# Francisco Saldanha-da-GamaUniversity of Lisbon | UL · Faculty of Science

Francisco Saldanha-da-Gama

PhD in Statistics and Operations Research

Professor of Operations Research, Faculty of Science, University of Lisbon

## About

80

Publications

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4,810

Citations

Citations since 2016

## Publications

Publications (80)

This article aims at contributing to the celebration of the 25th Anniversary of Transportation Research Part E: Logistics and Transportation Review (TRE). It provides an overview of the role of Facility Location in Logistics and Transportation highlighting the contribution of TRE to such an enduring relationship. Several conventional problems are r...

This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different normed spaces are simultaneously decided to maximize the demand generated by a set of points. From the need of intertwining location decisions in discrete and in continuous sets, a general hybridized...

In this work a districting problem with stochastic demand is investigated. Chance-constraints are used to model the balancing requirements. Explicit contiguity constraints are also considered. After motivating the problem and discussing several modeling aspects, an approximate deterministic counterpart is proposed which is the core of new solution...

This work focuses on a broad class of facility location problems in the context of adaptive robust stochastic optimization under the state-dependent demand uncertainty. The demand is assumed to be significantly affected by related state information, such as the seasonal or socio-economic information. In particular, a state-wise ambiguity set is ado...

This work provides new insights on bi-criteria resource-constrained project scheduling problems. We define a realistic problem where the objectives to combine are the makespan and the total cost for resource usage. Time-dependent costs are assumed for the resources, i.e., they depend on when a resource is used. An optimization model is presented an...

In this work different repositioning rules are investigated and compared in the context of free-floating bike-sharing systems. A static complete reposition setting is adopted, i.e., the system is operated (re-balanced) when the number of users riding bicycles can be neglected as it happens in many cities, for instance during the night. The popular...

This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different metric spaces are simultaneously decided to maximize the demand generated by a set of points. From the need of intertwining location decisions in discrete and in continuous sets, a general hybridized...

This work focuses on the optimization of a last-mile delivery system with multiple transportation modes. In this scenario, parcels need to be delivered to each customer point. The major feature of the problem is the combination of a fleet of road vehicles (vans) with a drone. Each van visits a subset of demand nodes to be determined according to th...

In this paper, a comprehensive production planning problem under uncertain demand is investigated. The problem intertwines two NP-hard optimization problems: an assembly line balancing problem and a capacitated lot-sizing problem. The problem is modelled as a two-stage stochastic program assuming a risk-averse decision maker. Efficient solution pro...

In an assembly line system, the production process may suffer a sudden disruption, and this may call for rebalancing. In this paper, the assembly line rebalancing problem is set in a multiperiod context considering stochastic processing times. It is assumed that there are specific moments in time chosen for rebalancing the line (if necessary). Two...

In this paper, a districting problem with stochastic demands is investigated. The goal is to divide a geographic area into p contiguous districts such that, with some given probability, the districts are balanced with respect to some given lower and upper thresholds. The problem is cast as a p-median problem with contiguity constraints that is furt...

This paper provides a comprehensive review of the research done on facility location problems under uncertainty in a humanitarian context. The major goal is to summarize and help structuring this topic, which has increasingly attracted the attention of the scientific community. The literature is reviewed from different perspectives namely, in terms...

In this paper a stochastic districting problem is investigated. Demand is assumed to be represented by a random vector with a given joint probability distribution function. A two-stage mixed-integer stochastic programming model is proposed. The first stage comprises the decision about the initial territory design: the districts are defined and all...

Third authors’ name should appear as: Francisco Saldanha-da-Gama.

This paper explores the concept of capacity transfer in the context of capacitated facility location problems. This is accomplished by assuming that facilities with surplus capacity/production can cooperate with those facing shortage by transferring part of that capacity/production. Such a transfer incurs a cost that nonetheless may be compensated...

This paper studies the location-routing problem of big event logistics. We propose a mathematical model framework, which considers many aspects of logistics network design for big event, some of which have not received enough attention in the literature. Aspects to be considered include: multi-commodity, perishability of goods, combined storage str...

In this work, we propose a heuristic procedure for a stochastic version of the uncapacitated r-allocation p-hub median problem with nonstop services. In particular, we assume that the number of hubs to which a terminal can be allocated is bounded from above by r. Additionally, we consider the possibility of shipping traffic directly between termina...

This work focuses on a broad class of uncapacitated p-hub median problems that includes non-stop services and setup costs for the network structures. In order to capture both the single and the multiple allocation patterns as well as any intermediate case of interest, we consider the so-called r-allocation pattern with r denoting the maximum number...

