The control of critical pollutant events has become one of the most relevant problems that the Lo... more The control of critical pollutant events has become one of the most relevant problems that the Local Authorities need to manage, in order to limit population exposure to high pollutant levels. The problem of the selection of suitable short terms plans allowing to maintain the pollutant concentrations under a certain threshold is particularly difficult due to the strong nonlinearity and due to the high number of parameters (sometimes not manageable, as in the case of meteorological conditions) that can affect the concentrations at a certain time. In order to help Local Authorities in taking these decision, suitable Integrated assessment Models (IAMs) have to be formalized and implemented. In this work, the formalization and implementation of an IAM for the selecting of short-term actions is presented. The system is based on a forecasting phase and on a receding horizon approach for the selection of suitable emission control actions. The system has been applied with encouraging results to the management of PM10 levels over a domain including the metropolitan area of the city of Brescia in Lombardy.
Hybridizing adaptive large neighborhood search with kernel search: a new solution approach for the nurse routing problem with incompatible services and minimum demand
International Transactions in Operational Research, 2022
In the multidimensional multiple choice knapsack problem (MMKP), items with nonnegative profits a... more In the multidimensional multiple choice knapsack problem (MMKP), items with nonnegative profits are partitioned into groups. Each item consumes a predefined nonnegative amount of a set of resources...
In recent years, large public hospitals have undergone a strong growth in healthcare services dem... more In recent years, large public hospitals have undergone a strong growth in healthcare services demand, not offset by resources increase. In this context, one of the most critical issues is the optimization of human resources. In this paper, we study the problem of finding the optimal assignment of tasks to physicians over a predefined time horizon in a large general surgery ward. Each task has to be executed by one or more physicians and assigned to one or more time slots in different days. Each physician has a minimum number of hours to work per week. The hours exceeding such a value constitute overtime. The problem minimizes the total time spent by all the physicians (and thus the global overtime) in the hospital to complete the execution of the assigned tasks, while complying with practical and legislative constraints. We propose two mathematical formulations for the problem and exploit both of them to develop repair heuristics of an Adaptive Large Neighborhood Search. A simple matheuristic is used to identify an initial feasible solution within a reasonable amount of time. To test algorithms, we have generated several classes of instances directly inspired by the studied real case. The performance of our solution approach (when setting a time limit of 15 min) has been compared to the results obtained by Gurobi 6.5.1 (with 1 h time limit) when solving both formulations. We show that our algorithm is extremely effective by frequently getting better solutions than Gurobi in a quarter of its computational time.
Introduction In recent times combinatorial auctions have become an interesting domain for theoret... more Introduction In recent times combinatorial auctions have become an interesting domain for theoretical and applied developments of the electronic market technology. A combinatorial auction allows the simultaneous selling of several items and each participant to the auction may bid for bundles of items. When items in a bid are all di#erent the auction is said a Single Unit Combinatorial Auction (SUCA), while when a bid may specify a number of units of a given item we call it a Multi-Unit Combinatorial Auction (MUCA). The bid taker's objective is to find that set of bids which maximizes his total revenue. It has been shown that the problem, known as Winner Determination Problem, also for the special case in which each item is available in single units, is NP-hard ([4]). Up to now the bulk of research work on this subject has been focused on SUCA while a limited number of papers are available on the problem of Winner Determination in a MUCA (see, for instance, [2], [3] and [5]). Fo...
The Markowitz model of portfolio optimization quantifies the problem in a lucid form of only two ... more The Markowitz model of portfolio optimization quantifies the problem in a lucid form of only two criteria: the mean, representing the expected outcome, and the risk, a scalar measure of the variability of outcomes. The classical Markowitz model uses the variance as the risk measure, thus resulting in a quadratic optimization problem. Following Sharpe’s work on linear approximation to the mean–variance model, many attempts have been made to linearize the portfolio optimization problem. There were introduced several alternative risk measures which are computationally attractive as (for discrete random variables) they result in solving linear programming (LP) problems. The LP solvability is very important for applications to real-life financial decisions where the constructed portfolios have to meet numerous side constraints and take into account transaction costs. The variety of LP solvable portfolio optimization models presented in the literature generates a need for their classifica...
