Ran Liu

A branch-and-price algorithm for the home health care scheduling and routing problem with stochastic service times and skill requirements

Home health care (HHC) is defined as providing medical and paramedical services for patients at their own domicile. In the HHC industry, it is crucial for health care organisations to assign caregivers to patients and devise reasonable visiting routes to save total operational cost and improve the service quality. However, some special constraints make the problem hard to solve. For example, patients’ service times are usually stochastic due to their varying health conditions; caregivers are organised in a hierarchical structure according to their skills to satisfy patients’ demands. In this paper, we address a HHC scheduling and routing problem with stochastic service times and skill requirements. A stochastic programming model with recourse is proposed to formulate the problem in which the expected penalty for late arrival at customers is considered. To solve the problem, it is equivalently transformed into a master problem and a pricing sub-problem. A column generation algorithm is developed to solve the relaxation of the master problem and obtain its lower bound. A label algorithm and several effective accelerating techniques are devised to solve the pricing sub-problem. To obtain feasible solutions, the column generation procedure is embedded within the branch and bound framework. The effectiveness of the proposed algorithm is validated through numerical experiments.

Mathematical model and exact algorithm for the home care worker scheduling and routing problem with lunch break requirements

Home health care or home care (HHC/HC) refers to the delivery of social, medical and paramedical services to clients in their own homes. Each day, care workers start from the HHC/HC centre, visit some clients and return to the centre. During the service delivery process, there is usually a lunch break for each worker. In this paper, we address a real-life home care worker scheduling and routing problem with the consideration of lunch break requirements. A three-index mathematical model is constructed for the problem. The problem is decomposed into a master problem and several pricing sub-problems, and is optimally solved by a branch-and-price (B&P) algorithm. Specifically, a sophisticated label-correcting algorithm is designed to address lunch break constraints in pricing sub-problems; some cutting-edge acceleration strategies are applied during the column generation process. Experimental results show that the proposed B&P algorithm is able to produce satisfied solutions within an acceptable runtime and outperforms the mixed integer programming solver CPLEX.

Simulation-based optimisation approach for the stochastic two-echelon logistics problem

This work proposes a simulation-based optimisation approach for the two-echelon vehicle routing problem with stochastic demands (2E-VRPSD). In the proposed 2E-VRPSD, freight delivery from the depot to the customers is managed by shipping the freight through intermediate satellites, while each customer has a stochastic demand. The 2E-VRPSD is an extension of the famous capacitated vehicle routing problem with stochastic demands and the two-echelon vehicle routing problem (2E-VRP). A tabu search algorithm is designed to solve the 2E-VRPSD, in which Monte Carlo sampling is adopted to tackle the issue of stochastic demands. Modified two-echelon vehicle routing problem benchmark instances are used in the numerical experiments. The computational results show the advantage of the proposed simulation-based approach.

A survey on simulation optimization for the manufacturing system operation

Abstract Stochastic effects exist in a great number of manufacturing system operation problems. Simulation optimization methods are widely used for tackling the stochasticity. In order to provide a comprehensive coverage of simulation optimization publications with a focus on applications in manufacturing system operation logically, we classify the literature into two general categories of local optimization and global optimization. The local optimization literature is further divided into two subclasses based on the parameter spaces (discrete or continuous parameters). In each class, we explain how the corresponding methods integrated with simulation solve major manufacturing system operation problems, such as long- and short-term production planning, flow shop scheduling, and job shop scheduling. Finally, the current research status on simulation optimization for manufacturing operations is summarized. Meanwhile, some key issues, such as lack of unified problem benchmarks for comparison and low computational efficiency for real-scale problems, which need future research in this field, are discussed as well.

A memetic algorithm for the close-open mixed Vehicle Routing Problem

Nowadays in the transportation industry carriers reduce the costs through collaboration, e.g., sharing the assets and tasks with other collaborative partners. In this paper, an optimization problem called the Close-Open Mixed Vehicle Routing Problem (COMVRP) is discussed, that can be used to assist in identifying routes when a carrier serves the customers through his private vehicles and vehicles hired from external carriers. The objective of the problem is to minimize the fixed and variable costs for operating the private vehicles and the hired vehicles. A mix integer programming (MIP) model and an effective memetic algorithm are established for the COMVRP. Computational experiments are conducted. The results show that the proposed algorithm is able to produce high reasonable solutions within an acceptable running time, and always outperforms the robust MIP solver CPLEX.