This paper introduces a new algorithmic scheme for two-stage stochastic mixed-integer programming assuming a risk averse decision maker. The focus is the minimization of the conditional value at risk for a hard combinatorial optimization problem. Some properties of a mixed-integer non-linear programming formulation for conditional value at risk are...

This chapter covers different aspects related with facility location problems involving time-dependent parameters. The emphasis is put on problems defined over a multi-period finite planning horizon. An overview of continuous and network problems is presented, although most of the chapter focuses on a discrete setting. Basic modeling aspects and so...

This chapter introduces modern Location Science. It traces the roots of the area and describes the path leading to the full establishment of this research field. It identifies several disciplines having strong links with Location Science and offers examples of areas in which the knowledge accumulated in the field of location has been applied with g...

This chapter covers some of the existing knowledge on facility location under uncertainty. The goal is to provide the reader with essential tools for modeling and tackling problems in the area. To a large extent, the focus is put on discrete facility location problems. Several issues related with uncertainty are discussed. A distinction is made bet...

This book presents essential information on modern location science – in a word, all you need to know about location. The second edition of this handbook has been fully revised throughout, with numerous updates and chapters added, to offer an even more comprehensive overview of methods and applications.
The book is divided into three parts: basic c...

In this work we propose a heuristic procedure for a stochastic version of the Unca-pacitated r-Allocation p-Hub Median Problem with non-stop services. In particular, we assume that the number of hubs to which a terminal can be allocated is bounded from above by r. Additionally, we consider the possibility of shipping traffic directly between termin...

This work focuses on a broad class of uncapacitated p-hub median problems that includes non-stop services and setup costs for the network structures. In order to capture both the single and the multiple allocation patterns as well as any intermediate case of interest, we consider the so-called r-allocation pattern with r denoting the maximum number...

In this paper, we study and compare several integer and mixed‐integer linear programming formulations for the multiskill resource‐constrained project scheduling problem. This is a problem characterized by a set of activities to be executed that in addition to the usual precedence constraints require several resources for each skill needed for their...

In this paper, we investigate a resource-constrained project scheduling problem with flexible resources. This is an \(\mathcal {NP}\)-hard combinatorial optimization problem that consists of scheduling a set of activities requiring specific resource units of several skills. The goal is to minimize the makespan of the project. We propose a biased ra...

In this work, we develop and test a new modeling framework for the shelter site location problem under demand uncertainty. In particular, we propose a maxmin probabilistic programming model that includes two types of probabilistic constraints: one concerning the utilization rate of the selected shelters and the other concerning the capacity of thos...

This work aims at investigating multi-criteria modeling frameworks for discrete stochastic facility location problems with single sourcing. We assume that demand is stochastic and also that a service level is imposed. This situation is modeled using a set of probabilistic constraints. We also consider a minimum throughput at the facilities to justi...

This paper introduces a very general discrete covering location model that accounts for uncertainty and time-dependent aspects. A MILP formulation is proposed for the problem. Afterwards, it is observed that most of the models existing in the literature related with covering location can be considered as particular cases of this formulation. In ord...

In this paper, a heuristic procedure is proposed for the facility location problem with general Bernoulli demands. This is a discrete facility location problem with stochastic demands that can be formulated as a two-stage stochastic program with recourse. In particular, facility locations and customer assignments must be decided here and now, i.e.,...

In this paper, we present a modeling framework for hub location problems with a service time limit considering congestion at hubs. Service time is modeled taking the traveling time on the hub network as well as the handling time and the delay caused by congestion at hubs into account. We develop mixed-integer linear programming formulations for the...

This study focus of the development of a modeling framework for multi-period stochastic capacitated multiple allocation hub location problems. We consider a planning horizon divided into several time periods. Uncertainty is assumed for the demands. The decisions to make concern the location of the hubs, their initial capacity, the capacity expansio...

We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited...

Operations Researchers support Supply Chain Management and Supply Chain Planning by developing adequate mathematical optimization models and providing suitable solution procedures. In this paper we discuss what . adequate could mean. Therefore, we may ask several questions concerning "optimality" in Supply Chain Planning under causal and temporal u...

In this work we propose a heuristic procedure for a stochastic version of the Uncapacitated r-Allocation p-Hub Median Problem with non-stop services. In particular, we assume that the number of hubs to which a terminal can be allocated, is bounded from above by r. Additionally we consider the possibility of shipping traffic directly between termina...