Asset-Backed Securitization (ABS) is a well-stated financial mechanism which allows an institutio... more Asset-Backed Securitization (ABS) is a well-stated financial mechanism which allows an institution (either a commercial bank or a firm) to get funds through the conversion of assets into capital market products called notes or asset-backed securities. In this paper, we analyze the combinatorial problem faced by the financial institution which has to optimally select the set of assets to be converted into notes. We assume that assets follow an amortization rule characterized by constant periodic principal installments (Italian amortization). The particular shape of the assets outstanding principal is exploited both in the mathematical formulation of the problem and in its solution. In particular, we study a model formulation for the special case where assets selection occurs at two dates during the securitization process. We introduce two heuristic approaches based on Lagrangian relaxation and analyze their worst-case behavior compared to the optimal solution value. The performance o...
We study a variant of the Nurse Routing Problem where each patient may require more than one serv... more We study a variant of the Nurse Routing Problem where each patient may require more than one service at possible different times during the day. Each executed service yields a profit, and an additional reward is gained if all services associated with a patient are fulfilled. The problem looks for nurse routes, each one not exceeding a predefined working time limit, that maximize the global collected service profits plus the patient rewards, while respecting the time windows associated with services. We first provide a compact Mixed-Integer Linear Programming formulation for the problem. Then, we develop an Iterative Kernel Search to solve the problem heuristically. Finally, we compare the heuristic performance on several instances with that of the plain model solved through a state-of-the-art exact solver and strengthened by the separation of valid inequalities. The obtained results clearly show that our heuristic algorithm finds fairly good solutions in terms of quality, despite the use of shorter computational times.
The control of critical pollutant events has become one of the most relevant problems that the Lo... more The control of critical pollutant events has become one of the most relevant problems that the Local Authorities need to manage, in order to limit population exposure to high pollutant levels. The problem of the selection of suitable short terms plans allowing to maintain the pollutant concentrations under a certain threshold is particularly difficult due to the strong nonlinearity and due to the high number of parameters (sometimes not manageable, as in the case of meteorological conditions) that can affect the concentrations at a certain time. In order to help Local Authorities in taking these decision, suitable Integrated assessment Models (IAMs) have to be formalized and implemented. In this work, the formalization and implementation of an IAM for the selecting of short-term actions is presented. The system is based on a forecasting phase and on a receding horizon approach for the selection of suitable emission control actions. The system has been applied with encouraging results to the management of PM10 levels over a domain including the metropolitan area of the city of Brescia in Lombardy.
Hybridizing adaptive large neighborhood search with kernel search: a new solution approach for the nurse routing problem with incompatible services and minimum demand
International Transactions in Operational Research, 2022
In the multidimensional multiple choice knapsack problem (MMKP), items with nonnegative profits a... more In the multidimensional multiple choice knapsack problem (MMKP), items with nonnegative profits are partitioned into groups. Each item consumes a predefined nonnegative amount of a set of resources...
In recent years, large public hospitals have undergone a strong growth in healthcare services dem... more In recent years, large public hospitals have undergone a strong growth in healthcare services demand, not offset by resources increase. In this context, one of the most critical issues is the optimization of human resources. In this paper, we study the problem of finding the optimal assignment of tasks to physicians over a predefined time horizon in a large general surgery ward. Each task has to be executed by one or more physicians and assigned to one or more time slots in different days. Each physician has a minimum number of hours to work per week. The hours exceeding such a value constitute overtime. The problem minimizes the total time spent by all the physicians (and thus the global overtime) in the hospital to complete the execution of the assigned tasks, while complying with practical and legislative constraints. We propose two mathematical formulations for the problem and exploit both of them to develop repair heuristics of an Adaptive Large Neighborhood Search. A simple matheuristic is used to identify an initial feasible solution within a reasonable amount of time. To test algorithms, we have generated several classes of instances directly inspired by the studied real case. The performance of our solution approach (when setting a time limit of 15 min) has been compared to the results obtained by Gurobi 6.5.1 (with 1 h time limit) when solving both formulations. We show that our algorithm is extremely effective by frequently getting better solutions than Gurobi in a quarter of its computational time.
