We introduce a dynamic and stochastic rematching problem with applications in request matching fo... more We introduce a dynamic and stochastic rematching problem with applications in request matching for ridesharing systems. We propose three mathematical programming formulations that can be used in a rolling horizon framework to solve this problem. We show how these models can be simplified provided that specific conditions that are typically found in practice are met.
The planning of agricultural cultivation and harvesting is a complex task. However, this area of ... more The planning of agricultural cultivation and harvesting is a complex task. However, this area of study is still relatively young. This work focuses on the operational planning for sugar cane cultivation and harvesting which determines the best moment to harvest the fields, maximizing the total profit given by the sugar content within the cane. It considers resources such as cutting and transport crews, processing capacities in sugar cane mills, the use of maturation products and the application of vinasse on harvested fields. The MIP model extends the classical Packing formulation, incorporating a network flow for the harvest scheduling. Heuristically obtained initial solutions are passed to the solver in order to facilitate the solution. This work also invests in valid inequalities in order to strengthen the MIP formulation. All experiments were performed with
The assortment of products carried by a store has a crucial impact on its success. However, findi... more The assortment of products carried by a store has a crucial impact on its success. However, finding the right mix of products to attract a large portion of the customers is a challenging task. Several mathematical models have been proposed to optimize assortments. In particular, rank-based choice models have been acknowledged for representing well high-dimensional product substitution effects, and therefore reflect customer preferences in a reasonably realistic manner. In this work, we extend the concept of (strictly) fully-ranked choice models to models with partial ranking that additionally allow for indifference among subsets of products, i.e., on which the customer does not have a strict preference. We show that partially-ranked choice models are theoretically equivalent to fully-ranked choice models, but a partially-ranked preference sequence would require a factorial number of fully-ranked sequences to represent the same buying behavior. We then show how partially-ranked choic...
The assortment of products carried by a store has a crucial impact on its success. However, findi... more The assortment of products carried by a store has a crucial impact on its success. However, finding the right mix of products to attract a large portion of the customers is a challenging task. Seve...
Due to increased traffic congestion and carbon emissions, Bike Sharing Systems (BSSs) are adopted... more Due to increased traffic congestion and carbon emissions, Bike Sharing Systems (BSSs) are adopted in various cities for short distance travels, specifically for last mile transportation. The success of a bike sharing system depends on its ability to have bikes available at the "right" base stations at the "right" times. Typically, carrier vehicles are used to perform repositioning of bikes between stations so as to satisfy customer requests. Owing to the uncertainty in customer demand and day-long repositioning, the problem of having bikes available at the right base stations at the right times is a challenging one. In this paper, we propose a multi-stage stochastic formulation, to consider expected future demand over a set of scenarios to find an efficient repositioning strategy for bike sharing systems. Furthermore, we provide a Lagrangian decomposition approach (that decouples the global problem into routing and repositioning slaves and employs a novel DP appr...
We study a dynamic matching and rematching problem with applications in ridesharing systems. Tran... more We study a dynamic matching and rematching problem with applications in ridesharing systems. Transportation requests for riders and passengers arrive dynamically and are represented as nodes of a bipartite graph, connected by edges that correspond to compatible requests. Matching requests by selecting the corresponding edge earns a profit. We further allow for unmatching previously matched requests. While this increases the system's flexibility to adjust to new matching opportunities, unmatching may degrade customer experience and therefore implies penalty costs. We evaluate myopic and stochastic multi-period mixed-integer programming models in a rolling horizon framework. All models are compared against a static model that has perfect knowledge about future requests, using an extensive benchmark set of realistic instances. Our results demonstrate the value of being able to unmatch, as well as the benefits of the stochastic strategies over the myopic strategy.
