Vahid Roshanaei | University of Toronto (original) (raw)

Papers by Vahid Roshanaei

Research paper thumbnail of A discrete event simulation evaluation of distributed operating room scheduling

IIE Transactions on Healthcare Systems Engineering, Aug 26, 2016

Operating room (OR) scheduling is a challenging combinatorial problem and hence most optimization... more Operating room (OR) scheduling is a challenging combinatorial problem and hence most optimization-based OR scheduling research makes simplifying assumptions for tractability, including deterministic surgical durations, absence of dynamic emergency arrivals, and the existence of sufficient downstream resources. In this study, we use discrete event simulation to assess the performance of deterministically optimized OR schedules in a network of collaborating hospitals with shared resources, called distributed OR scheduling (DORS), in the face of uncertain surgical durations, emergency arrivals, and limited downstream resources. We quantify the individual and combined disruptive impact of these stochastic factors on the DORS schedule, using real data obtained from the University Health Network (UHN) in Toronto, Canada. We show that the schedule constructed by DORS results in higher OR utilization and lower average surgery cost compared to the simulated current UHN schedule.

Research paper thumbnail of Collaborative Operating Room Planning and Scheduling

Informs Journal on Computing, Aug 1, 2017

Large-scale decomposition strategies for collaborative operating room planning and scheduling

Research paper thumbnail of Branch-and-check methods for multi-level operating room planning and scheduling

International Journal of Production Economics, Feb 1, 2020

Abstract We develop the first exact decomposition approaches for a multi-level operating room pla... more Abstract We develop the first exact decomposition approaches for a multi-level operating room planning and scheduling problem that integrates case mix planning, master surgical scheduling, and surgery sequencing in the presence of multiple surgical specialties. Our approaches consist of novel uni-level and bi-level branch-and-check algorithms that solve the problem using a hybridization of integer programming and constraint programming. We demonstrate that our approaches outperform an existing time-indexed integer programming model, yielding significant improvements on solution quality. Our methods are competitive with an existing genetic algorithm while providing provable bounds on solution quality. We conduct an investigation into the impact of time discretization on our algorithms, illustrating that our decompositions, unlike the previously proposed integer programming approach, are much less sensitive to time discretization and produce more accurate solutions as a result. Finally, we introduce and investigate benchmark instances with a more diverse case mix. Overall, we conclude that our decompositions are the most appropriate approaches for this multi-level operating room planning and scheduling problem.

Research paper thumbnail of Critical-Path-Search Logic-Based Benders Decomposition Approaches for Flexible Job Shop Scheduling

INFORMS journal on optimization, 2022

We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we comp... more We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we compare the constraint programming (CP) model with the mixed-integer programming (MIP) model for F-JSSPs. Second, we exploit the decomposable structure within the models and develop an efficient CP–logic-based Benders decomposition (CP-LBBD) technique that combines the complementary strengths of MIP and CP models. Using 193 instances from the literature, we demonstrate that MIP, CP, and CP-LBBD achieve average optimality gaps of 25.50%, 13.46%, and 0.37% and find optima in 49, 112, and 156 instances of the problem, respectively. We also compare the performance of the CP-LBBD with an efficient Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, which has been appraised for finding 125 optima on 178 instances. CP-LBBD finds 143 optima on the same set of instances. We further examine the performance of the algorithms on 96 newly (and much larger) generated instances and demonstrate that the average optimality gap of the CP increases to 47.26%, whereas the average optimality of CP-LBBD remains around 1.44%. Finally, we conduct analytics on the performance of our models and algorithms and counterintuitively find out that as flexibility increases in data sets the performance CP-LBBD ameliorates, whereas that of the CP and MIP significantly deteriorates.

Research paper thumbnail of Loss Ratio as a Risk Constraint: Analysis and Optimization

Social Science Research Network, 2023

Research paper thumbnail of A robust optimization formulation for dynamic pricing of a web service with limited total shared capacity

Optimal Control Applications and Methods, 2022

Research paper thumbnail of A Novel and Efficient Exact Technique for Integrated Staffing, Assignment, Routing, and Scheduling of Home Care Services Under Uncertainty

Social Science Research Network, 2021

Research paper thumbnail of Large-scale decomposition strategies for collaborative operating room planning and scheduling

Large-scale decomposition strategies for collaborative operating room planning and scheduling

Research paper thumbnail of Solving the Type-2 Assembly Line Balancing with Setups Using Logic-Based Benders Decomposition

Informs Journal on Computing, 2021

We solve the type-2 assembly line balancing problem in the presence of sequence-dependent setup t... more We solve the type-2 assembly line balancing problem in the presence of sequence-dependent setup times, denoted SUALBP-2. The problem consists of a set of tasks of a product, requiring to be process...

