European Journal of Operational Research, Oct 1, 2005
This paper describes the problem of managing a fleet of load-haul-dump (LHD) vehicles in an under... more This paper describes the problem of managing a fleet of load-haul-dump (LHD) vehicles in an underground mine. The problem consists of dispatching, routing and scheduling vehicles whenever they need to be assigned to a new task. The solution approach is based on a shortest-path algorithm. Each decision takes into account the current status of the mine, the current traffic on all single-lane bi-directional road segments of the haulage network and operational constraints such as the fact that, while LHD vehicles move in forward or reverse modes, their bucket must be in dumping/ loading position at destination.
This paper presents an enumeration algorithm based on dynamic programming for optimally solving t... more This paper presents an enumeration algorithm based on dynamic programming for optimally solving the fleet management problem in underground mines. This problem consists of routing and scheduling bidirectional vehicles on a haulage network composed of one-lane bidirectional road segments. The method takes into account the displacement modes of the vehicles, either forward or in reverse, and makes sure that these vehicles move forward when they arrive at their service point. The method has been developed for the underground mine context, but it can be extended to the industrial environment.
La collection Les Cahiers du GERAD est constituée des travaux de recherche menés par nos membres.... more La collection Les Cahiers du GERAD est constituée des travaux de recherche menés par nos membres. La plupart de ces documents de travail aété soumisà des revues avec comité de révision. Lorsqu'un document est accepté et publié, le pdf original est retiré si c'est nécessaire et un lien vers l'article publié est ajouté.
This paper proposes a new approach to the mining exploration drillholes positioning problem (DPP)... more This paper proposes a new approach to the mining exploration drillholes positioning problem (DPP) that incorporates both geostatistical and optimization techniques. A metaheuristic was developed to solve the DPP taking into account an uncertainty index that quantifies the reliability of the current interpretation of the mineral deposit. The uncertainty index was calculated from multiple deposit realizations obtained by truncated Gaussian simulations conditional to the available drillholes samplings. A linear programming model was defined to select the subset of future drillholes that maximizes coverage of the uncertainty. A Tabu Search algorithm was developed to solve large instances of this set partitioning problem. The proposed Tabu Search algorithm is shown to provide good quality solutions approaching 95% of the optimal solution in a reasonable computing time, allowing close to optimal coverage of uncertainty for a fixed investment in drilling.
This paper introduces the first exact approach for constructing aircrew member personalized month... more This paper introduces the first exact approach for constructing aircrew member personalized monthly work schedules when a preferential bidding system (PBS) is used. With such a system, each employee bids for his/her preferred activities, yielding a bidding score for each feasible schedule. The PBS problem thus consists of assigning to each employee a schedule that maximizes his/her preferences, in order of seniority, while covering all crew pairings. The proposed exact solution approach relies on column generation, and when a tentative maximum score for a crew member is established, it explicitly enumerates for that employee all feasible schedules with that score. Tests on real-life cases show that this approach can substantially improve the quality of the solutions produced by the best known existing method in similar computational times.
This paper presents a prototype method for optimally solving the rostering problem, i.e., constru... more This paper presents a prototype method for optimally solving the rostering problem, i.e., constructing work schedules for airline crew members. The main goal is to show the possibilities of solving the rostering problem using optimal methods. The prototype uses a column generation approach embedded in a branch and bound algorithm to solve the rostering problem. To the knowledge of the
Scheduling activities in an underground mine is a very complex task. Precedence relations, the gr... more Scheduling activities in an underground mine is a very complex task. Precedence relations, the great number of resources and the large number of work sites are some of the reasons for this complexity. This paper presents an optimization model for short-term planning that takes into consideration all parts of the development and production as well as specific limitations on equipment and workers. A preemptive mixed integer program is used in order to produce optimal planning over a short-term time horizon. Multiple tests made with various data sets and scenarios are then presented, including a comparison to a non-preemptive model and a case study.