Introduction In recent times combinatorial auctions have become an interesting domain for theoret... more Introduction In recent times combinatorial auctions have become an interesting domain for theoretical and applied developments of the electronic market technology. A combinatorial auction allows the simultaneous selling of several items and each participant to the auction may bid for bundles of items. When items in a bid are all di#erent the auction is said a Single Unit Combinatorial Auction (SUCA), while when a bid may specify a number of units of a given item we call it a Multi-Unit Combinatorial Auction (MUCA). The bid taker's objective is to find that set of bids which maximizes his total revenue. It has been shown that the problem, known as Winner Determination Problem, also for the special case in which each item is available in single units, is NP-hard ([4]). Up to now the bulk of research work on this subject has been focused on SUCA while a limited number of papers are available on the problem of Winner Determination in a MUCA (see, for instance, [2], [3] and [5]). Fo...
The Markowitz model of portfolio optimization quantifies the problem in a lucid form of only two ... more The Markowitz model of portfolio optimization quantifies the problem in a lucid form of only two criteria: the mean, representing the expected outcome, and the risk, a scalar measure of the variability of outcomes. The classical Markowitz model uses the variance as the risk measure, thus resulting in a quadratic optimization problem. Following Sharpe’s work on linear approximation to the mean–variance model, many attempts have been made to linearize the portfolio optimization problem. There were introduced several alternative risk measures which are computationally attractive as (for discrete random variables) they result in solving linear programming (LP) problems. The LP solvability is very important for applications to real-life financial decisions where the constructed portfolios have to meet numerous side constraints and take into account transaction costs. The variety of LP solvable portfolio optimization models presented in the literature generates a need for their classifica...
Asset-Backed Securitization (ABS) is a well-stated financial mechanism which allows an institutio... more Asset-Backed Securitization (ABS) is a well-stated financial mechanism which allows an institution (either a commercial bank or a firm) to get funds through the conversion of assets into capital market products called notes or asset-backed securities. In this paper, we analyze the combinatorial problem faced by the financial institution which has to optimally select the set of assets to be converted into notes. We assume that assets follow an amortization rule characterized by constant periodic principal installments (Italian amortization). The particular shape of the assets outstanding principal is exploited both in the mathematical formulation of the problem and in its solution. In particular, we study a model formulation for the special case where assets selection occurs at two dates during the securitization process. We introduce two heuristic approaches based on Lagrangian relaxation and analyze their worst-case behavior compared to the optimal solution value. The performance o...
We study a variant of the Nurse Routing Problem where each patient may require more than one serv... more We study a variant of the Nurse Routing Problem where each patient may require more than one service at possible different times during the day. Each executed service yields a profit, and an additional reward is gained if all services associated with a patient are fulfilled. The problem looks for nurse routes, each one not exceeding a predefined working time limit, that maximize the global collected service profits plus the patient rewards, while respecting the time windows associated with services. We first provide a compact Mixed-Integer Linear Programming formulation for the problem. Then, we develop an Iterative Kernel Search to solve the problem heuristically. Finally, we compare the heuristic performance on several instances with that of the plain model solved through a state-of-the-art exact solver and strengthened by the separation of valid inequalities. The obtained results clearly show that our heuristic algorithm finds fairly good solutions in terms of quality, despite the use of shorter computational times.
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Papers by Renata Mansini