Research paper thumbnail of Critical-Path-Search Logic-Based Benders Decomposition Approaches for Flexible Job Shop Scheduling

INFORMS Journal on Optimization, 2021

We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we comp... more We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we compare the constraint programming (CP) model with the mixed-integer programming (MIP) model for F-JSSPs. Second, we exploit the decomposable structure within the models and develop an efficient CP–logic-based Benders decomposition (CP-LBBD) technique that combines the complementary strengths of MIP and CP models. Using 193 instances from the literature, we demonstrate that MIP, CP, and CP-LBBD achieve average optimality gaps of 25.50%, 13.46%, and 0.37% and find optima in 49, 112, and 156 instances of the problem, respectively. We also compare the performance of the CP-LBBD with an efficient Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, which has been appraised for finding 125 optima on 178 instances. CP-LBBD finds 143 optima on the same set of instances. We further examine the performance of the algorithms on 96 newly (and much larger) generated instances and demonstrate t...

Research paper thumbnail of Increased Surgical Capacity without Additional Resources: Generalized Operating Room Planning and Scheduling

Production and Operations Management

We study a generalized operating room planning and scheduling (GORPS) problem at the Toronto Gene... more We study a generalized operating room planning and scheduling (GORPS) problem at the Toronto General Hospital (TGH) in Ontario, Canada GORPS allocates elective patients and resources (i e , operating rooms, surgeons, anesthetists) to days, assigns resources to patients, and sequences patients in each day We consider patients’ due-date, resource eligibility, heterogeneous performances of resources, downstream unit requirements, and lag times between resources The goal is to create a weekly surgery schedule that minimizes fixed- and over-time costs We model GORPS using mixed-integer and constraint programming models To efficiently and effectively solve these models, we develop new‘ multi-featured logic-based Benders decomposition approaches Using data from TGH, we demonstrate that our best algorithm solves GORPS with an average optimality gap of 2 71% which allows us to provide our practical recommendations First, we can increase daily OR utilization to reach 80%—25% higher than the status quo in TGH Second, we do not require to optimize for the daily selection of anesthetists—this finding allows for the development of effective dominance rules that significantly mitigate intractability Third, solving GORPS without downstream capacities (like many papers in literature) makes GORPS easier to solve, but such OR schedules are only feasible in 24% of instances Finally, with existing ORs’ safety capacities, TGH can manage 40% increase in its surgical volumes We provide recommendations on how TGH must adjust its downstream capacities for varying levels of surgical volume increases (e g , current urgent need for more capacity due to the current Covid-19 pandemic) © 2021 Production and Operations Management Society

Research paper thumbnail of Solving integrated operating room planning and scheduling: Logic-based Benders decomposition versus Branch-Price-and-Cut

European Journal of Operational Research

Research paper thumbnail of Branch-Relax-and-Check: A tractable decomposition method for order acceptance and identical parallel machine scheduling

European Journal of Operational Research

Abstract We model and solve an order acceptance and scheduling problem in an identical parallel m... more Abstract We model and solve an order acceptance and scheduling problem in an identical parallel machine setting. The goal is to maximize profit by making four decisions: (i) accept or reject an order, (ii) assign accepted orders to identical parallel machines, (iii) sequence accepted orders, and (iv) schedule order starting times. First, we develop a mixed-integer model that simultaneously optimizes the above four decisions. We enhance the model with pre-processing techniques, valid inequalities, and dominance rules. Second, we show that the model has a special structure that allows us to develop both classical and combinatorial Benders decomposition. We thus develop a classical Benders decomposition approach and two combinatorial Benders variants: (i) logic-based Benders decomposition and (ii) Branch-Relax-and-Check (BRC). The BRC, as the primary contribution of this paper, extends the literature in three ways: (1) it incorporates novel sequencing sub-problem relaxations that expedite convergence, (2) it employs a novel cutting-plane partitioning procedure that allows these sub-problem relaxations to be separately optimized outside the master problem, and (3) it uses temporary Benders cuts that communicate sub-problem relaxation solutions to the master problem. Third, we demonstrate that the BRC outperforms significantly other methods and finds integer feasible solutions for 100% of instances, guarantees optimality in 50% of instances, and achieves an average optimality gap of 3.20% within our time limit.

Research paper thumbnail of Branch-and-check methods for multi-level operating room planning and scheduling

International Journal of Production Economics

Abstract We develop the first exact decomposition approaches for a multi-level operating room pla... more Abstract We develop the first exact decomposition approaches for a multi-level operating room planning and scheduling problem that integrates case mix planning, master surgical scheduling, and surgery sequencing in the presence of multiple surgical specialties. Our approaches consist of novel uni-level and bi-level branch-and-check algorithms that solve the problem using a hybridization of integer programming and constraint programming. We demonstrate that our approaches outperform an existing time-indexed integer programming model, yielding significant improvements on solution quality. Our methods are competitive with an existing genetic algorithm while providing provable bounds on solution quality. We conduct an investigation into the impact of time discretization on our algorithms, illustrating that our decompositions, unlike the previously proposed integer programming approach, are much less sensitive to time discretization and produce more accurate solutions as a result. Finally, we introduce and investigate benchmark instances with a more diverse case mix. Overall, we conclude that our decompositions are the most appropriate approaches for this multi-level operating room planning and scheduling problem.

