining the lowest-cost optimal solution to an ore blending problem for blast furnaces by using the traditional trial-and-error method in iron and steel enterprises. To solve this problem, we developed a cost optimization model which we have implemented in a multi-role-based decision support system (DSS). On the basis of analyzing the business flow and working process of ore blending, we propose an architecture of DSS which is built based on multi-roles. This DSS construction pre-processes the data for materials and elements, builds a general database, abstracts the related optimal operations research models and introduces the reasoning mechanism of an expert system. A non-linear model of ore blending for blast furnaces and its solutions are provided. A database, a model base and a knowledge base are integrated into the expert system-based multi-role DSS to meet the different demands of data, information and decision-making knowledge for the various roles of users. A comparison of the results for the DSS and the trial-and-error method is provided. The system has produced excellent economic benefits since it was implemented at the Xiangtan Iron & Steel Group Co. Ltd., China.     

A simulation optimization approach for a two-echelon inventory system with service level constraints

In this paper, we present a simulation optimization algorithm for solving the two-echelon constrained inventory problem. The goal is to determine the optimal setting of stocking levels to minimize the total inventory investment costs while satisfying the expected response time targets for each field depot. The proposed algorithm is more adaptive than ordinary optimization algorithms, and can be applied to any multi-item multi-echelon inventory system, where the cost structure and service level function resemble what we assume. Empirical studies are performed to compare the efficiency of the proposed algorithms with other existing simulation algorithms.     

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.     

Retrospective optimization of mixed-integer stochastic systems using dynamic simplex linear interpolation

We propose a family of retrospective optimization (RO) algorithms for optimizing stochastic systems with both integer and continuous decision variables. The algorithms are continuous search procedures embedded in a RO framework using dynamic simplex interpolation (RODSI). By decreasing dimensions (corresponding to the continuous variables) of simplex, the retrospective solutions become closer to an optimizer of the objective function. We present convergence results of RODSI algorithms for stochastic “convex” systems. Numerical results show that a simple implementation of RODSI algorithms significantly outperforms some random search algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO).     

Staff optimization for time-dependent acute patient flow

The emergency department is a key element of acute patient flow, but due to high demand and an alternating rate of arriving patients, the department is often challenged by insufficient capacity. Proper allocation of resources to match demand is, therefore, a vital task for many emergency departments.Constrained by targets on patient waiting time, we consider the problem of minimizing the total amount of staff-resources allocated to an emergency department. We test a matheuristic approach to this problem, accounting for both patient flow and staff scheduling restrictions. Using a continuous-time Markov chain, patient flow is modeled as a time-dependent queueing network where inhomogeneous behavior is evaluated using the uniformization method. Based on this modeling approach, we recursively evaluate and allocate staff to the system using integer linear programming until the waiting time targets are respected in all queues of the network. By comparing to discrete-event simulations of the associated system, we show that this approach is adequate for both modeling and optimizing the patient flow. In addition, we demonstrate robustness to the service time distribution and the associated system with multiple classes of patients.     

Simulation-based framework to improve patient experience in an emergency department

The global economic crisis has a significant impact on healthcare resource provision worldwide. The management of limited healthcare resources is further challenged by the high level of uncertainty in demand, which can lead to unbalanced utilization of the available resources and a potential deterioration of patient satisfaction in terms of longer waiting times and perceived reduced quality of services. Therefore, healthcare managers require timely and accurate tools to optimize resource utility in a complex and ever-changing patient care process. An interactive simulation-based decision support framework is presented in this paper for healthcare process improvement. Complexity and different levels of variability within the process are incorporated into the process modeling phase, followed by developing a simulation model to examine the impact of potential alternatives. As a performance management tool, balanced scorecard (BSC) is incorporated within the framework to support continual and sustainable improvement by using strategic-linked performance measures and actions. These actions are evaluated by the simulation model developed, whilst the trade-off between objectives, though somewhat conflicting, is analysed by a preference model. The preference model is designed in an interactive and iterative process considering decision makers preferences regarding the selected key performance indicators (KPIs). A detailed implementation of the framework is demonstrated on an emergency department (ED) of an adult teaching hospital in north Dublin, Ireland. The results show that the unblocking of ED outflows by in-patient bed management is more effective than increasing only the ED physical capacity or the ED workforce.     

Competition under different reimbursement systems: The concept of an internet-based hospital management game

We have developed an internet-based management game to illustrate the economic and organisational decision-making process in a hospital by using discrete event simulation. Up to six hospitals compete against each other for inpatients with different disease categories and budget depending on hospital mission, regional health policy, inpatient reimbursement system (day-, case- and global-budget based) as well as labour and radiology technology market for 12 decision periods. Players can evaluate alternative actions for capacity planning as well as patient scheduling and control problems depending on different game situations. The uniqueness of COREmain hospital game consists of the internet-based framework, the combination of resource, process and financial result management, the competition of hospitals within a region and the consideration of different inpatient reimbursement systems. The deployment of this game in teaching, policy and research might improve policy making both at a hospital, regional and national level and also induce further research in these fields.     

A linear optimization problem to derive relative weights using an interval judgement matrix

In this paper, we propose a new Decision Making model, enabling to assess a finite number of alternatives according to a set of bounds on the preference ratios for the pairwise comparisons between alternatives, that is, an “interval judgement matrix”. In the case in which these bounds cannot be achieved by any assessment vector, we analyze the problem of determining of an efficient or Pareto-optimal solution from a multi-objective optimization problem. This multi-objective formulation seeks for assessment vectors that are near to simultaneously fulfil all the bound requirements imposed by the interval judgement matrix. Our new model introduces a linear optimization problem in order to define a consistency index for the interval matrix. By solving this optimization problem it can be associated a weakly efficient assessment vector to the consistency index in those cases in which the bound requirements are infeasible. Otherwise, this assessment vector fulfils all the bound requirements and has geometrical properties that make it appropriate as a representative assessment vector of the set of feasible weights.     