We consider a recently introduced multi-period facility location problem with multiple commoditie... more We consider a recently introduced multi-period facility location problem with multiple commodities and multiple capacity levels, motivated by an application in the forestry sector. The problem allows for the relocation of facilities, as well as for the temporary closing of parts of the facilities, while other parts remain open. In addition, it uses particular capacity constraints that involve integer rounding of the allocated demands. In this paper, we propose a strong formulation for the problem, as well as a hybrid heuristic that first applies Lagrangian relaxation and then constructs a restricted mixed-integer programming model based on the previously obtained Lagrangian solutions. Computational results for large-scale instances emphasize the usefulness of the heuristic in practice. While general-purpose mixed-integer programming solvers do not find feasible solutions for about half of the instances, the heuristic consistently provides high-quality solutions in short computing ti...
The Random Utility Maximization model is by far the most adopted framework to estimate consumer c... more The Random Utility Maximization model is by far the most adopted framework to estimate consumer choice behavior. However, behavioral economics has provided strong empirical evidence of irrational choice behavior, such as halo effects, that are incompatible with this framework. Models belonging to the Random Utility Maximization family may therefore not accurately capture such irrational behavior. Hence, more general choice models, overcoming such limitations, have been proposed. However, the flexibility of such models comes at the price of increased risk of overfitting. As such, estimating such models remains a challenge. In this work, we propose an estimation method for the recently proposed Generalized Stochastic Preference choice model, which subsumes the family of Random Utility Maximization models and is capable of capturing halo effects. Specifically, we show how to use partially-ranked preferences to efficiently model rational and irrational customer types from transaction da...
The classical Prize-collecting Steiner Tree Problem aims at finding a connected subgraph that max... more The classical Prize-collecting Steiner Tree Problem aims at finding a connected subgraph that maximizes the revenues collected from connected vertices minus the costs to utilize the connecting edges. We consider a multi-period variant in which, additionally: (a) vertices are allowed to be added to the tree at different time periods; (b) a predefined budget is imposed on edges selected over specified sets of time periods; and (c) the total length of the edges that can be added over a time period is limited. We propose a branchand-cut algorithm that satisfactorily solves in reasonable time benchmark instances from the literature, adapted to a multi-period setting, with up to 3300 vertices and 300 terminal vertices.
Abstract. Harvesting plans for Canadian logging companies tend to cover wider territories than be... more Abstract. Harvesting plans for Canadian logging companies tend to cover wider territories than before. Long transportation distances for the workers involved in logging activities have thus become a significant issue. Often, cities or villages to accommodate the workers are ...
Location decisions are frequently subject to dynamic aspects such as changes in customer demand. ... more Location decisions are frequently subject to dynamic aspects such as changes in customer demand. Often, flexibility regarding the geographic location of facilities, as well as their capacities, is the only solution to such issues. Even when demand can be forecast, finding the optimal schedule for the deployment and dynamic adjustment of capacities remains a challenge. In this thesis, we focus on multi-period facility location problems that allow for dynamic capacity adjustment, in particular those with complex cost structures. We investigate such problems from different Operations Research perspectives, presenting and comparing several mixed-integer programming (MIP) models, assessing their use in practice and developing efficient solution algorithms. The thesis is divided into four parts. We first motivate our research by an industrial application, in which a logging company needs to locate camps to host the workers involved in forestry operations. We present a MIP model that allows for the construction of additional camps, the expansion and relocation of existing ones, as well as partial closing and reopening of facilities. The model uses particular capacity constraints that involve integer rounding on the left hand side. Economies of scale are considered on several levels of the cost structure. The usefulness of the model is assessed by two case studies. The second part introduces the Dynamic Facility Location Problem with Generalized Modular Capacities (DFLPG). The model generalizes existing formulations for several dynamic facility location problems and provides stronger linear programming relaxations than the specialized formulations. The model can address facility location problems where the costs for capacity changes are defined for all pairs of capacity levels, as it is the case in the previously introduced industrial problem. It is applied to three special cases: capacity expansion and reduction, temporary facility closing and reopening, and the combination of both. We prove dominance relationships between our formulation and existing models for the special cases. Computational experiments on a large set of randomly generated instances with up to 100 facility locations and 1000 customers show that our model can obtain optimal solutions in shorter computing times than the existing specialized formulations. Given the complexity of such models for large instances, the third part of the thesis proposes efficient Lagrangian heuristics. Based on subgradient and bundle methods, good quality solutions are found even for large-scale instances with up to 250 facility locations and 1000 customers. To improve the final solution quality, a restricted model is solved based on the information collected through the solution of the Lagrangian dual. Computational results show that the Lagrangian based heuristics provide highly reliable results, producing good quality solutions in short computing times even for instances where generic solvers do not find feasible solutions. Finally, we adapt the Lagrangian heuristics to solve the industrial application. Two different relaxations are proposed and compared. Extensions of the previous concepts are presented to ensure a reliable solution of the problem, providing high quality solutions in reasonable computing times.