Research paper thumbnail of A mixed-integer program and a Lagrangian-based decomposition algorithm for the supply chain network design with quantity discount and transportation modes

Expert Systems with Applications

Abstract We study the design of a two-echelon supply chain network in the presence of suppliers’ ... more Abstract We study the design of a two-echelon supply chain network in the presence of suppliers’ all-unit quantity discount and transportation mode selection. The problem involves determining the best location for plants and the allocation of customers to open plants. The problem additionally entails making decisions for the order quantity from each supplier for each plant and accordingly selecting the best transportation mode that can accommodate these order quantities among echelons. The objective is to minimize the total cost associated with fixed opening and operating costs of plants, fixed and variable costs of transportation modes, and purchasing costs of raw materials. To characterize and solve this problem, we develop a mixed-integer programming (MIP) model. We demonstrate that the MIP model has a special mathematical structure that makes it amenable to decomposition techniques. We, therefore, exploit this decomposable structure and develop an effective Lagrangian-based decomposition for solving the MIP. Our Lagrangian Relaxation (LR) method relaxes the complicating constraints associated with commodity flow conservation among echelons in the MIP, yielding more tractable subproblems, one for each echelon. Solutions obtained from the relaxed problem may be infeasible, e.g., the demand for some of the customers may not be satisfied. We remedy these subproblems’ infeasibilities using novel feasibility algorithms and appropriate Lagrangian multipliers that penalize constraints’ violations in the subproblems, leading the algorithm towards global feasibility/optimality. We appraise the performance of the MIP model and the LR algorithm on instances of varying sizes. We show that the MIP model solved via CPLEX finds integer feasible solutions for 42% of large problem instances and its average optimality gap for these solved instances is 64.56%. The LR algorithm significantly improves the solvability and optimality gap of the MIP model and finds integer feasible solutions for 100% of problem instances and achieves an average optimality gap of 1.78%. We investigate the robustness of our algorithm by conducting sensitivity analyses on the model parameters. We demonstrate that the LR technique remains robust and tractable with respect to various parameters’ values.

Research paper thumbnail of Reformulation, linearization, and decomposition techniques for balanced distributed operating room scheduling

Omega

Abstract We study the balanced distributed operating room (OR) scheduling (BDORS) problem as a lo... more Abstract We study the balanced distributed operating room (OR) scheduling (BDORS) problem as a location-allocation model, encompassing two levels of balancing decisions: (i) daily macro imbalance among collaborating hospitals in terms of the number of allocated ORs and (ii) daily micro imbalance among open ORs in each hospital in terms of the total caseload assigned. BDORS is formulated as a novel mixed-integer nonlinear programming (MINLP) in which the macro and micro imbalance are penalized using absolute value and quadratic functions. We develop various reformulation-linearization techniques (RLTs) for the MINLP models, leading to three mathematical modelling variants: (i) a mixed-integer quadratically constrained program (MIQCP) and (ii) two mixed-integer programs (MIPs) for the absolute value penalty function and an MIQCP for the quadratic penalty function. Two novel exact techniques based on reformulation-decomposition techniques (RDTs) are developed to solve these models: a uni- and a bi-level logic-based Benders decomposition (LBBD). We motivate the LBBD methods with an application to BDORS in the University Health Network (UHN), consisting of three collaborating hospitals: Toronto General Hospital, Toronto Western Hospital, and Princess Margaret Cancer Centre in Toronto, Ontario, Canada. The uni-level LBBD method decomposes the model into a surgical suite location, OR allocation, and macro balancing master problem (MP) and micro OR balancing sub-problems (SPs) for each hospital-day. The bi-level approach uses a relaxed MP, consisting of a surgical suite location and relaxed allocation/macro balancing MP and two optimization SPs. The primary SP is formulated as a bin-packing problem to allocate patients to open operating rooms to minimize the number of ORs, while the secondary SP is the uni-level micro balancing SP. Using UHN datasets consisting of two datasets, hard MP/easy SPs and easy MP/hard SPs, we show that both LBBD approaches and both MIP models solved via Gurobi converge to ≈ 2% and ≈ 1–2% optimality gaps, on average, respectively, within 30 minutes runtime, whereas the MIQCP solved via Gurobi could not solve any instance of the UHN datasets given the same runtime. The uni- and bi-level LBBD approaches solved all instances of hard MP/easy SPs dataset to ≈ 11% and ≈ 2% optimality gaps, on average, respectively, within 30 minutes runtime, whereas MIQCP solved via Gurobi could not solve any of these instances. Additionally, we show that convergence of each LBBD varies depending on where in the decomposition the actual computational complexity lies.