In this paper we investigate one of the most recent extensions of the Resource Constrained Project Scheduling Problem (RCPSP): the Multi-Skill Resource Constrained Project Scheduling Problem (MSRCPSP). For this complex problem we propose the use of a parallel scheduling scheme. Such scheme has been successfully applied to the RCPSP. Nevertheless, i...

In this paper, we investigate the problem of choosing the location and number of ambulances and their bases in a certain region. The goal is to minimize the total cost for installing (and maintaining) these facilities but assuring a minimum coverage level. Demand is assumed to be stochastic. A scenario-indexed formulation is considered for the prob...

In this paper, a modeling framework is proposed for multi-period hub location. The problems to be studied are extensions of classical hub location problems to the situation in which the hub network can be progressively built and its capacity gradually expanded over time. Both the single allocation and the multiple allocation cases are considered. F...

In this chapter, we cover basic aspects related with facility location problems involving time dependent parameters. The emphasis is put on problems defined over a multi-period finite planning horizon. A brief overview of continuous and network problems is presented. Nevertheless, most of the chapter focus on a discrete setting. Basic modeling aspe...

In this chapter, we cover some essential knowledge on facility location under uncertainty. We put a major emphasis on modeling aspects related with discrete facility location problems. Different modeling frameworks are discussed. In particular, we distinguish between robust optimization, stochastic programming and chance-constrained models. We also...

This chapter introduces modern Location Science. It traces the roots of the area and describes the path leading to the full establishment of this research field. It identifies several disciplines having strong links with Location Science and offers examples of areas in which the knowledge accumulated in the field of location has been applied with g...

This chapter addresses modeling issues associated with project staffing and scheduling problems. Emphasis is given to mixed-integer linear programming formulations. The need for such formulations is motivated and a general modeling framework is introduced, which captures many features that have been considered in the literature on project staffing...

Multi-skill Resource-Constrained Project Scheduling Problems consist of an extension of resource-constrained project scheduling problems in which resources are assumed to be flexible or, as they are more commonly referred to in the literature, multi-skilled. In many project scheduling problems that we find in the real world, resources can often mas...

In this paper, a transportation problem comprising stochastic demands, fixed handling costs at the origins, and fixed costs associated with the links is addressed. It is assumed that uncertainty is adequately captured via a finite set of scenarios. The problem is formulated as a two-stage stochastic program. The goal is to minimize the total cost a...

In a recent paper published in Optimization Letters, Montoya et al. (Optim Lett 8:1721–1734, 2014) proposed a branch-and-price approach for a multi-skill project scheduling problem. In that paper, an integer linear programming formulation was first introduced which, unfortunately, has a number of inconsistences. At the interest of mathematical rigo...

In this paper, we address a cost-oriented multi-skill project scheduling problem. The project consists on a set of activities such that, for some pairs, a start-to-start time dependency exists. The execution of each activity requires several skills. More than one resource of each skill may be required for processing an activity. A pull of multi-ski...

In this paper we extend the classical capacitated single-allocation hub location problem by considering that multiple products are to be shipped through the network. We propose a unified modeling framework for the situation in which no more than one hub can be located in each node. In particular, we consider the case in which all hubs are dedicated...

This paper addresses a new problem to design a two-echelon supply chain network over a multi-period horizon. Strategic decisions are subject to a given budget and concern the location of new facilities in the upper and intermediate echelons of the network as well as the installation of storage areas to handle different product families. A finite se...

Scheduling problems received substantial attention during the last decennia. The job-shop problem is a very important scheduling problem, which is NP-hard in the strong sense and with well-known benchmark instances of relatively small size which attest the practical difficulty in solving it. The literature on the job-shop scheduling problem include...

In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the in...

The configuration of the reverse logistics network is a complex problem comprising the determination of the optimal sites and capacities of collection centers, inspection centers, remanufacturing facilities, and/or recycling plants. In this paper, we propose a profit maximization modeling framework for reverse logistics network design problems. We...

In this paper, we study a variant of the resource-constrained project scheduling problem in which resources are flexible,
i.e., each resource has several skills. Each activity in the project may need several resources for each required skill. We
present a mixed-integer linear programming formulation for this problem. Several sets of additional ineq...

This paper addresses the problem of redesigning a supply chain network with multiple echelons and commodities. The problem belongs to a comprehensive class of network redesign problems previously introduced in the literature. Redesign decisions comprise the relocation of existing facilities to new sites under an available budget over a finite time...

In this paper, an extension of the capacitated single-allocation hub location problem is considered in which the capacity of the hubs is part of the decision making process and balancing requirements are imposed on the network. The decisions to be made comprise (i) the selection of the hubs, (ii) the allocation of the spoke nodes to the hubs, (iii)...