We introduce a dynamic and stochastic rematching problem with applications in request matching fo... more We introduce a dynamic and stochastic rematching problem with applications in request matching for ridesharing systems. We propose three mathematical programming formulations that can be used in a rolling horizon framework to solve this problem. We show how these models can be simplified provided that specific conditions that are typically found in practice are met.
The planning of agricultural cultivation and harvesting is a complex task. However, this area of ... more The planning of agricultural cultivation and harvesting is a complex task. However, this area of study is still relatively young. This work focuses on the operational planning for sugar cane cultivation and harvesting which determines the best moment to harvest the fields, maximizing the total profit given by the sugar content within the cane. It considers resources such as cutting and transport crews, processing capacities in sugar cane mills, the use of maturation products and the application of vinasse on harvested fields. The MIP model extends the classical Packing formulation, incorporating a network flow for the harvest scheduling. Heuristically obtained initial solutions are passed to the solver in order to facilitate the solution. This work also invests in valid inequalities in order to strengthen the MIP formulation. All experiments were performed with
The assortment of products carried by a store has a crucial impact on its success. However, findi... more The assortment of products carried by a store has a crucial impact on its success. However, finding the right mix of products to attract a large portion of the customers is a challenging task. Several mathematical models have been proposed to optimize assortments. In particular, rank-based choice models have been acknowledged for representing well high-dimensional product substitution effects, and therefore reflect customer preferences in a reasonably realistic manner. In this work, we extend the concept of (strictly) fully-ranked choice models to models with partial ranking that additionally allow for indifference among subsets of products, i.e., on which the customer does not have a strict preference. We show that partially-ranked choice models are theoretically equivalent to fully-ranked choice models, but a partially-ranked preference sequence would require a factorial number of fully-ranked sequences to represent the same buying behavior. We then show how partially-ranked choic...
The assortment of products carried by a store has a crucial impact on its success. However, findi... more The assortment of products carried by a store has a crucial impact on its success. However, finding the right mix of products to attract a large portion of the customers is a challenging task. Seve...
Due to increased traffic congestion and carbon emissions, Bike Sharing Systems (BSSs) are adopted... more Due to increased traffic congestion and carbon emissions, Bike Sharing Systems (BSSs) are adopted in various cities for short distance travels, specifically for last mile transportation. The success of a bike sharing system depends on its ability to have bikes available at the "right" base stations at the "right" times. Typically, carrier vehicles are used to perform repositioning of bikes between stations so as to satisfy customer requests. Owing to the uncertainty in customer demand and day-long repositioning, the problem of having bikes available at the right base stations at the right times is a challenging one. In this paper, we propose a multi-stage stochastic formulation, to consider expected future demand over a set of scenarios to find an efficient repositioning strategy for bike sharing systems. Furthermore, we provide a Lagrangian decomposition approach (that decouples the global problem into routing and repositioning slaves and employs a novel DP appr...