Research paper thumbnail of Almost Robust Discrete Optimization

European Journal of Operational Research

Abstract The main goal of this paper is to present a simple and tractable methodology for incorpo... more Abstract The main goal of this paper is to present a simple and tractable methodology for incorporating data uncertainty into optimization models in the presence of binary variables. We introduce the Almost Robust Discrete Optimization (ARDO). ARDO extends the Integrated Chance-Constrained approach, developed for linear programs, to include binary integer variables. Both models trade off the objective function value with robustness and find optimal solutions that are almost robust (feasible under most realizations). These models are attractive due to their simplicity, ability to capture dependency among uncertain parameters, and that they incorporate the decision maker’s attitude towards risk by controlling the degree of conservatism of the optimal solution. To solve the ARDO model efficiently, we decompose it into a deterministic master problem and a single subproblem that checks the master problem solution under different realizations and generates cuts if needed. In contrast to other robust optimization models that are less tractable with binary decision variables, we demonstrate that with these cuts, the ARDO remains tractable. Computational experiments for the capacitated single-source facility location problem where demands in each node are uncertain demonstrate the effectiveness of our approach.

Research paper thumbnail of Reformulation, linearization, and a hybrid iterated local search algorithm for economic lot-sizing and sequencing in hybrid flow shop problems

Computers & Operations Research

Abstract We study an integrated economic lot-sizing and sequencing problem (ELSP) in the hybrid f... more Abstract We study an integrated economic lot-sizing and sequencing problem (ELSP) in the hybrid flow shop manufacturing setting with unlimited intermediate buffers in a finite planning horizon. The ELSP entails making two simultaneous decisions regarding (i) the manufacturing sequences of products, and (ii) their production quantity. The objective is to minimize the total cost, consisting of inventory holding and set-up costs. To solve this problem, we first develop a novel mixed-integer nonlinear programming (MINLP) model that improves an existing MINLP model in the literature. We then present a novel linearization technique that transforms these two MINLP models into effective mixed-integer linear programming (MILP) models. Additionally, we develop an effective algorithm that hybridizes the iterated local search algorithm with an approximate function. We conduct comprehensive experiments to compare the performance of MILPs+CPLEX with that of MINLPs+BARON. Additionally, our proposed algorithm is compared with four existing metaheuristic algorithms in the literature. Computational results demonstrate that our novel MINLP formulation and its linearized variant significantly improve the solvability and optimality gap of an existing MINLP formulation and its linearized variant. We also show that our new hybrid iterated local search algorithm substantially improves computational performance and optimality gap of the mathematical models and the existing algorithms in the literature, on large-size instances of the problem.

Research paper thumbnail of Collaborative Operating Room Planning and Scheduling

INFORMS Journal on Computing

Operating rooms (ORs) play a substantial role in hospital profitability, and their optimal utiliz... more Operating rooms (ORs) play a substantial role in hospital profitability, and their optimal utilization is conducive to containing the cost of surgical service delivery, shortening surgical patient wait times, and increasing patient admissions. We extend the OR planning and scheduling problem from a single independent hospital to a coalition of multiple hospitals in a strategic network, where a pool of patients, surgeons, and ORs are collaboratively planned. To solve the resulting mixed-integer dual resource constrained model, we develop a novel logic-based Benders’ decomposition approach that employs an allocation master problem, sequencing sub-problems for each hospital-day, and novel multistrategy Benders’ feasibility and optimality cuts. We investigate various patient-to-surgeon allocation flexibilities, as well as the impact of surgeon schedule tightness. Using real data obtained from the General Surgery Departments of the University Health Network (UHN) hospitals, consisting of Toronto General Hospit...

Research paper thumbnail of A discrete event simulation evaluation of distributed operating room scheduling

IIE Transactions on Healthcare Systems Engineering, 2016

ABSTRACT Operating room (OR) scheduling is a challenging combinatorial problem and hence most opt... more ABSTRACT Operating room (OR) scheduling is a challenging combinatorial problem and hence most optimization-based OR scheduling research makes simplifying assumptions for tractability, including deterministic surgical durations, absence of dynamic emergency arrivals, and the existence of sufficient downstream resources. In this study, we use discrete event simulation to assess the performance of deterministically optimized OR schedules in a network of collaborating hospitals with shared resources, called distributed OR scheduling (DORS), in the face of uncertain surgical durations, emergency arrivals, and limited downstream resources. We quantify the individual and combined disruptive impact of these stochastic factors on the DORS schedule, using real data obtained from the University Health Network (UHN) in Toronto, Canada. We show that the schedule constructed by DORS results in higher OR utilization and lower average surgery cost compared to the simulated current UHN schedule.