Daily scheduling of caregivers with stochastic times

This paper addresses a daily caregiver scheduling and routing problem arising in home health care or home care service providers. The problem is quite challenging due to its uncertainties in terms of travel and service times derived from changes in road traffic conditions and customer health status in practice. We first model the problem as a stochastic programme with recourse, where the recourse action is to skip customers without services if the caregiver arrives later than their latest starting service time (i.e. hard time window requirements). Then, we formulate the problem as a set partitioning model and solve it with a branch-and-price (B&P) algorithm. Specifically, we devise an effective discrete approximation method to calculate the arrival time distribution of caregivers, incorporate it into a problem-specific label algorithm, and use a removal-and-insertion-based heuristic and the decremental state-space relaxation technique to accelerate the pricing process. Finally, we conduct numerical experiments on randomly generated instances to validate the effectiveness of the discrete approximation method and the proposed B&P algorithm.

Optimal patient assignment for W queueing network in a diagnostic facility setting

Quick examination is becoming increasingly critical for the diagnosis of patients. Increasing demand and insufficient diagnostic facilities lead to longer patient waiting times. It is important for hospital managers to reduce the waiting time of high-priority patients. To reduce the patients’ waiting time, the capacity in working time is divided into special time slots for high-priority patients and regular time slots for all patients. Low-priority patients are allowed to be referred to extra time slots by overtime or using the capacity of other hospitals. Two types of patients and three types of capacities form a W queueing network. This paper proposes an average-cost Markov Decision Process (MDP) model to assign the patients to the appropriate queue with the objective of minimising the weighted waiting cost and referral penalty. Structural properties of the optimal control policy under a given capacity are proved via discount-cost MDP. Extensive numerical experiments are performed to show the efficiency of the proposed patient assignment policy and to explore the impact of different parameters on the control policy.

Real-time scheduling home caregivers based on disruption management

Unexpected disruptions often occur when home caregivers provide service for customers, such as new requests of customers, cancellations of customers services, and changes of customers time windows. These disruptions sometimes may make the original plan non optimal or even infeasible. In practice the strategy of rescheduling is usually utilized to obtain a new plan with minimal operational cost, but largely deviates from the original one. To address this kind of situation, we introduce the principle of disruption management into the real-time or disrupted home caregiver scheduling problem. We first define the disruption measurements on customers, caregivers and companies, then take them as the minimization objective, and finally employ a tabu search algorithm with a cost record mechanism to solve the proposed problem. The performance of the strategies of rescheduling and disruption management is compared and discussed in the case study.

A heuristic algorithm for the Load-dependent Capacitated Vehicle Routing Problem with Time Windows

In this paper we introduce an extension of the vehicle routing problem with time windows (VRPTW) called the Load-dependent Capacitated Vehicle Routing Problem with Time Windows (LDVRPTW). This problem differs from the classical VRP and VRPTW on the transportation costs, which are calculated not only on the travel distance, but also the loads on the arcs. We propose a metaheuristic to address this LDVRPTW problem. The proposed algorithm is tested on benchmark instances on special case problems of LDVRPTW. Numerical results show that on some LDVRPTW variants our metaheuristic outperforms the available state-of-the-art exact and heuristic methods.

A decentralized VPLs based control policy for semiconductor manufacturing

In this paper, we propose a decentralized VPLs based control policy for semiconductor manufacturing. Based on utilizations and entropies, a new classification method is designed to decentralize global objectives into local objectives of workstations. Then a decentralized multi-objective scheduling policy is proposed to control Virtual Production Lines (VPLs). We generate two SMS cases from a test bed in order to evaluate multiple performances of the proposed policy. Experimental results validate the effectiveness in solving multi-objective scheduling problems for the semiconductor manufacturing system.