Maria Elena Bruni

Designing robust emergency medical service via stochastic programming

Abstract This paper addresses the problem of designing robust emergency medical services. Under this respect, the main issue to consider is the inherent uncertainty which characterizes real life situations. Several approaches can be used to design robust mathematical models which are able to hedge uncertain conditions. We are using here the stochastic programming framework and, in particular, the probabilistic paradigm. More specifically, we develop a stochastic programming model with probabilistic constraints aimed to solve both the location and the dimensioning problems, i.e. where service sites must be located and how many emergency vehicles must be assigned to each site, in order to achieve a reliable level of service and minimize the overall costs. In doing so, we consider the randomness of the system as far as the demand of emergency service is concerned. The numerical results, which have been collected on a large set of test problems, demonstrate the validity of the proposed model, particularly in dealing with the trade-off between quality of service and costs management.

A heuristic approach for resource constrained project scheduling with uncertain activity durations

In this paper, we address the resource constrained project scheduling problem with uncertain activity durations. Project activities are assumed to have known deterministic renewable resource requirements and uncertain durations, described by independent random variables with a known probability distribution function. To tackle the problem solution we propose a heuristic method which relies on a stage wise decomposition of the problem and on the use of joint probabilistic constraints.

An exact approach for solving integer problems under probabilistic constraints with random technology matrix

This paper addresses integer programming problems under probabilistic constraints involving discrete distributions. Such problems can be reformulated as large scale integer problems with knapsack constraints. For their solution we propose a specialized Branch and Bound approach where the feasible solutions of the knapsack constraint are used as partitioning rules of the feasible domain. The numerical experience carried out on a set covering problem with random covering matrix shows the validity of the solution approach and the efficiency of the implemented algorithm.

A scheduling methodology for dealing with uncertainty in construction projects

Purpose – The purpose of this paper is to address the problem of scheduling under uncertainty in construction projects. The existing methods for determining a project schedule are based on assumption of complete knowledge of project parameters; but in reality there is uncertainty in construction projects, deriving from a multitude of context‐dependent sources and often provided as outcome of a risk analysis process. Thus, classical deterministic analysis might provide a schedule which is not sufficiently protected against possible disruptions.Design/methodology/approach – A quantitative methodology is developed for planning construction projects under uncertainty aimed at determining a reliable resource feasible project schedule by taking into account the available probabilistic information to produce solutions that are less sensitive to perturbations that occur on line. The methodology relies on a computer‐supported system that allows to identify, analyze and quantify the schedule reliability and the imp...

The stochastic trim-loss problem

The cutting stock problem (CSP) is one of the most fascinating problems in operations research. The problem aims at determining the optimal plan to cut a number of parts of various length from an inventory of standard-size material so to satisfy the customers demands. The deterministic CSP ignores the uncertain nature of the demands thus typically providing recommendations that may result in overproduction or in profit loss. This paper proposes a stochastic version of the CSP which explicitly takes into account uncertainty. Using a scenario-based approach, we develop a two-stage stochastic programming formulation. The highly non-convex nature of the model together with its huge size prevent the application of standard software. We use a solution approach designed to exploit the specific problem structure. Encouraging preliminary computational results are provided.

Capital rationing problems under uncertainty and risk

Capital rationing is a major problem in managerial decision making. The classical mathematical formulation of the problem relies on a multi-dimensional knapsack model with known input parameters. Since capital rationing is carried out in conditions where uncertainty is the rule rather than the exception, the hypothesis of deterministic data limits the applicability of deterministic formulations in real settings. This paper proposes a stochastic version of the capital rationing problem which explicitly accounts for uncertainty. In particular, a mathematical formulation is provided in the framework of stochastic programming with joint probabilistic constraints and a novel solution approach is proposed. The basic model is also extended to include specific risk measures. Preliminary computational results are presented and discussed.

The mixed capacitated general routing problem under uncertainty

We study the General Routing Problem defined on a mixed graph and with stochastic demands. The problem under investigation is aimed at finding the minimum cost set of routes to satisfy a set of clients whose demand is not deterministically known. Since each vehicle has a limited capacity, the demand uncertainty occurring at some clients affects the satisfaction of the capacity constraints, that, hence, become stochastic. The contribution of this paper is twofold: firstly we present a chance-constrained integer programming formulation of the problem for which a deterministic equivalent is derived. The introduction of uncertainty into the problem poses severe computational challenges addressed by the design of a branch-and-cut algorithm, for the exact solution of limited size instances, and of a heuristic solution approach exploring promising parts of the search space. The effectiveness of the solution approaches is shown on a probabilistically constrained version of the benchmark instances proposed in the literature for the mixed capacitated general routing problem.

The Express heuristic for probabilistically constrained integer problems

Integer problems under joint probabilistic constraints with random coefficients in both sides of the constraints are extremely hard from a computational standpoint since two different sources of complexity are merged. The first one is related to the challenging presence of probabilistic constraints which assure the satisfaction of the stochastic constraints with a given probability, whereas the second one is due to the integer nature of the decision variables. In this paper we present a tailored heuristic approach based on alternating phases of exploration and feasibility repairing which we call Express (Explore and Repair Stochastic Solution) heuristic. The exploration is carried out by the iterative solution of simplified reduced integer problems in which probabilistic constraints are discarded and deterministic additional constraints are adjoined. Feasibility is restored through a penalty approach. Computational results, collected on a probabilistically constrained version of the classical 0–1 multiknapsack problem, show that the proposed heuristic is able to determine good quality solutions in a limited amount of time.

A HYBRID GREEDY RANDOMIZED ADAPTIVE SEARCH HEURISTIC TO SOLVE THE DIAL-A-RIDE PROBLEM

This paper presents a hybrid metaheuristic for solving the static dial-a-ride problem with heterogeneous vehicles and fixed costs. The hybridization combines a reactive greedy randomized adaptive search, used as outer scheme, with a tabu search heuristic in the local search phase. The algorithm is evaluated on well-known instances taken from the literature and on a set of randomly generated test problems, varying in the number of customers. Extensive computational results show the effectiveness of the hybrid approach in terms of trade-off between solution quality and computational time.

Using DEA and financial ratings for credit risk evaluation: an empirical analysis

The article deals with the methodologies for credit risk evaluation. It describes an empirical analysis carried out on a sample of Italian firms belonging to the leather manufacturing and wholesale industry. The study uses the efficiency, calculated through data envelopment analysis (DEA), and the credit rating at the same time. As long as efficiency is calculated by using inputs and outputs strictly linked to the credit reliability of the firm, the study confirms that there is a relationship between efficiency and credit rating, and then that efficiency can be considered as an early warning index for evaluating credit risk.