A robust optimization model for multi-site production planning problem in an uncertain environment

This paper addresses the multi-site production planning problem for a multinational lingerie company in Hong Kong subject to production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers’ preferences, as well as production capacity, workforce level, storage space and resource conditions at the factories. In this paper, a robust optimization model is developed to solve multi-site production planning problem with uncertainty data, in which the total costs consisting of production cost, labor cost, inventory cost, and workforce changing cost are minimized. By adjusting penalty parameters, production management can determine an optimal medium-term production strategy including the production loading plan and workforce level while considering different economic growth scenarios. The robustness and effectiveness of the developed model are demonstrated by numerical results. The trade-off between solution robustness and model robustness is also analyzed.     

On the application of a transportation model for revenue optimization in waste management: a case study

This paper describes an interactive decision support system called Opti-Link which has been developed for a company operating in the area of waste and raw material management. Built around a specific transportation problem, the system is used to maximize the revenue generated by selling waste paper to paper mills. Furthermore, the dual variables of the linear program allow the planner to identify upper bounds for setting bid prices to buy waste paper from waste collection companies. First operational results indicate a significant increase in profit while at the same time the duration of the planning process could be cut by more than half.     

Two algorithms for global optimization

In this paper, we develop and compare two methods for solving the problem of determining the global maximum of a function over a feasible set. The two methods begin with a random sample of points over the feasible set. Both methods then seek to combine these points into “regions of attraction” which represent subsets of the points which will yield the same local maximums when an optimization procedure is applied to points in the subset. The first method for constructing regions of attraction is based on approximating the function by a mixture of normal distributions over the feasible region and the second involves attempts to apply cluster analysis to form regions of attraction. The two methods are then compared on a set of well-known test problems.     

Stochastic preference analysis in numerical preference relations

Numerical preference relations (NPRs) consisting of numerical judgments can be considered as a general form of the existing preference relations, such as multiplicative preference relations (MPRs), fuzzy preference relations (FPRs), interval MPRs (IV-MPRs) and interval FPRs (IV-FPRs). On the basis of NPRs, we develop a stochastic preference analysis (SPA) method to aid the decision makers (DMs) in decision making. The numerical judgments in NPRs can also be characterized by different probability distributions in accordance with practice. By exploring the judgment space of NPRs, SPA produces several outcomes including the rank acceptability index, the expected priority vector, the expected rank and the confidence factor. The outcomes are obtained by Monte Carlo simulation with at least 95% confidence degree. Based on the outcomes, the DMs can choose some of them which they find most useful to make reliable decisions.     

Enhancing PSO methods for global optimization

The Particle Swarm Optimization (PSO) method is a well-established technique for global optimization. During the past years several variations of the original PSO have been proposed in the relevant literature. Because of the increasing necessity in global optimization methods in almost all fields of science there is a great demand for efficient and fast implementations of relative algorithms. In this work we propose three modifications of the original PSO method in order to increase the speed and its efficiency that can be applied independently in almost every PSO variant. These modifications are: (a) a new stopping rule, (b) a similarity check and (c) a conditional application of some local search method. The proposed were tested using three popular PSO variants and a variety test functions. We have found that the application of these modifications resulted in significant gain in speed and efficiency.     

Self-adaptive velocity particle swarm optimization for solving constrained optimization problems

Particle swarm optimization (PSO) is originally developed as an unconstrained optimization technique, therefore lacks an explicit mechanism for handling constraints. When solving constrained optimization problems (COPs) with PSO, the existing research mainly focuses on how to handle constraints, and the impact of constraints on the inherent search mechanism of PSO has been scarcely explored. Motivated by this fact, in this paper we mainly investigate how to utilize the impact of constraints (or the knowledge about the feasible region) to improve the optimization ability of the particles. Based on these investigations, we present a modified PSO, called self-adaptive velocity particle swarm optimization (SAVPSO), for solving COPs. To handle constraints, in SAVPSO we adopt our recently proposed dynamic-objective constraint-handling method (DOCHM), which is essentially a constituent part of the inherent search mechanism of the integrated SAVPSO, i.e., DOCHM + SAVPSO. The performance of the integrated SAVPSO is tested on a well-known benchmark suite and the experimental results show that appropriately utilizing the knowledge about the feasible region can substantially improve the performance of the underlying algorithm in solving COPs.     

The anticipative concept in warehouse optimization using simulation in an uncertain environment

The modern business environment is highly unpredictable. An anticipation approach in a real case study is presented to cope with such instability and minimize the total inventory cost without stock-outs occurring and inventory capacity being exceeded. The anticipation concept is performed using simulation models supported by inventory control algorithms on a selected sample of representative items. The inventory control algorithms include Silver–Meal, Part period balancing, Least-unit cost, and Fuzzy inventory control algorithm based on fuzzy stock-outs, highest inventory level and total cost. Transportation cost is explicitly defined as a discrete function of shipment size. The algorithms are tested on historic data. Simulation results are presented and the risk of accepting them as reliable is discussed. The process of simulation model implementation is briefly discussed to further validate the model and train order managers to use the simulation model in their order placement process.     

Modeling and solution strategies for unconstrained stochastic optimization problems

We review some modeling alternatives for handling risk in decision-making processes for unconstrained stochastic optimization problems. Solution strategies are discussed and compared.Invited lecture at the International Institute on Stochastics and Optimization, Gargnano, Italy, September 1–10, 1982.Supported in part by a Guggenheim Fellowship and a grant of the National Science Foundation.