This paper presents the facility location problem with Bernoulli demands. In this capacitated discrete location stochastic problem the goal is to define an a priori solution for the locations of the facilities and for the allocation of customers to the operating facilities that minimizes the sum of the fixed costs of the open facilities plus the ex...

In this paper, a multi-period logistics network redesign problem arising in the context of strategic supply chain planning
is studied. Several aspects of practical relevance are captured, namely, multiple echelons with different types of facilities,
product flows between facilities in the same echelon, direct shipments to customers, and facility re...

In this paper a well-known formulation for the capacitated single-allocation hub loca- tion problem is revisited. An example is presented showing that for some instances this formulation is incomplete. The reasons for the incompleteness are identifled leading to the inclusion of an additional set of constraints. Computational experiments are perfor...

In this paper, an extension of the classical capacitated single-allocation hub location problem is studied in which the size of the hubs is part of the decision making process. For each potential hub a set of capacities is assumed to be available among which one can be chosen. Several formulations are proposed for the problem, which are compared in...

In this paper we propose a comprehensive model for reverse logistics planning where many real-world features are considered
such as the existence of several facility echelons, multiple commodities, choice of technology and stochasticity associated
with transportation costs and waste generation. Moreover, we adopt a bi-objective model for the proble...

In this paper we study a discretization reformulation technique in the context of a facility location problem with modular link costs. We present a so-called 'traditional' model and a straightforward discretized model with a general objective function whose variable coefficients are computed by solving a simple knapsack problem. We show that the li...

Facility location decisions play a critical role in the strategic design of supply chain networks. In this paper, a literature review of facility location models in the context of supply chain management is given. We identify basic features that such models must capture to support decision-making involved in strategic supply chain planning. In part...

The choice of an appropriate social rate of discount is critical in the decision-making process on public investments. In this paper we review the literature on social discounting, and address in particular a recently growing field of related research, that is, individual time preferences. We argue that an explicit consideration and analysis of the...

In any large organization, it is essential to have mechanisms that ensure
constant operation. This is the reality faced everyday by the large logistics companies operating worldwide. When there is an unexpected disruption, an appropriate contingency plan can make a huge difference. The definition of an optimal contingency plan is a complex problem...

In this paper we study the Variable Size Bin Packing Problem (VSBPP) which is a generalization of the Bin Packing Problem where bins of different capacities (and different costs) are available for packing a set of items. The objective is to pack all the items minimizing the total cost associated with the bins. We discuss applications of the VSBPP a...

Structuring global supply chain networks is a complex decision-making process. The typical inputs to such a process consist of a set of customer zones to serve, a set of products to be manufactured and distributed, demand projections for the different customer zones, and information about future conditions, costs (e.g.
for production and transporta...

Facility location decisions play a critical role in the strategic design of supply chain networks. In this paper, an extensive literature review of facility location models in the context of supply chain management is given. Following a brief review of core models in facility location, we identify basic features that such models must capture to sup...

In this paper, we present and discuss a discretized model for the two versions of the capacitated concentrator location problem: a simple version (SCCLP) and a version with modular capacities (MCCLP). We show that the linear programming relaxation of the discretized model is at least as good as the linear programming relaxation of conventional mode...

In this paper, we focus on the strategic design of supply chain networks. We propose a mathematical modeling framework that captures many practical aspects of network design problems simultaneously but which have not received adequate attention in the literature. The aspects considered include: dynamic planning horizon, generic supply chain network...

We propose a mathematical modeling framework for supply chain network design which captures many aspects of practical problems that have not received adequate attention in the literature. The aspects considered include: dynamic planning horizon, generic supply chain structure, inventory and distribution opportunities for goods, facility configurati...

We consider a dynamic capacitated facility location problem. Given a set of cus- tomers with known demands for a single product, a set of facilities operating at the beginning of the planning horizon, and a set of potential sites to locate new facilities, the objective is to find the location-allocation plan that minimizes the overall costs and sat...

In this paper a two-phase heuristic approach for the discrete dynamic location problem with establishment and removal costs is presented. The first phase consists of a drop procedure. In the second phase, a local search is performed as an attempt to correct bad decisions that might have been made. Computational tests with random generated data are...

In this paper we present a discretization reformulation technique in the context of a facility location problem with modular link costs. We present a 'traditional' model and a straightforward discretized model with a general objective function. The linear relaxation bounds provided by both formulations are compared. Furthermore, we state that a res...

Se presenta un modelo estocástico bietapa con dos criteros (coste, efecto obnoxio) para el diseño de una red de recogida de residuos.

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