ABSTRACT This paper presents two solution approaches for taking into account the displacement mod... more ABSTRACT This paper presents two solution approaches for taking into account the displacement mode (forward or in reverse) of vehicles during the solution of the shortest path problem. In the first approach, a graph including all aspects of the problem is constructed and a classical shortest path algorithm is used to solve the problem. In the second approach, a more simple graph is constructed, and all the constraints of the problem are considered during the solution of the shortest path problem. This problem is important for routing a fleet of automated vehicles on a one-lane bidirectional graph.
Scheduling activities in an underground mine is a very complex task. This paper presents an optim... more Scheduling activities in an underground mine is a very complex task. This paper presents an optimization model for short-term planning that takes into consideration all parts of the development and production as well as specific limitations on equipment and workers. To do so, a mix integer program is used in order to maximize mined tonnage on a given time horizon. Test results of the application to a mine are presented to confirm the model accuracy and solvability.
This paper presents a framework for the use of unmanned aerial vehicles (UAVs) equipped with came... more This paper presents a framework for the use of unmanned aerial vehicles (UAVs) equipped with cameras and wireless sensors to search an area after the occurrence of a tornado. This paper attempts to demonstrate how tornado weather data can be incorporated into search and rescue procedures to allocate and route the UAVs. Traditionally, the time to assess and search an area after a tornado strikes is on the order of several days. Incorporating UAVs into a search and rescue team’s available tools can reduce this time span to the order of hours. These methods are applied and model in this project to three real-world cases. Several methods for creating ”waypoints,” points of interest for the UAVs to inspect, to route the UAVs were tested. An analysis was performed to compare the time it took to generate the waypoints and the resulting objective function value. It is observed that while there is an opportunity to use exact methods to generate waypoints, our proposed heuristic is sufficient for the rapid response needed in post-disaster relief.
This paper presents a new branching strategy that is applied on the cost of a subproblem during t... more This paper presents a new branching strategy that is applied on the cost of a subproblem during the solution of a large-scale linear program by a column generation technique. This branch and cut strategy has been used to improve the solution time for the preferential bidding problems encountered in the airline industry. Moreover, it is shown that this strategy can also be applied to other problems with particular structures.
International Journal of Production Research, Mar 15, 2005
This paper presents two solution approaches for taking into account the displacement mode (forwar... more This paper presents two solution approaches for taking into account the displacement mode (forward or in reverse) of vehicles during the solution of the shortest path problem. In the first approach, a graph including all aspects of the problem is constructed and a classical shortest path algorithm is used to solve the problem. In the second approach, a more simple graph is constructed, and all the constraints of the problem are considered during the solution of the shortest path problem. This problem is important for routing a fleet of automated vehicles on a one-lane bidirectional graph.
International Journal of Mining, Reclamation and Environment, Feb 15, 2022
ABSTRACT This article describes a new model aiming at optimising short- and medium-term undergrou... more ABSTRACT This article describes a new model aiming at optimising short- and medium-term underground mine scheduling. The problem complexity and the frequency at which planners must revise these schedules are among the primary motivations for developing such a model. To address this problem, a Mixed Integer Programming model is proposed with a flexible time discretisation to accurately represent both shortand medium-term operational constraints in a single model. The results of a preliminary mathematical formulation are presented with in-depth analyses. Further, an improved formulation is presented with associated results and benefits. Extensive experiments with scenarios similar to long-term planning show promising results for the improved formulation. Among other things, these results show that the modified formulation makes it possible to solve for scenarios that include a large number of activities and locations while generating more applicable solutions.
We present a mixed-integer programming model for solving the long-term planning problem of an und... more We present a mixed-integer programming model for solving the long-term planning problem of an underground mine. This model, which establishes the sequence of mining for a horizon of 20 years, determines which lens of the geological model will be mined and in what order, while respecting the operational constraints. For each lens to be mined, a specific cut-off grade has to be selected to maximize the net present value. The choice of a cut-off grade affects the volume and the average grade of each lens, which increases the size of problems to be solved. To reduce the computation time, different acceleration strategies and a Fix-and-Optimize heuristic are proposed. Computational experiments on instances of different sizes are performed to (1) assess the quality of the solution found by each method and (2) present the impact of the variable cut-off grade.