We study a dynamic matching and rematching problem with applications in ridesharing systems. Tran... more We study a dynamic matching and rematching problem with applications in ridesharing systems. Transportation requests for riders and passengers arrive dynamically and are represented as nodes of a bipartite graph, connected by edges that correspond to compatible requests. Matching requests by selecting the corresponding edge earns a profit. We further allow for unmatching previously matched requests. While this increases the system's flexibility to adjust to new matching opportunities, unmatching may degrade customer experience and therefore implies penalty costs. We evaluate myopic and stochastic multi-period mixed-integer programming models in a rolling horizon framework. All models are compared against a static model that has perfect knowledge about future requests, using an extensive benchmark set of realistic instances. Our results demonstrate the value of being able to unmatch, as well as the benefits of the stochastic strategies over the myopic strategy.
We consider a recently introduced multi-period facility location problem with multiple commoditie... more We consider a recently introduced multi-period facility location problem with multiple commodities and multiple capacity levels, motivated by an application in the forestry sector. The problem allows for the relocation of facilities, as well as for the temporary closing of parts of the facilities, while other parts remain open. In addition, it uses particular capacity constraints that involve integer rounding of the allocated demands. In this paper, we propose a strong formulation for the problem, as well as a hybrid heuristic that first applies Lagrangian relaxation and then constructs a restricted mixed-integer programming model based on the previously obtained Lagrangian solutions. Computational results for large-scale instances emphasize the usefulness of the heuristic in practice. While general-purpose mixed-integer programming solvers do not find feasible solutions for about half of the instances, the heuristic consistently provides high-quality solutions in short computing ti...
The Random Utility Maximization model is by far the most adopted framework to estimate consumer c... more The Random Utility Maximization model is by far the most adopted framework to estimate consumer choice behavior. However, behavioral economics has provided strong empirical evidence of irrational choice behavior, such as halo effects, that are incompatible with this framework. Models belonging to the Random Utility Maximization family may therefore not accurately capture such irrational behavior. Hence, more general choice models, overcoming such limitations, have been proposed. However, the flexibility of such models comes at the price of increased risk of overfitting. As such, estimating such models remains a challenge. In this work, we propose an estimation method for the recently proposed Generalized Stochastic Preference choice model, which subsumes the family of Random Utility Maximization models and is capable of capturing halo effects. Specifically, we show how to use partially-ranked preferences to efficiently model rational and irrational customer types from transaction da...
The classical Prize-collecting Steiner Tree Problem aims at finding a connected subgraph that max... more The classical Prize-collecting Steiner Tree Problem aims at finding a connected subgraph that maximizes the revenues collected from connected vertices minus the costs to utilize the connecting edges. We consider a multi-period variant in which, additionally: (a) vertices are allowed to be added to the tree at different time periods; (b) a predefined budget is imposed on edges selected over specified sets of time periods; and (c) the total length of the edges that can be added over a time period is limited. We propose a branchand-cut algorithm that satisfactorily solves in reasonable time benchmark instances from the literature, adapted to a multi-period setting, with up to 3300 vertices and 300 terminal vertices.
Abstract. Harvesting plans for Canadian logging companies tend to cover wider territories than be... more Abstract. Harvesting plans for Canadian logging companies tend to cover wider territories than before. Long transportation distances for the workers involved in logging activities have thus become a significant issue. Often, cities or villages to accommodate the workers are ...
