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On degenerate doubly nonnegative projection problems

Ying Cui, Ling Liang, Defeng Sun, Kim-Chuan Toh
The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable completely positive cone. The major difficulty for implementing a Newton-type method to compute the projection of a given large scale matrix onto the DNN…
This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
Mathematics of Operations Research
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On degenerate doubly nonnegative projection problems

Ying Cui, Ling Liang, Defeng Sun, Kim-Chuan Toh
The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable completely positive cone. The major difficulty for implementing a Newton-type method to compute the projection of a given large scale matrix onto the DNN…
Mathematics of Operations Research
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This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
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An Inexact Augmented Lagrangian Method for Second-order Cone Programming with Applications

Ling Liang, Defeng Sun, Kim-Chuan Toh
In this paper, we adopt the augmented Lagrangian method (ALM) to solve convex quadratic second-order cone programming problems (SOCPs). Fruitful results on the efficiency of the ALM have been established in the literature. Recently, it has been shown in [Cui, Sun, and Toh, {\em Math. Program.}, 178 (2019), pp….
This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
SIAM J. Optimization
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An Inexact Augmented Lagrangian Method for Second-order Cone Programming with Applications

Ling Liang, Defeng Sun, Kim-Chuan Toh
In this paper, we adopt the augmented Lagrangian method (ALM) to solve convex quadratic second-order cone programming problems (SOCPs). Fruitful results on the efficiency of the ALM have been established in the literature. Recently, it has been shown in [Cui, Sun, and Toh, {\em Math. Program.}, 178 (2019), pp….
SIAM J. Optimization
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This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
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An augmented Lagrangian method with constraint generations for shape-constrained convex regression problems

Meixia Lin, Defeng Sun, Kim-Chuan Toh
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a unified framework for computing the least squares estimator of a multivariate shape-constrained convex regression function in ℝd. We…
This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
Mathematical Programming Computation
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An augmented Lagrangian method with constraint generations for shape-constrained convex regression problems

Meixia Lin, Defeng Sun, Kim-Chuan Toh
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a unified framework for computing the least squares estimator of a multivariate shape-constrained convex regression function in ℝd. We…
Mathematical Programming Computation
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This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
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A Representative Consumer Model in Data-Driven Multi-product Pricing Optimization

Zhenzhen Yan, Karthik Natarajan, Chung Piaw Teo, Cong Cheng
We develop a data-driven approach for the multi-product pricing problem, using the theory of a represen- tative consumer in discrete choice. We establish a set of mathematical relationships between product prices and demand for each product in the system, including that of the outside option. We provide identification conditions…
This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
Management Science
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A Representative Consumer Model in Data-Driven Multi-product Pricing Optimization

Zhenzhen Yan, Karthik Natarajan, Chung Piaw Teo, Cong Cheng
We develop a data-driven approach for the multi-product pricing problem, using the theory of a represen- tative consumer in discrete choice. We establish a set of mathematical relationships between product prices and demand for each product in the system, including that of the outside option. We provide identification conditions…
Management Science
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This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
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Robot Scheduling for Mobile-Rack Warehouses: Human–Robot Coordinated Order Picking Systems

Zheng Wang, Jiuh-Biing Sheu, Chung-Piaw Teo, Guiqin Xue
Intelligent part-to-picker systems are spreading across a broad range of industries as preferred solutions for agile order fulfillment, wherein mobile racks are carried by robots and moved to stations where human pickers can pick items from them. Such systems raise the challenge of designing good work schedules for human…
This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
Production and Operations Management
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Robot Scheduling for Mobile-Rack Warehouses: Human–Robot Coordinated Order Picking Systems

Zheng Wang, Jiuh-Biing Sheu, Chung-Piaw Teo, Guiqin Xue
Intelligent part-to-picker systems are spreading across a broad range of industries as preferred solutions for agile order fulfillment, wherein mobile racks are carried by robots and moved to stations where human pickers can pick items from them. Such systems raise the challenge of designing good work schedules for human…
Production and Operations Management
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This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
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A feasibility-based heuristic for the container pre-marshalling problem

Ning Wang, Bo Jin, Zizhen Zhang, Andrew Lim
This paper addresses the container pre-marshalling problem (CPMP) which rearranges containers inside a storage bay to a desired layout. By far, target-driven algorithms have relatively good performance among all algorithms; they have two key components: first, containers are rearranged to their desired slots one by one in a certain…
European Journal of Operational Research
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A feasibility-based heuristic for the container pre-marshalling problem

Ning Wang, Bo Jin, Zizhen Zhang, Andrew Lim
This paper addresses the container pre-marshalling problem (CPMP) which rearranges containers inside a storage bay to a desired layout. By far, target-driven algorithms have relatively good performance among all algorithms; they have two key components: first, containers are rearranged to their desired slots one by one in a certain…
European Journal of Operational Research
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An enhanced branch-and-bound algorithm for the talent scheduling problem