European Journal of Operational Research, Oct 1, 2005
This paper describes the problem of managing a fleet of load-haul-dump (LHD) vehicles in an under... more This paper describes the problem of managing a fleet of load-haul-dump (LHD) vehicles in an underground mine. The problem consists of dispatching, routing and scheduling vehicles whenever they need to be assigned to a new task. The solution approach is based on a shortest-path algorithm. Each decision takes into account the current status of the mine, the current traffic on all single-lane bi-directional road segments of the haulage network and operational constraints such as the fact that, while LHD vehicles move in forward or reverse modes, their bucket must be in dumping/ loading position at destination.
This paper presents an enumeration algorithm based on dynamic programming for optimally solving t... more This paper presents an enumeration algorithm based on dynamic programming for optimally solving the fleet management problem in underground mines. This problem consists of routing and scheduling bidirectional vehicles on a haulage network composed of one-lane bidirectional road segments. The method takes into account the displacement modes of the vehicles, either forward or in reverse, and makes sure that these vehicles move forward when they arrive at their service point. The method has been developed for the underground mine context, but it can be extended to the industrial environment.
La collection Les Cahiers du GERAD est constituée des travaux de recherche menés par nos membres.... more La collection Les Cahiers du GERAD est constituée des travaux de recherche menés par nos membres. La plupart de ces documents de travail aété soumisà des revues avec comité de révision. Lorsqu'un document est accepté et publié, le pdf original est retiré si c'est nécessaire et un lien vers l'article publié est ajouté.
This paper proposes a new approach to the mining exploration drillholes positioning problem (DPP)... more This paper proposes a new approach to the mining exploration drillholes positioning problem (DPP) that incorporates both geostatistical and optimization techniques. A metaheuristic was developed to solve the DPP taking into account an uncertainty index that quantifies the reliability of the current interpretation of the mineral deposit. The uncertainty index was calculated from multiple deposit realizations obtained by truncated Gaussian simulations conditional to the available drillholes samplings. A linear programming model was defined to select the subset of future drillholes that maximizes coverage of the uncertainty. A Tabu Search algorithm was developed to solve large instances of this set partitioning problem. The proposed Tabu Search algorithm is shown to provide good quality solutions approaching 95% of the optimal solution in a reasonable computing time, allowing close to optimal coverage of uncertainty for a fixed investment in drilling.
This paper introduces the first exact approach for constructing aircrew member personalized month... more This paper introduces the first exact approach for constructing aircrew member personalized monthly work schedules when a preferential bidding system (PBS) is used. With such a system, each employee bids for his/her preferred activities, yielding a bidding score for each feasible schedule. The PBS problem thus consists of assigning to each employee a schedule that maximizes his/her preferences, in order of seniority, while covering all crew pairings. The proposed exact solution approach relies on column generation, and when a tentative maximum score for a crew member is established, it explicitly enumerates for that employee all feasible schedules with that score. Tests on real-life cases show that this approach can substantially improve the quality of the solutions produced by the best known existing method in similar computational times.
This paper presents a prototype method for optimally solving the rostering problem, i.e., constru... more This paper presents a prototype method for optimally solving the rostering problem, i.e., constructing work schedules for airline crew members. The main goal is to show the possibilities of solving the rostering problem using optimal methods. The prototype uses a column generation approach embedded in a branch and bound algorithm to solve the rostering problem. To the knowledge of the
Scheduling activities in an underground mine is a very complex task. Precedence relations, the gr... more Scheduling activities in an underground mine is a very complex task. Precedence relations, the great number of resources and the large number of work sites are some of the reasons for this complexity. This paper presents an optimization model for short-term planning that takes into consideration all parts of the development and production as well as specific limitations on equipment and workers. A preemptive mixed integer program is used in order to produce optimal planning over a short-term time horizon. Multiple tests made with various data sets and scenarios are then presented, including a comparison to a non-preemptive model and a case study.