Research paper thumbnail of A discrete event simulation evaluation of distributed operating room scheduling

IIE Transactions on Healthcare Systems Engineering, Aug 26, 2016

Operating room (OR) scheduling is a challenging combinatorial problem and hence most optimization... more Operating room (OR) scheduling is a challenging combinatorial problem and hence most optimization-based OR scheduling research makes simplifying assumptions for tractability, including deterministic surgical durations, absence of dynamic emergency arrivals, and the existence of sufficient downstream resources. In this study, we use discrete event simulation to assess the performance of deterministically optimized OR schedules in a network of collaborating hospitals with shared resources, called distributed OR scheduling (DORS), in the face of uncertain surgical durations, emergency arrivals, and limited downstream resources. We quantify the individual and combined disruptive impact of these stochastic factors on the DORS schedule, using real data obtained from the University Health Network (UHN) in Toronto, Canada. We show that the schedule constructed by DORS results in higher OR utilization and lower average surgery cost compared to the simulated current UHN schedule.

Research paper thumbnail of Collaborative Operating Room Planning and Scheduling

Informs Journal on Computing, Aug 1, 2017

Large-scale decomposition strategies for collaborative operating room planning and scheduling

Research paper thumbnail of Branch-and-check methods for multi-level operating room planning and scheduling

International Journal of Production Economics, Feb 1, 2020

Abstract We develop the first exact decomposition approaches for a multi-level operating room pla... more Abstract We develop the first exact decomposition approaches for a multi-level operating room planning and scheduling problem that integrates case mix planning, master surgical scheduling, and surgery sequencing in the presence of multiple surgical specialties. Our approaches consist of novel uni-level and bi-level branch-and-check algorithms that solve the problem using a hybridization of integer programming and constraint programming. We demonstrate that our approaches outperform an existing time-indexed integer programming model, yielding significant improvements on solution quality. Our methods are competitive with an existing genetic algorithm while providing provable bounds on solution quality. We conduct an investigation into the impact of time discretization on our algorithms, illustrating that our decompositions, unlike the previously proposed integer programming approach, are much less sensitive to time discretization and produce more accurate solutions as a result. Finally, we introduce and investigate benchmark instances with a more diverse case mix. Overall, we conclude that our decompositions are the most appropriate approaches for this multi-level operating room planning and scheduling problem.

Research paper thumbnail of Critical-Path-Search Logic-Based Benders Decomposition Approaches for Flexible Job Shop Scheduling

INFORMS journal on optimization, 2022

We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we comp... more We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we compare the constraint programming (CP) model with the mixed-integer programming (MIP) model for F-JSSPs. Second, we exploit the decomposable structure within the models and develop an efficient CP–logic-based Benders decomposition (CP-LBBD) technique that combines the complementary strengths of MIP and CP models. Using 193 instances from the literature, we demonstrate that MIP, CP, and CP-LBBD achieve average optimality gaps of 25.50%, 13.46%, and 0.37% and find optima in 49, 112, and 156 instances of the problem, respectively. We also compare the performance of the CP-LBBD with an efficient Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, which has been appraised for finding 125 optima on 178 instances. CP-LBBD finds 143 optima on the same set of instances. We further examine the performance of the algorithms on 96 newly (and much larger) generated instances and demonstrate that the average optimality gap of the CP increases to 47.26%, whereas the average optimality of CP-LBBD remains around 1.44%. Finally, we conduct analytics on the performance of our models and algorithms and counterintuitively find out that as flexibility increases in data sets the performance CP-LBBD ameliorates, whereas that of the CP and MIP significantly deteriorates.

Research paper thumbnail of Loss Ratio as a Risk Constraint: Analysis and Optimization

Social Science Research Network, 2023

Research paper thumbnail of A robust optimization formulation for dynamic pricing of a web service with limited total shared capacity

Optimal Control Applications and Methods, 2022

Research paper thumbnail of A Novel and Efficient Exact Technique for Integrated Staffing, Assignment, Routing, and Scheduling of Home Care Services Under Uncertainty

Social Science Research Network, 2021

Research paper thumbnail of Large-scale decomposition strategies for collaborative operating room planning and scheduling

Large-scale decomposition strategies for collaborative operating room planning and scheduling

Research paper thumbnail of Solving the Type-2 Assembly Line Balancing with Setups Using Logic-Based Benders Decomposition

Informs Journal on Computing, 2021

We solve the type-2 assembly line balancing problem in the presence of sequence-dependent setup t... more We solve the type-2 assembly line balancing problem in the presence of sequence-dependent setup times, denoted SUALBP-2. The problem consists of a set of tasks of a product, requiring to be process...

