Transportation Research Part E: Logistics and Transportation Review, 2018
The global supply chain for liquid helium presents a complex structure due to increasing foreign ... more The global supply chain for liquid helium presents a complex structure due to increasing foreign demand, elaborate recovery techniques, and costly forms of distribution. Although the problem contains parallels to the liquid natural gas supply chain, supply requirements and problemspecific network constraints require a unique optimization model. We develop a large-scale, discrete time, path-based integer-programming model which solves optimally with CPLEX. Computational results implementing a rolling horizon structure and testing based on historical data are presented. A detailed sensitivity analysis demonstrates the effective use of our model, testing a variety of realistic parameter settings for the liquid helium supply chain.
Transportation Research Record: Journal of the Transportation Research Board, 2019
Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or ... more Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or (2) they have perception errors of the decision environment. The notion of generalized bounded rationality has been recently proposed to create a unified framework for these two sources of behavioral uncertainty in route choices. When the notion of generalized bounded rationality is used in robust network design problems, we obtain a bi-level optimization problem with the min–max objective function at the upper level, with three layers of optimization in total. In this paper, we derive equivalent single-level path-based formulations that are readily solvable by available optimization libraries. We show how to incorporate them into robust multi-commodity network design problems in hazardous materials transportation.
Abstracts of papers presented at the conference but not included in the proceedings
Lecture Notes in Economics and Mathematical Systems, 1989
Distributed decision making regarding agricultural loans by evaluating different criteria that af... more Distributed decision making regarding agricultural loans by evaluating different criteria that affecting the procedure paths and regulating the operation is examined in this paper. Decision making nodes function as multitasking operators in a complex cybernetic system by executing command decomposition for the concurrent implementation of various loan procedures. A hierarchical organisation of N decision makers is examined where each one deals with a finite number of objects. An illustrative example for the concurrent operation is given.
Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or ... more Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or (2) they have perception errors of the decision environment. The notion of generalized bounded rationality has been recently proposed to create a unified framework for these two sources of behavioral uncertainty in route choices. When the notion of generalized bounded rationality is used in robust network design problems, we obtain a bi-level optimization problem with the min-max objective function at the upper level, with three layers of optimization in total. In this paper, we derive equivalent single-level path-based formulations that are readily solvable by available optimization libraries. We show how to incorporate them into robust multi-commodity network design problems in hazardous materials transportation.
Transportation Research Part E-logistics and Transportation Review, Feb 1, 2018
The global supply chain for liquid helium presents a complex structure due to increasing foreign ... more The global supply chain for liquid helium presents a complex structure due to increasing foreign demand, elaborate recovery techniques, and costly forms of distribution. Although the problem contains parallels to the liquid natural gas supply chain, supply requirements and problemspecific network constraints require a unique optimization model. We develop a large-scale, discrete time, path-based integer-programming model which solves optimally with CPLEX. Computational results implementing a rolling horizon structure and testing based on historical data are presented. A detailed sensitivity analysis demonstrates the effective use of our model, testing a variety of realistic parameter settings for the liquid helium supply chain.
In view of the extended formulations (EFs) developments (e.g. "Fiorini, S., S. Massar, S. Pokutta... more In view of the extended formulations (EFs) developments (e.g. "Fiorini, S., S. Massar, S. Pokutta, H.R. Tiwary, and R. de Wolf [2015]. Exponential Lower Bounds for Polytopes in Combinatorial Optimization. Journal of the ACM 62:2"), we focus in this paper on the question of whether it is possible to model an NP-Complete problem as a polynomial-sized linear program. For the sake of simplicity of exposition, the discussions are focused on the TSP. We show that a finding that there exists no polynomial-sized extended formulation of "the TSP polytope" does not (necessarily) imply that it is "impossible" for a polynomial-sized linear program to solve the TSP optimization problem. We show that under appropriate conditions the TSP optimization problem can be solved without recourse to the traditional city-to-city ("travel leg") variables, thereby sidestepping/"escaping from" "the TSP polytope" and hence, the "barriers." Some illustrative examples are discussed.