ABSTRACT This paper presents two solution approaches for taking into account the displacement mod... more ABSTRACT This paper presents two solution approaches for taking into account the displacement mode (forward or in reverse) of vehicles during the solution of the shortest path problem. In the first approach, a graph including all aspects of the problem is constructed and a classical shortest path algorithm is used to solve the problem. In the second approach, a more simple graph is constructed, and all the constraints of the problem are considered during the solution of the shortest path problem. This problem is important for routing a fleet of automated vehicles on a one-lane bidirectional graph.
Scheduling activities in an underground mine is a very complex task. This paper presents an optim... more Scheduling activities in an underground mine is a very complex task. This paper presents an optimization model for short-term planning that takes into consideration all parts of the development and production as well as specific limitations on equipment and workers. To do so, a mix integer program is used in order to maximize mined tonnage on a given time horizon. Test results of the application to a mine are presented to confirm the model accuracy and solvability.
This paper presents a framework for the use of unmanned aerial vehicles (UAVs) equipped with came... more This paper presents a framework for the use of unmanned aerial vehicles (UAVs) equipped with cameras and wireless sensors to search an area after the occurrence of a tornado. This paper attempts to demonstrate how tornado weather data can be incorporated into search and rescue procedures to allocate and route the UAVs. Traditionally, the time to assess and search an area after a tornado strikes is on the order of several days. Incorporating UAVs into a search and rescue team’s available tools can reduce this time span to the order of hours. These methods are applied and model in this project to three real-world cases. Several methods for creating ”waypoints,” points of interest for the UAVs to inspect, to route the UAVs were tested. An analysis was performed to compare the time it took to generate the waypoints and the resulting objective function value. It is observed that while there is an opportunity to use exact methods to generate waypoints, our proposed heuristic is sufficient for the rapid response needed in post-disaster relief.
This paper presents a new branching strategy that is applied on the cost of a subproblem during t... more This paper presents a new branching strategy that is applied on the cost of a subproblem during the solution of a large-scale linear program by a column generation technique. This branch and cut strategy has been used to improve the solution time for the preferential bidding problems encountered in the airline industry. Moreover, it is shown that this strategy can also be applied to other problems with particular structures.
International Journal of Production Research, Mar 15, 2005
This paper presents two solution approaches for taking into account the displacement mode (forwar... more This paper presents two solution approaches for taking into account the displacement mode (forward or in reverse) of vehicles during the solution of the shortest path problem. In the first approach, a graph including all aspects of the problem is constructed and a classical shortest path algorithm is used to solve the problem. In the second approach, a more simple graph is constructed, and all the constraints of the problem are considered during the solution of the shortest path problem. This problem is important for routing a fleet of automated vehicles on a one-lane bidirectional graph.
International Journal of Mining, Reclamation and Environment, Feb 15, 2022
ABSTRACT This article describes a new model aiming at optimising short- and medium-term undergrou... more ABSTRACT This article describes a new model aiming at optimising short- and medium-term underground mine scheduling. The problem complexity and the frequency at which planners must revise these schedules are among the primary motivations for developing such a model. To address this problem, a Mixed Integer Programming model is proposed with a flexible time discretisation to accurately represent both shortand medium-term operational constraints in a single model. The results of a preliminary mathematical formulation are presented with in-depth analyses. Further, an improved formulation is presented with associated results and benefits. Extensive experiments with scenarios similar to long-term planning show promising results for the improved formulation. Among other things, these results show that the modified formulation makes it possible to solve for scenarios that include a large number of activities and locations while generating more applicable solutions.
We present a mixed-integer programming model for solving the long-term planning problem of an und... more We present a mixed-integer programming model for solving the long-term planning problem of an underground mine. This model, which establishes the sequence of mining for a horizon of 20 years, determines which lens of the geological model will be mined and in what order, while respecting the operational constraints. For each lens to be mined, a specific cut-off grade has to be selected to maximize the net present value. The choice of a cut-off grade affects the volume and the average grade of each lens, which increases the size of problems to be solved. To reduce the computation time, different acceleration strategies and a Fix-and-Optimize heuristic are proposed. Computational experiments on instances of different sizes are performed to (1) assess the quality of the solution found by each method and (2) present the impact of the variable cut-off grade.
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Papers by Michel Gamache