Research paper thumbnail of Critical-Path-Search Logic-Based Benders Decomposition Approaches for Flexible Job Shop Scheduling

INFORMS Journal on Optimization, 2021

We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we comp... more We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we compare the constraint programming (CP) model with the mixed-integer programming (MIP) model for F-JSSPs. Second, we exploit the decomposable structure within the models and develop an efficient CP–logic-based Benders decomposition (CP-LBBD) technique that combines the complementary strengths of MIP and CP models. Using 193 instances from the literature, we demonstrate that MIP, CP, and CP-LBBD achieve average optimality gaps of 25.50%, 13.46%, and 0.37% and find optima in 49, 112, and 156 instances of the problem, respectively. We also compare the performance of the CP-LBBD with an efficient Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, which has been appraised for finding 125 optima on 178 instances. CP-LBBD finds 143 optima on the same set of instances. We further examine the performance of the algorithms on 96 newly (and much larger) generated instances and demonstrate t...

Research paper thumbnail of Increased Surgical Capacity without Additional Resources: Generalized Operating Room Planning and Scheduling

Production and Operations Management

We study a generalized operating room planning and scheduling (GORPS) problem at the Toronto Gene... more We study a generalized operating room planning and scheduling (GORPS) problem at the Toronto General Hospital (TGH) in Ontario, Canada GORPS allocates elective patients and resources (i e , operating rooms, surgeons, anesthetists) to days, assigns resources to patients, and sequences patients in each day We consider patients’ due-date, resource eligibility, heterogeneous performances of resources, downstream unit requirements, and lag times between resources The goal is to create a weekly surgery schedule that minimizes fixed- and over-time costs We model GORPS using mixed-integer and constraint programming models To efficiently and effectively solve these models, we develop new‘ multi-featured logic-based Benders decomposition approaches Using data from TGH, we demonstrate that our best algorithm solves GORPS with an average optimality gap of 2 71% which allows us to provide our practical recommendations First, we can increase daily OR utilization to reach 80%—25% higher than the status quo in TGH Second, we do not require to optimize for the daily selection of anesthetists—this finding allows for the development of effective dominance rules that significantly mitigate intractability Third, solving GORPS without downstream capacities (like many papers in literature) makes GORPS easier to solve, but such OR schedules are only feasible in 24% of instances Finally, with existing ORs’ safety capacities, TGH can manage 40% increase in its surgical volumes We provide recommendations on how TGH must adjust its downstream capacities for varying levels of surgical volume increases (e g , current urgent need for more capacity due to the current Covid-19 pandemic) © 2021 Production and Operations Management Society

Research paper thumbnail of Solving integrated operating room planning and scheduling: Logic-based Benders decomposition versus Branch-Price-and-Cut

European Journal of Operational Research

Research paper thumbnail of Branch-Relax-and-Check: A tractable decomposition method for order acceptance and identical parallel machine scheduling

European Journal of Operational Research

Abstract We model and solve an order acceptance and scheduling problem in an identical parallel m... more Abstract We model and solve an order acceptance and scheduling problem in an identical parallel machine setting. The goal is to maximize profit by making four decisions: (i) accept or reject an order, (ii) assign accepted orders to identical parallel machines, (iii) sequence accepted orders, and (iv) schedule order starting times. First, we develop a mixed-integer model that simultaneously optimizes the above four decisions. We enhance the model with pre-processing techniques, valid inequalities, and dominance rules. Second, we show that the model has a special structure that allows us to develop both classical and combinatorial Benders decomposition. We thus develop a classical Benders decomposition approach and two combinatorial Benders variants: (i) logic-based Benders decomposition and (ii) Branch-Relax-and-Check (BRC). The BRC, as the primary contribution of this paper, extends the literature in three ways: (1) it incorporates novel sequencing sub-problem relaxations that expedite convergence, (2) it employs a novel cutting-plane partitioning procedure that allows these sub-problem relaxations to be separately optimized outside the master problem, and (3) it uses temporary Benders cuts that communicate sub-problem relaxation solutions to the master problem. Third, we demonstrate that the BRC outperforms significantly other methods and finds integer feasible solutions for 100% of instances, guarantees optimality in 50% of instances, and achieves an average optimality gap of 3.20% within our time limit.

Research paper thumbnail of Branch-and-check methods for multi-level operating room planning and scheduling

International Journal of Production Economics

Abstract We develop the first exact decomposition approaches for a multi-level operating room pla... more Abstract We develop the first exact decomposition approaches for a multi-level operating room planning and scheduling problem that integrates case mix planning, master surgical scheduling, and surgery sequencing in the presence of multiple surgical specialties. Our approaches consist of novel uni-level and bi-level branch-and-check algorithms that solve the problem using a hybridization of integer programming and constraint programming. We demonstrate that our approaches outperform an existing time-indexed integer programming model, yielding significant improvements on solution quality. Our methods are competitive with an existing genetic algorithm while providing provable bounds on solution quality. We conduct an investigation into the impact of time discretization on our algorithms, illustrating that our decompositions, unlike the previously proposed integer programming approach, are much less sensitive to time discretization and produce more accurate solutions as a result. Finally, we introduce and investigate benchmark instances with a more diverse case mix. Overall, we conclude that our decompositions are the most appropriate approaches for this multi-level operating room planning and scheduling problem.