Location decisions are frequently subject to dynamic aspects such as changes in customer demand. ... more Location decisions are frequently subject to dynamic aspects such as changes in customer demand. Often, flexibility regarding the geographic location of facilities, as well as their capacities, is the only solution to such issues. Even when demand can be forecast, finding the optimal schedule for the deployment and dynamic adjustment of capacities remains a challenge. In this thesis, we focus on multi-period facility location problems that allow for dynamic capacity adjustment, in particular those with complex cost structures. We investigate such problems from different Operations Research perspectives, presenting and comparing several mixed-integer programming (MIP) models, assessing their use in practice and developing efficient solution algorithms. The thesis is divided into four parts. We first motivate our research by an industrial application, in which a logging company needs to locate camps to host the workers involved in forestry operations. We present a MIP model that allows for the construction of additional camps, the expansion and relocation of existing ones, as well as partial closing and reopening of facilities. The model uses particular capacity constraints that involve integer rounding on the left hand side. Economies of scale are considered on several levels of the cost structure. The usefulness of the model is assessed by two case studies. The second part introduces the Dynamic Facility Location Problem with Generalized Modular Capacities (DFLPG). The model generalizes existing formulations for several dynamic facility location problems and provides stronger linear programming relaxations than the specialized formulations. The model can address facility location problems where the costs for capacity changes are defined for all pairs of capacity levels, as it is the case in the previously introduced industrial problem. It is applied to three special cases: capacity expansion and reduction, temporary facility closing and reopening, and the combination of both. We prove dominance relationships between our formulation and existing models for the special cases. Computational experiments on a large set of randomly generated instances with up to 100 facility locations and 1000 customers show that our model can obtain optimal solutions in shorter computing times than the existing specialized formulations. Given the complexity of such models for large instances, the third part of the thesis proposes efficient Lagrangian heuristics. Based on subgradient and bundle methods, good quality solutions are found even for large-scale instances with up to 250 facility locations and 1000 customers. To improve the final solution quality, a restricted model is solved based on the information collected through the solution of the Lagrangian dual. Computational results show that the Lagrangian based heuristics provide highly reliable results, producing good quality solutions in short computing times even for instances where generic solvers do not find feasible solutions. Finally, we adapt the Lagrangian heuristics to solve the industrial application. Two different relaxations are proposed and compared. Extensions of the previous concepts are presented to ensure a reliable solution of the problem, providing high quality solutions in reasonable computing times.
The assortment of products carried by a store has a crucial impact on its success. However, findi... more The assortment of products carried by a store has a crucial impact on its success. However, finding the right mix of products to attract a large portion of the customers is a challenging task. Several mathematical models have been proposed to optimize assortments. In particular, rank-based choice models have been acknowledged for representing well high-dimensional product substitution effects, and therefore reflect customer preferences in a reasonably realistic manner. In this work, we extend the concept of (strictly) fully-ranked choice models to models with partial ranking that additionally allow for indifference among subsets of products, i.e., on which the customer does not have a strict preference. We show that partially-ranked choice models are theoretically equivalent to fully-ranked choice models, but a partially-ranked preference sequence would require a factorial number of fully-ranked sequences to represent the same buying behavior. We then show how partially-ranked choice models can be learned efficiently from historical transaction and assortment data. The embedded column generation procedure involves subproblems that can be efficiently solved by using a growing decision tree that represents partially-ranked preferences, enabling us to learn preferences and optimize assortments for thousands of products. Computational experiments on artificially generated data and case studies on real industrial retail data suggest a significant potential to increase profits when performing data-driven assortment optimization and provide useful insights on customer segmentation to the decision makers, in our real case, the store managers. When comparing to existing algorithms, our method increases by one order of magnitude the scale of problems that can be learned by non-parametric choice models.