Hu Qin, Zizhen Zhang, Andrew Lim, Xiaocong Liang
The talent scheduling problem is a simplified version of the real-world film shooting problem, which aims to determine a shooting sequence so as to minimize the total cost of the actors involved. In this article, we first formulate the problem as an integer linear programming model. Next, we devise…
European Journal of Operational Research
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An enhanced branch-and-bound algorithm for the talent scheduling problem

Hu Qin, Zizhen Zhang, Andrew Lim, Xiaocong Liang
The talent scheduling problem is a simplified version of the real-world film shooting problem, which aims to determine a shooting sequence so as to minimize the total cost of the actors involved. In this article, we first formulate the problem as an integer linear programming model. Next, we devise…
European Journal of Operational Research
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Transportation service procurement problem with transit time

Qian Hu, Zhenzhen Zhang, Andrew Lim
In this work, we investigate transit time in transportation service procurement, which is conducted by shippers using auctions to purchase transportation service from carriers in the planning stage. Besides cost, we find that many shippers are most concerned with transit time in practice; shorter transit time indicates better transportation…
Transportation Research Part B: Methodological
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Transportation service procurement problem with transit time

Qian Hu, Zhenzhen Zhang, Andrew Lim
In this work, we investigate transit time in transportation service procurement, which is conducted by shippers using auctions to purchase transportation service from carriers in the planning stage. Besides cost, we find that many shippers are most concerned with transit time in practice; shorter transit time indicates better transportation…
Transportation Research Part B: Methodological
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Branch‐and‐price‐and‐cut for the manpower routing problem with synchronization constraints

Zhixing Luo, Hu Qin, Wenbin Zhu, Andrew Lim
In this article, we propose a branch‐and‐price‐and‐cut (BPC) algorithm to exactly solve the manpower routing problem with synchronization constraints (MRPSC). Compared with the classical vehicle routing problems (VRPs), the defining characteristic of the MRPSC is that multiple workers are required to work together and start at the same time…
Naval Research Logistics
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Branch‐and‐price‐and‐cut for the manpower routing problem with synchronization constraints

Zhixing Luo, Hu Qin, Wenbin Zhu, Andrew Lim
In this article, we propose a branch‐and‐price‐and‐cut (BPC) algorithm to exactly solve the manpower routing problem with synchronization constraints (MRPSC). Compared with the classical vehicle routing problems (VRPs), the defining characteristic of the MRPSC is that multiple workers are required to work together and start at the same time…
Naval Research Logistics
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A fast implementation for the 2D/3D box placement problem

Wenbin Zhu, Zhixing Luo, Andrew Lim, Wee-Chong Oon
The box placement problem involves finding a location to place a rectangular box into a container given n rectangular boxes that have already been placed. It commonly arises as a subproblem in many algorithms for cutting stock problems as well as 2D/3D packing problems. We show that the box…
Computational Optimization and Applications
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A fast implementation for the 2D/3D box placement problem

Wenbin Zhu, Zhixing Luo, Andrew Lim, Wee-Chong Oon
The box placement problem involves finding a location to place a rectangular box into a container given n rectangular boxes that have already been placed. It commonly arises as a subproblem in many algorithms for cutting stock problems as well as 2D/3D packing problems. We show that the box…
Computational Optimization and Applications
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Exact approaches for the pickup and delivery problem with loading cost

Li Xue, Zhixing Luo, Andrew Lim
In this paper, we propose a branch-and-cut algorithm and a branch-and-price algorithm to solve the pickup and delivery problem with loading cost (PDPLC), which is a new problem derived from the classic pickup and delivery problem (PDP) by considering the loading cost in the objective function. Applications of the…
OMEGA
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Exact approaches for the pickup and delivery problem with loading cost

Li Xue, Zhixing Luo, Andrew Lim
In this paper, we propose a branch-and-cut algorithm and a branch-and-price algorithm to solve the pickup and delivery problem with loading cost (PDPLC), which is a new problem derived from the classic pickup and delivery problem (PDP) by considering the loading cost in the objective function. Applications of the…
OMEGA
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Adaptive large neighborhood search heuristics for the vehicle routing problem with stochastic demands and weight-related cost

Zhixing Luo, Hu Qin, Dezhi Zhang and Andrew Lim
The vehicle routing problem (VRP) with stochastic demands and weight-related cost is an extension of the VRP. Although some researchers have studied the VRP with either stochastic demands or weight-related cost, the literature on this problem is quite limited. We adopt the a priori optimization to tackle this problem…
Transportation Research Part E: Logistics and Transportation Review
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Adaptive large neighborhood search heuristics for the vehicle routing problem with stochastic demands and weight-related cost

Zhixing Luo, Hu Qin, Dezhi Zhang and Andrew Lim
The vehicle routing problem (VRP) with stochastic demands and weight-related cost is an extension of the VRP. Although some researchers have studied the VRP with either stochastic demands or weight-related cost, the literature on this problem is quite limited. We adopt the a priori optimization to tackle this problem…
Transportation Research Part E: Logistics and Transportation Review
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