We present an O(n 6) linear programming model for the traveling salesman (TSP) and quadratic assi... more We present an O(n 6) linear programming model for the traveling salesman (TSP) and quadratic assignment (QAP) problems. The basic model is developed within the framework of the TSP. It does not involve the city-to-city variables-based, traditional TSP polytope referred to in the literature as "the TSP polytope." We do not model explicit Hamiltonian cycles of the cities. Instead, we use a time-dependent abstraction of TSP tours and develop a direct extended formulation of the linear assignment problem (LAP) polytope. The model is exact in the sense that it has integral extreme points which are in one-to-one correspondence with LAP assignment solutions and TSP tours. It can be solved optimally using any linear programming (LP) solver, hence offering a new (incidental) proof of the equality of the computational complexity classes "P " and "N P ." The extensions of the model to the time-dependent traveling salesman problem (TDTSP) as well as the quadratic assignment problem (QAP) are straightforward. The reasons for the non-applicability of existing negative extended formulations results for "the TSP polytope" to the model in this paper as well as our software implementation and the computational experimentation we conducted are briefly discussed.
Customer selection and incentivization for SKU rationalization in a packaged gas supply chain
International Journal of Production Economics, 2021
This paper presents customer selection and incentivization methodologies necessary for the implem... more This paper presents customer selection and incentivization methodologies necessary for the implementation of many SKU rationalization schemes. Our work accounts for the problem of business demand loss, which is undesirably associated with the benefits of rationalized product offerings. We apply our methodologies to a particularly complex instance of SKU rationalization established in the literature, namely a case of demand substitution within a packaged gas supply chain planning problem. This is done both to display the value of our contributions, and to provide a business setting for the workflow process we prescribe for decision makers. In our first contribution, we develop a customer selection heuristic which pre-processes targets for demand substitution, subject to demand characteristics and the supply chain features. The heuristic is shown to outperform objectives utilizing random customer selection by 10–20%, dependent on the desired amount of substitution required of the dema...
Implicit enumeration algorithms for solving 0-1 integer linear programming problems
The implicit enumeration approaches allow us solving a variety of combinatorial problems, specifi... more The implicit enumeration approaches allow us solving a variety of combinatorial problems, specifically binary integer linear programs. A number of real world problems can be formulated using 0-1 integer linear programming. This resulted in the development of many implicit enumeration algorithms with varying degree of success in their implementation. However, the computational effectiveness of some of the early algorithms has not been fully explored. We study the implicit enumeration approaches by considering a number of algorithms. To compare the computational effectiveness we implement three early implicit enumeration algorithms. We synthesize effective techniques present in different algorithms and develop new relaxation problems to obtain stronger bounds. Fathoming and variable setting tests form the core of any implicit enumeration algorithm. We develop an approach to unify implicit enumeration algorithms by analyzing the tests used in different algorithms. This unifying approac...
Household use of autonomous vehicles with ride sourcing
Transportation Research Part C: Emerging Technologies, 2021
Abstract The prospect of autonomous vehicles (AVs) offers the possibility that a household could ... more Abstract The prospect of autonomous vehicles (AVs) offers the possibility that a household could reduce household owned vehicles to a single vehicle. At the same time, with AVs, a Shared Autonomous Vehicle (SAV) system will rise as a primary mode of serving travel demands. This study aims to model households’ activity/travel decisions using both household owned AVs as well as readily available SAVs to perform daily activities. We formulate the Household Activity Pattern Problem with Autonomous Vehicles and Ride Sourcing (HAPPAV-RS), as a mixed integer linear program. The model generates an optimal activity/travel patterns for household members under spatial and temporal constraints. The model can capture driverless operations such as AV pick-up and drop-off, parking availability, empty trips and ridesharing among household members, as well as the use of SAVs with the request waiting time. A decomposition method is used to solve the NP-hard problem HAPPAV-RS. scenarios on using AVs and SAVs with different travel mode availability, AV/SAV cost and SAV waiting time are designed to enable sensitivity analysis. Various travel metrics such as activity pattern feasibility, household’s total travel disutility, travel mode VMT and AV-SAV trip coverage are reported.
