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International Journal of Networking and Computing

Applying Quantum Annealing for Shift Scheduling Problem for Call Centers

Natsuki Hamada, Kazuhiro Saito, Hideyuki Kawashima

Published Jan 1, 2023• 4 citations
Publisher

Abstract

Quantum annealing (QA) has shown good solutions quickly in benchmarks of combinatorial optimization problems. There are not many real-world problems that illustrate the effectiveness of QA compared to the typical optimization methods. We applied QA to a shift scheduling problem for call centers with four conditions. The shift scheduling problem for call centers optimizes shifts for a specific period of time while satisfying various constraints, such as satisfying the desired worker's shifts. In this paper, we formulated the shift scheduling problem for call centers in QUBO to apply QA. We tuned various parameters required to execute the QA. Then, we compared QA with six typical optimization methods using a classical computer to investigate QA's effectiveness for the shift scheduling problem for call centers. The results show that for three instances with up to 126 variables, QA is about 3-14 times faster than other methods and obtains enough quality of solutions. This shows that QA can be one of the effective methods to solve practical applications in the real-world.

DOI
10.15803/ijnc.13.1_2

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Quantum annealing (QA) has shown good solutions quickly in benchmarks of combinatorial optimization problems. There are not many real-world problems that illustrate the effectiveness of QA compared to the typical optimization methods. We applied QA to a shift scheduling problem for call centers with four conditions. The shift scheduling problem for call centers optimizes shifts for a specific period of time while satisfying various constraints, such as satisfying the desired worker's shifts. In this paper, we formulated the shift scheduling problem for call centers in QUBO to apply QA. We tuned various parameters required to execute the QA. Then, we compared QA with six typical optimization methods using a classical computer to investigate QA's effectiveness for the shift scheduling problem for call centers. The results show that for three instances with up to 126 variables, QA is about 3-14 times faster than other methods and obtains enough quality of solutions. This shows that QA can be one of the effective methods to solve practical applications in the real-world.
Quantum annealing (QA) is a novel computing approach for solving computationally demanding problems more rapidly than approaches using classical computers by exploiting parallelism in the variable state updates (spin updates). A number of previous studies have shown that QA performs well in benchmarking combinatorial optimization problems, but no works have evaluated QA in the shift scheduling problem. This paper formulates it for QA and evaluates the effectiveness of QA in comparison with other methods on a classical computer. We confirmed that QA is up to about 14 times faster than classical methods in obtaining high-quality solutions for several instances.
Quantum annealing is a promising heuristic method to solve combinatorial optimization problems, and efforts to quantify performance on real-world problems provide insights into how this approach may be best used in practice. We investigate the empirical performance of quantum annealing to solve the Nurse Scheduling Problem (NSP) with hard constraints using the D-Wave 2000Q quantum annealing device. NSP seeks the optimal assignment for a set of nurses to shifts under an accompanying set of constraints on schedule and personnel. After reducing NSP to a novel Ising-type Hamiltonian, we evaluate the solution quality obtained from the D-Wave 2000Q against the constraint requirements as well as the diversity of solutions. For the test problems explored here, our results indicate that quantum annealing recovers satisfying solutions for NSP and suggests the heuristic method is potentially achievable for practical use. Moreover, we observe that solution quality can be greatly improved through the use of reverse annealing, in which it is possible to refine returned results by using the annealing process a second time. We compare the performance of NSP using both forward and reverse annealing methods and describe how this approach might be used in practice.
Abstract Quantum Annealing (QA) is a metaheuristic for solving optimization problems in a time-efficient manner. Therefore, quantum mechanical effects are used to compute and evaluate many possible solutions of an optimization problem simultaneously. Recent studies have shown the potential of QA for solving such complex assignment problems within milliseconds. This also applies for the field of job shop scheduling, where the existing approaches however focus on small problem sizes. To assess the full potential of QA in this area for industry-scale problem formulations, it is necessary to consider larger problem instances and to evaluate the potentials of computing these job shop scheduling problems while finding a near-optimal solution in a time-efficient manner. Consequently, this paper presents a QA-based job shop scheduling. In particular, flexible job shop scheduling problems in various sizes are computed with QA, demonstrating the efficiency of the approach regarding scalability, solutions quality, and computing time. For the evaluation of the proposed approach, the solutions are compared in a scientific benchmark with state-of-the-art algorithms for solving flexible job shop scheduling problems. The results indicate that QA has the potential for solving flexible job shop scheduling problems in a time efficient manner. Even large problem instances can be computed within seconds, which offers the possibility for application in industry.
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of qubits and their connectivity, the QA hardware did not show such an advantage over classical methods in past benchmarking studies. Recent advancements in QA with more than 5000 qubits, enhanced qubit connectivity, and the hybrid architecture promise to realize the quantum advantage. Here, we use a quantum annealer with state-of-the-art techniques and benchmark its performance against classical solvers. To compare their performance, we solve over 50 optimization problem instances represented by large and dense Hamiltonian matrices using quantum and classical solvers. The results demonstrate that a state-of-the-art quantum solver has higher accuracy (~0.013%) and a significantly faster problem-solving time (~6561×) than the best classical solver. Our results highlight the advantages of leveraging QA over classical counterparts, particularly in hybrid configurations, for achieving high accuracy and substantially reduced problem solving time in large-scale real-world optimization problems.
Job Shop Scheduling is a combinatorial optimization problem of particular importance for production environments where the goal is to complete a production task in the shortest possible time given limitations in the resources available. Due to its computational complexity it quickly becomes intractable for problems of interesting size. The emerging technology of Quantum Annealing provides an alternative computational architecture that promises improved scalability and solution quality. However, several limitations as well as open research questions exist in this relatively new and rapidly developing technology. This paper studies the application of quantum annealing to solve the job shop scheduling problem, describing each step required from the problem formulation to the fine-tuning of the quantum annealer and compares the solution quality with various classical solvers. Particular attention is devoted to aspects that are often overlooked, such as the computational cost of representing the problem in the formulation required by the quantum annealer, the relative qubits requirements and how to mitigate chain breaks. Furthermore, the impact of advanced tools such as reverse annealing is presented and its effectiveness discussed. The results indicate several challenges emerging at various stages of the experimental pipeline which bring forward important research questions and directions of improvement.
Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling problems, have been applied to automate this process, solving large-scale production planning problems remains computationally demanding. Moreover, many practical scenarios involve conflicting objectives, making traditional scalarization techniques ineffective in finding diverse and useful Pareto-optimal solutions. To address these challenges, we developed a quantum-classical hybrid algorithm that decomposes the problem into two subproblems: resource allocation and task scheduling. Resource allocation is formulated as a quadratic unconstrained binary optimization problem and solved using annealing-based methods that efficiently explore complex solutions. Task scheduling is modeled as a mixed-integer linear programming problem and solved using conventional solvers to satisfy detailed scheduling constraints. We validated the proposed method using benchmark instances based on foundry production scenarios. Experimental results demonstrate that our hybrid approach achieves superior solution quality and computational efficiency compared to traditional monolithic methods. This work offers a promising direction for high-speed, multi-objective scheduling in industrial applications.