Research paper thumbnail of A mixed-integer program and a Lagrangian-based decomposition algorithm for the supply chain network design with quantity discount and transportation modes

Expert Systems with Applications

Abstract We study the design of a two-echelon supply chain network in the presence of suppliers’ ... more Abstract We study the design of a two-echelon supply chain network in the presence of suppliers’ all-unit quantity discount and transportation mode selection. The problem involves determining the best location for plants and the allocation of customers to open plants. The problem additionally entails making decisions for the order quantity from each supplier for each plant and accordingly selecting the best transportation mode that can accommodate these order quantities among echelons. The objective is to minimize the total cost associated with fixed opening and operating costs of plants, fixed and variable costs of transportation modes, and purchasing costs of raw materials. To characterize and solve this problem, we develop a mixed-integer programming (MIP) model. We demonstrate that the MIP model has a special mathematical structure that makes it amenable to decomposition techniques. We, therefore, exploit this decomposable structure and develop an effective Lagrangian-based decomposition for solving the MIP. Our Lagrangian Relaxation (LR) method relaxes the complicating constraints associated with commodity flow conservation among echelons in the MIP, yielding more tractable subproblems, one for each echelon. Solutions obtained from the relaxed problem may be infeasible, e.g., the demand for some of the customers may not be satisfied. We remedy these subproblems’ infeasibilities using novel feasibility algorithms and appropriate Lagrangian multipliers that penalize constraints’ violations in the subproblems, leading the algorithm towards global feasibility/optimality. We appraise the performance of the MIP model and the LR algorithm on instances of varying sizes. We show that the MIP model solved via CPLEX finds integer feasible solutions for 42% of large problem instances and its average optimality gap for these solved instances is 64.56%. The LR algorithm significantly improves the solvability and optimality gap of the MIP model and finds integer feasible solutions for 100% of problem instances and achieves an average optimality gap of 1.78%. We investigate the robustness of our algorithm by conducting sensitivity analyses on the model parameters. We demonstrate that the LR technique remains robust and tractable with respect to various parameters’ values.

Research paper thumbnail of Reformulation, linearization, and decomposition techniques for balanced distributed operating room scheduling

Omega

Abstract We study the balanced distributed operating room (OR) scheduling (BDORS) problem as a lo... more Abstract We study the balanced distributed operating room (OR) scheduling (BDORS) problem as a location-allocation model, encompassing two levels of balancing decisions: (i) daily macro imbalance among collaborating hospitals in terms of the number of allocated ORs and (ii) daily micro imbalance among open ORs in each hospital in terms of the total caseload assigned. BDORS is formulated as a novel mixed-integer nonlinear programming (MINLP) in which the macro and micro imbalance are penalized using absolute value and quadratic functions. We develop various reformulation-linearization techniques (RLTs) for the MINLP models, leading to three mathematical modelling variants: (i) a mixed-integer quadratically constrained program (MIQCP) and (ii) two mixed-integer programs (MIPs) for the absolute value penalty function and an MIQCP for the quadratic penalty function. Two novel exact techniques based on reformulation-decomposition techniques (RDTs) are developed to solve these models: a uni- and a bi-level logic-based Benders decomposition (LBBD). We motivate the LBBD methods with an application to BDORS in the University Health Network (UHN), consisting of three collaborating hospitals: Toronto General Hospital, Toronto Western Hospital, and Princess Margaret Cancer Centre in Toronto, Ontario, Canada. The uni-level LBBD method decomposes the model into a surgical suite location, OR allocation, and macro balancing master problem (MP) and micro OR balancing sub-problems (SPs) for each hospital-day. The bi-level approach uses a relaxed MP, consisting of a surgical suite location and relaxed allocation/macro balancing MP and two optimization SPs. The primary SP is formulated as a bin-packing problem to allocate patients to open operating rooms to minimize the number of ORs, while the secondary SP is the uni-level micro balancing SP. Using UHN datasets consisting of two datasets, hard MP/easy SPs and easy MP/hard SPs, we show that both LBBD approaches and both MIP models solved via Gurobi converge to ≈ 2% and ≈ 1–2% optimality gaps, on average, respectively, within 30 minutes runtime, whereas the MIQCP solved via Gurobi could not solve any instance of the UHN datasets given the same runtime. The uni- and bi-level LBBD approaches solved all instances of hard MP/easy SPs dataset to ≈ 11% and ≈ 2% optimality gaps, on average, respectively, within 30 minutes runtime, whereas MIQCP solved via Gurobi could not solve any of these instances. Additionally, we show that convergence of each LBBD varies depending on where in the decomposition the actual computational complexity lies.