This research considers the problem of maximizing information collection and exchange between unm... more This research considers the problem of maximizing information collection and exchange between unmanned resources and a control station in a bandwidth constrained environment. Unmanned aerial vehicles (UAVs) are utilized in disaster response to gather data and aid in intelligence, surveillance, and reconnaissance (ISR). They are regularly equipped with multiple gimbal-mounted heterogeneous sensors, generating large amounts of data which are to be routed through a communications network back to mission managers. A mixed integer linear program (MILP) is formulated for this problem. However, due to the complexity of this problem, the MILP is only able to solve trivially-sized problems. A three-phase heuristic approach is proposed which, through extensive testing, is proven to efficiently solve large-sized problems. Our analysis also gives insight into the features of this problem and their impact on mission success.
This paper discusses the problem of predicting the length of Traveling Salesman Problem (TSP) tou... more This paper discusses the problem of predicting the length of Traveling Salesman Problem (TSP) tour in dynamic and uncertain environments. Our findings, which are guided by extensive simulation runs, provide statistical estimations for the tour length under different scenarios. One of the applications that can benefit from these estimates includes warehouse order picking, which has seen increased importance due to online shopping. The utility of statistical estimates for TSP tour length for order picking is demonstrated on a common warehouse layout.
We propose an indefinite period traveling salesman problem (TSP), in which customer nodes need to... more We propose an indefinite period traveling salesman problem (TSP), in which customer nodes need to be visited an unknown multiple or infinite number of times but cannot be visited more than once in the same trip. The optimal solution seeks a visiting strategy for the long run including the routing and planning horizon decisions. We show that an optimal solution may be a set of routes in which a given customer is grouped with a number of different subsets of customers rather than simply repeated TSP or multiple TSP optimal routes. The problem is proven to be NP-hard, and important properties are explored theoretically. We propose exact as well as heuristic procedures for solving this problem. Our computational experiments show that the proposed heuristic produces high quality solutions for problems with certain sizes, and that the proposed exact algorithm can be implemented within a practical time tolerance. The numerical results demonstrate the importance of this problem for cost reduction in practice and the concerns about scheduling solution tours have been discussed for practical implementation.
Transportation Research Part E: Logistics and Transportation Review, 2018
The global supply chain for liquid helium presents a complex structure due to increasing foreign ... more The global supply chain for liquid helium presents a complex structure due to increasing foreign demand, elaborate recovery techniques, and costly forms of distribution. Although the problem contains parallels to the liquid natural gas supply chain, supply requirements and problemspecific network constraints require a unique optimization model. We develop a large-scale, discrete time, path-based integer-programming model which solves optimally with CPLEX. Computational results implementing a rolling horizon structure and testing based on historical data are presented. A detailed sensitivity analysis demonstrates the effective use of our model, testing a variety of realistic parameter settings for the liquid helium supply chain.
Transportation Research Record: Journal of the Transportation Research Board, 2019
Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or ... more Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or (2) they have perception errors of the decision environment. The notion of generalized bounded rationality has been recently proposed to create a unified framework for these two sources of behavioral uncertainty in route choices. When the notion of generalized bounded rationality is used in robust network design problems, we obtain a bi-level optimization problem with the min–max objective function at the upper level, with three layers of optimization in total. In this paper, we derive equivalent single-level path-based formulations that are readily solvable by available optimization libraries. We show how to incorporate them into robust multi-commodity network design problems in hazardous materials transportation.
Abstracts of papers presented at the conference but not included in the proceedings
Lecture Notes in Economics and Mathematical Systems, 1989
Distributed decision making regarding agricultural loans by evaluating different criteria that af... more Distributed decision making regarding agricultural loans by evaluating different criteria that affecting the procedure paths and regulating the operation is examined in this paper. Decision making nodes function as multitasking operators in a complex cybernetic system by executing command decomposition for the concurrent implementation of various loan procedures. A hierarchical organisation of N decision makers is examined where each one deals with a finite number of objects. An illustrative example for the concurrent operation is given.
Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or ... more Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or (2) they have perception errors of the decision environment. The notion of generalized bounded rationality has been recently proposed to create a unified framework for these two sources of behavioral uncertainty in route choices. When the notion of generalized bounded rationality is used in robust network design problems, we obtain a bi-level optimization problem with the min-max objective function at the upper level, with three layers of optimization in total. In this paper, we derive equivalent single-level path-based formulations that are readily solvable by available optimization libraries. We show how to incorporate them into robust multi-commodity network design problems in hazardous materials transportation.
Transportation Research Part E-logistics and Transportation Review, Feb 1, 2018
The global supply chain for liquid helium presents a complex structure due to increasing foreign ... more The global supply chain for liquid helium presents a complex structure due to increasing foreign demand, elaborate recovery techniques, and costly forms of distribution. Although the problem contains parallels to the liquid natural gas supply chain, supply requirements and problemspecific network constraints require a unique optimization model. We develop a large-scale, discrete time, path-based integer-programming model which solves optimally with CPLEX. Computational results implementing a rolling horizon structure and testing based on historical data are presented. A detailed sensitivity analysis demonstrates the effective use of our model, testing a variety of realistic parameter settings for the liquid helium supply chain.
In view of the extended formulations (EFs) developments (e.g. "Fiorini, S., S. Massar, S. Pokutta... more In view of the extended formulations (EFs) developments (e.g. "Fiorini, S., S. Massar, S. Pokutta, H.R. Tiwary, and R. de Wolf [2015]. Exponential Lower Bounds for Polytopes in Combinatorial Optimization. Journal of the ACM 62:2"), we focus in this paper on the question of whether it is possible to model an NP-Complete problem as a polynomial-sized linear program. For the sake of simplicity of exposition, the discussions are focused on the TSP. We show that a finding that there exists no polynomial-sized extended formulation of "the TSP polytope" does not (necessarily) imply that it is "impossible" for a polynomial-sized linear program to solve the TSP optimization problem. We show that under appropriate conditions the TSP optimization problem can be solved without recourse to the traditional city-to-city ("travel leg") variables, thereby sidestepping/"escaping from" "the TSP polytope" and hence, the "barriers." Some illustrative examples are discussed.
We present an O(n 6) linear programming model for the traveling salesman (TSP) and quadratic assi... more We present an O(n 6) linear programming model for the traveling salesman (TSP) and quadratic assignment (QAP) problems. The basic model is developed within the framework of the TSP. It does not involve the city-to-city variables-based, traditional TSP polytope referred to in the literature as "the TSP polytope." We do not model explicit Hamiltonian cycles of the cities. Instead, we use a time-dependent abstraction of TSP tours and develop a direct extended formulation of the linear assignment problem (LAP) polytope. The model is exact in the sense that it has integral extreme points which are in one-to-one correspondence with LAP assignment solutions and TSP tours. It can be solved optimally using any linear programming (LP) solver, hence offering a new (incidental) proof of the equality of the computational complexity classes "P " and "N P ." The extensions of the model to the time-dependent traveling salesman problem (TDTSP) as well as the quadratic assignment problem (QAP) are straightforward. The reasons for the non-applicability of existing negative extended formulations results for "the TSP polytope" to the model in this paper as well as our software implementation and the computational experimentation we conducted are briefly discussed.
Customer selection and incentivization for SKU rationalization in a packaged gas supply chain
International Journal of Production Economics, 2021
This paper presents customer selection and incentivization methodologies necessary for the implem... more This paper presents customer selection and incentivization methodologies necessary for the implementation of many SKU rationalization schemes. Our work accounts for the problem of business demand loss, which is undesirably associated with the benefits of rationalized product offerings. We apply our methodologies to a particularly complex instance of SKU rationalization established in the literature, namely a case of demand substitution within a packaged gas supply chain planning problem. This is done both to display the value of our contributions, and to provide a business setting for the workflow process we prescribe for decision makers. In our first contribution, we develop a customer selection heuristic which pre-processes targets for demand substitution, subject to demand characteristics and the supply chain features. The heuristic is shown to outperform objectives utilizing random customer selection by 10–20%, dependent on the desired amount of substitution required of the dema...