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Papers by Sanjay Dominik Jena
as their capacities, is the only solution to such issues. Even when demand can be forecast, finding the optimal schedule for the deployment and dynamic adjustment of capacities remains a challenge. In this thesis, we focus on multi-period facility location problems that allow for dynamic capacity adjustment, in particular those with complex cost structures. We investigate such problems from different Operations Research perspectives, presenting and comparing several mixed-integer programming (MIP) models, assessing their use in practice and developing efficient solution algorithms. The thesis is divided into four parts. We first motivate our research by an industrial
application, in which a logging company needs to locate camps to host the workers involved in forestry operations. We present a MIP model that allows for the construction of additional camps, the expansion and relocation of existing ones, as well as partial closing and reopening of facilities. The model uses particular capacity constraints that involve integer rounding on the left hand side. Economies of scale are considered on several levels of the cost structure. The usefulness of the model is assessed by two case studies. The second part introduces the Dynamic Facility Location Problem with Generalized Modular Capacities (DFLPG). The model generalizes existing formulations for several dynamic
facility location problems and provides stronger linear programming relaxations than the specialized formulations. The model can address facility location problems where the costs for capacity changes are defined for all pairs of capacity levels, as it is the case in the previously introduced industrial problem. It is applied to three special cases: capacity expansion and reduction, temporary facility closing and reopening, and
the combination of both. We prove dominance relationships between our formulation and existing models for the special cases. Computational experiments on a large set of
randomly generated instances with up to 100 facility locations and 1000 customers show that our model can obtain optimal solutions in shorter computing times than the existing
specialized formulations. Given the complexity of such models for large instances, the third part of the thesis proposes efficient Lagrangian heuristics. Based on subgradient
and bundle methods, good quality solutions are found even for large-scale instances with up to 250 facility locations and 1000 customers. To improve the final solution quality, a restricted model is solved based on the information collected through the solution of the Lagrangian dual. Computational results show that the Lagrangian based heuristics provide highly reliable results, producing good quality solutions in short computing times even for instances where generic solvers do not find feasible solutions. Finally, we adapt the Lagrangian heuristics to solve the industrial application. Two different relaxations
are proposed and compared. Extensions of the previous concepts are presented to ensure a reliable solution of the problem, providing high quality solutions in reasonable
computing times.
as their capacities, is the only solution to such issues. Even when demand can be forecast, finding the optimal schedule for the deployment and dynamic adjustment of capacities remains a challenge. In this thesis, we focus on multi-period facility location problems that allow for dynamic capacity adjustment, in particular those with complex cost structures. We investigate such problems from different Operations Research perspectives, presenting and comparing several mixed-integer programming (MIP) models, assessing their use in practice and developing efficient solution algorithms. The thesis is divided into four parts. We first motivate our research by an industrial
application, in which a logging company needs to locate camps to host the workers involved in forestry operations. We present a MIP model that allows for the construction of additional camps, the expansion and relocation of existing ones, as well as partial closing and reopening of facilities. The model uses particular capacity constraints that involve integer rounding on the left hand side. Economies of scale are considered on several levels of the cost structure. The usefulness of the model is assessed by two case studies. The second part introduces the Dynamic Facility Location Problem with Generalized Modular Capacities (DFLPG). The model generalizes existing formulations for several dynamic
facility location problems and provides stronger linear programming relaxations than the specialized formulations. The model can address facility location problems where the costs for capacity changes are defined for all pairs of capacity levels, as it is the case in the previously introduced industrial problem. It is applied to three special cases: capacity expansion and reduction, temporary facility closing and reopening, and
the combination of both. We prove dominance relationships between our formulation and existing models for the special cases. Computational experiments on a large set of
randomly generated instances with up to 100 facility locations and 1000 customers show that our model can obtain optimal solutions in shorter computing times than the existing
specialized formulations. Given the complexity of such models for large instances, the third part of the thesis proposes efficient Lagrangian heuristics. Based on subgradient
and bundle methods, good quality solutions are found even for large-scale instances with up to 250 facility locations and 1000 customers. To improve the final solution quality, a restricted model is solved based on the information collected through the solution of the Lagrangian dual. Computational results show that the Lagrangian based heuristics provide highly reliable results, producing good quality solutions in short computing times even for instances where generic solvers do not find feasible solutions. Finally, we adapt the Lagrangian heuristics to solve the industrial application. Two different relaxations
are proposed and compared. Extensions of the previous concepts are presented to ensure a reliable solution of the problem, providing high quality solutions in reasonable
computing times.