Research paper thumbnail of Almost Robust Discrete Optimization

European Journal of Operational Research

Abstract The main goal of this paper is to present a simple and tractable methodology for incorpo... more Abstract The main goal of this paper is to present a simple and tractable methodology for incorporating data uncertainty into optimization models in the presence of binary variables. We introduce the Almost Robust Discrete Optimization (ARDO). ARDO extends the Integrated Chance-Constrained approach, developed for linear programs, to include binary integer variables. Both models trade off the objective function value with robustness and find optimal solutions that are almost robust (feasible under most realizations). These models are attractive due to their simplicity, ability to capture dependency among uncertain parameters, and that they incorporate the decision maker’s attitude towards risk by controlling the degree of conservatism of the optimal solution. To solve the ARDO model efficiently, we decompose it into a deterministic master problem and a single subproblem that checks the master problem solution under different realizations and generates cuts if needed. In contrast to other robust optimization models that are less tractable with binary decision variables, we demonstrate that with these cuts, the ARDO remains tractable. Computational experiments for the capacitated single-source facility location problem where demands in each node are uncertain demonstrate the effectiveness of our approach.

Research paper thumbnail of Reformulation, linearization, and a hybrid iterated local search algorithm for economic lot-sizing and sequencing in hybrid flow shop problems

Computers & Operations Research

Abstract We study an integrated economic lot-sizing and sequencing problem (ELSP) in the hybrid f... more Abstract We study an integrated economic lot-sizing and sequencing problem (ELSP) in the hybrid flow shop manufacturing setting with unlimited intermediate buffers in a finite planning horizon. The ELSP entails making two simultaneous decisions regarding (i) the manufacturing sequences of products, and (ii) their production quantity. The objective is to minimize the total cost, consisting of inventory holding and set-up costs. To solve this problem, we first develop a novel mixed-integer nonlinear programming (MINLP) model that improves an existing MINLP model in the literature. We then present a novel linearization technique that transforms these two MINLP models into effective mixed-integer linear programming (MILP) models. Additionally, we develop an effective algorithm that hybridizes the iterated local search algorithm with an approximate function. We conduct comprehensive experiments to compare the performance of MILPs+CPLEX with that of MINLPs+BARON. Additionally, our proposed algorithm is compared with four existing metaheuristic algorithms in the literature. Computational results demonstrate that our novel MINLP formulation and its linearized variant significantly improve the solvability and optimality gap of an existing MINLP formulation and its linearized variant. We also show that our new hybrid iterated local search algorithm substantially improves computational performance and optimality gap of the mathematical models and the existing algorithms in the literature, on large-size instances of the problem.

Research paper thumbnail of Collaborative Operating Room Planning and Scheduling

INFORMS Journal on Computing

Operating rooms (ORs) play a substantial role in hospital profitability, and their optimal utiliz... more Operating rooms (ORs) play a substantial role in hospital profitability, and their optimal utilization is conducive to containing the cost of surgical service delivery, shortening surgical patient wait times, and increasing patient admissions. We extend the OR planning and scheduling problem from a single independent hospital to a coalition of multiple hospitals in a strategic network, where a pool of patients, surgeons, and ORs are collaboratively planned. To solve the resulting mixed-integer dual resource constrained model, we develop a novel logic-based Benders’ decomposition approach that employs an allocation master problem, sequencing sub-problems for each hospital-day, and novel multistrategy Benders’ feasibility and optimality cuts. We investigate various patient-to-surgeon allocation flexibilities, as well as the impact of surgeon schedule tightness. Using real data obtained from the General Surgery Departments of the University Health Network (UHN) hospitals, consisting of Toronto General Hospit...

Research paper thumbnail of A discrete event simulation evaluation of distributed operating room scheduling

IIE Transactions on Healthcare Systems Engineering, 2016

ABSTRACT Operating room (OR) scheduling is a challenging combinatorial problem and hence most opt... more ABSTRACT Operating room (OR) scheduling is a challenging combinatorial problem and hence most optimization-based OR scheduling research makes simplifying assumptions for tractability, including deterministic surgical durations, absence of dynamic emergency arrivals, and the existence of sufficient downstream resources. In this study, we use discrete event simulation to assess the performance of deterministically optimized OR schedules in a network of collaborating hospitals with shared resources, called distributed OR scheduling (DORS), in the face of uncertain surgical durations, emergency arrivals, and limited downstream resources. We quantify the individual and combined disruptive impact of these stochastic factors on the DORS schedule, using real data obtained from the University Health Network (UHN) in Toronto, Canada. We show that the schedule constructed by DORS results in higher OR utilization and lower average surgery cost compared to the simulated current UHN schedule.