Implicit enumeration algorithms for solving 0-1 integer linear programming problems
The implicit enumeration approaches allow us solving a variety of combinatorial problems, specifi... more The implicit enumeration approaches allow us solving a variety of combinatorial problems, specifically binary integer linear programs. A number of real world problems can be formulated using 0-1 integer linear programming. This resulted in the development of many implicit enumeration algorithms with varying degree of success in their implementation. However, the computational effectiveness of some of the early algorithms has not been fully explored. We study the implicit enumeration approaches by considering a number of algorithms. To compare the computational effectiveness we implement three early implicit enumeration algorithms. We synthesize effective techniques present in different algorithms and develop new relaxation problems to obtain stronger bounds. Fathoming and variable setting tests form the core of any implicit enumeration algorithm. We develop an approach to unify implicit enumeration algorithms by analyzing the tests used in different algorithms. This unifying approac...
Household use of autonomous vehicles with ride sourcing
Transportation Research Part C: Emerging Technologies, 2021
Abstract The prospect of autonomous vehicles (AVs) offers the possibility that a household could ... more Abstract The prospect of autonomous vehicles (AVs) offers the possibility that a household could reduce household owned vehicles to a single vehicle. At the same time, with AVs, a Shared Autonomous Vehicle (SAV) system will rise as a primary mode of serving travel demands. This study aims to model households’ activity/travel decisions using both household owned AVs as well as readily available SAVs to perform daily activities. We formulate the Household Activity Pattern Problem with Autonomous Vehicles and Ride Sourcing (HAPPAV-RS), as a mixed integer linear program. The model generates an optimal activity/travel patterns for household members under spatial and temporal constraints. The model can capture driverless operations such as AV pick-up and drop-off, parking availability, empty trips and ridesharing among household members, as well as the use of SAVs with the request waiting time. A decomposition method is used to solve the NP-hard problem HAPPAV-RS. scenarios on using AVs and SAVs with different travel mode availability, AV/SAV cost and SAV waiting time are designed to enable sensitivity analysis. Various travel metrics such as activity pattern feasibility, household’s total travel disutility, travel mode VMT and AV-SAV trip coverage are reported.
This research considers the problem of maximizing information collection and exchange between unm... more This research considers the problem of maximizing information collection and exchange between unmanned resources and a control station in a bandwidth constrained environment. Unmanned aerial vehicles (UAVs) are utilized in disaster response to gather data and aid in intelligence, surveillance, and reconnaissance (ISR). They are regularly equipped with multiple gimbal-mounted heterogeneous sensors, generating large amounts of data which are to be routed through a communications network back to mission managers. A mixed integer linear program (MILP) is formulated for this problem. However, due to the complexity of this problem, the MILP is only able to solve trivially-sized problems. A three-phase heuristic approach is proposed which, through extensive testing, is proven to efficiently solve large-sized problems. Our analysis also gives insight into the features of this problem and their impact on mission success.
This paper discusses the problem of predicting the length of Traveling Salesman Problem (TSP) tou... more This paper discusses the problem of predicting the length of Traveling Salesman Problem (TSP) tour in dynamic and uncertain environments. Our findings, which are guided by extensive simulation runs, provide statistical estimations for the tour length under different scenarios. One of the applications that can benefit from these estimates includes warehouse order picking, which has seen increased importance due to online shopping. The utility of statistical estimates for TSP tour length for order picking is demonstrated on a common warehouse layout.
We propose an indefinite period traveling salesman problem (TSP), in which customer nodes need to... more We propose an indefinite period traveling salesman problem (TSP), in which customer nodes need to be visited an unknown multiple or infinite number of times but cannot be visited more than once in the same trip. The optimal solution seeks a visiting strategy for the long run including the routing and planning horizon decisions. We show that an optimal solution may be a set of routes in which a given customer is grouped with a number of different subsets of customers rather than simply repeated TSP or multiple TSP optimal routes. The problem is proven to be NP-hard, and important properties are explored theoretically. We propose exact as well as heuristic procedures for solving this problem. Our computational experiments show that the proposed heuristic produces high quality solutions for problems with certain sizes, and that the proposed exact algorithm can be implemented within a practical time tolerance. The numerical results demonstrate the importance of this problem for cost reduction in practice and the concerns about scheduling solution tours have been discussed for practical implementation.
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Papers by Mark Karwan