Uncertain Service Times Research Articles

A Bi-Objective Home Health Care Routing and Scheduling Problem under Uncertainty.

Home health care companies provide health care services to patients in their homes. Due to increasing demand, the provision of home health care services requires effective management of operational costs while satisfying both patients and caregivers. In practice, uncertain service times might lead to considerable delays that adversely affect service quality. To this end, this paper proposes a new bi-objective optimization problem to model the routing and scheduling problems under uncertainty in home health care, considering the qualification and workload of caregivers. A mixed-integer linear programming formulation is developed. Motivated by the challenge of computational time, we propose the Adaptive Large Neighborhood Search embedded in an Enhanced Multi-Directional Local Search framework (ALNS-EMDLS). A stochastic ALNS-EMDLS is introduced to handle uncertain service times for patients. Three kinds of metrics for evaluating the Pareto fronts highlight the efficiency of our proposed method. The sensitivity analysis validates the robustness of the proposed model and method. Finally, we apply the method to a real-life case and provide managerial recommendations.

Multi-objective migrating birds optimization for solving stochastic home health care routing and scheduling problems considering caregiver working time constraints

Currently, many countries are suffering from a heavy burden caused by population aging since the elderly occupy a large number of medical resources. Home health care (HHC) is a prospective approach to relieve and cope with this issue. This study addresses a multi-objective HHC routing and scheduling problem (HHCRSP) considering uncertainties and caregivers’ working time balance. First, a stochastic programming method is employed to formulate the uncertain service time and travel time, and then a chance-constrained programming model is developed to minimize the total operation cost and penalty cost of violating allowable time windows. Second, a multi-objective migrating birds optimization incorporating a stochastic simulation method is proposed. An ensemble of population iteration and external archive search is designed to obtain high-quality solutions. A stochastic simulation strategy is devised to evaluate the feasibility of obtained solutions and calculate their objective values. At last, numerical experiments are implemented for solving an extending benchmark set. The comparisons and discussions verify the better performance of the proposed algorithm compared with its peers.

Stochastic optimization models for a home service routing and appointment scheduling problem with random travel and service times

We address a routing and appointment scheduling problem with uncertain service and travel times arising from home service practice. Specifically, given a set of customers within a service region that an operator needs to serve, we seek to find the operator’s route and time schedule. The quality of routing and scheduling decisions is a function of the total operational cost, consisting of customers’ waiting time, and the operator’s travel time, idle time and overtime. We propose and rigorously analyze a stochastic programming model and two distributionally robust optimization (DRO) models to solve the problem, assuming known and unknown service and travel time distributions, respectively. We consider two popular types of ambiguity sets for the DRO models: mean-support and 1-Wasserstein ambiguity sets. We derive equivalent mixed-integer linear programming (MILP) reformulations of both DRO models that can be implemented and efficiently solved using off-the-shelf optimization software, thereby enabling practitioners to use these models. In an extensive numerical experiment, we investigate the proposed models’ computational and operational performance and derive insights into the problem.

Demand prediction based slice reconfiguration using dueling deep Q-network

To satisfy diversified service demands of vertical industries, network slicing enables efficient resource allocation of a common infrastructure by creating isolated logical networks. However, uncertainty and dynamics of service demands will cause performance degradation. Due to operation costs and resource constraints, it is challenging to maintain high quality of user experience while obtaining high revenue for service providers (SPs). This paper develops an optimal and fast slice reconfiguration (OFSR) framework based on reinforcement learning, where a novel scheme is proposed to offer optimal decisions for reconfiguring diverse slices. A demand prediction model is proposed to capture changes in resource requirements, based on which the OFSR scheme is triggered to determine whether to perform slice reconfiguration. Considering the large state and action spaces generated from uncertain service time and resource requirements, deep dueling architecture is adopted to improve the convergence rate. Extensive simulations validate the effectiveness of the proposed framework in achieving higher long-term revenue for SPs.

Modeling stochastic service time for complex on-demand food delivery

Uncertainty is everywhere in the food delivery process, which significantly influences decision-making for complex on-demand food delivery problems, affecting delivery efficiency and customer satisfaction. Especially, the service time is an indispensable part of the delivery process impacted by various uncertain factors. Due to the simplicity and high accuracy requirement, we model the uncertain service time as a Gaussian mixture model (GMM). In detail, we transform the distribution estimation problem into a clustering problem by determining the probability of each data belonging to each component (each cluster as well). A hybrid estimation of distribution algorithm is proposed to intelligently solve the clustering problem with the criterion to optimize quality and simplicity simultaneously. First, to optimize the simplicity, problem-specific encoding and decoding methods are designed. Second, to generate initial solutions with good clustering results, a Chinese restaurant process-based initialization mechanism is presented. Third, a weighted-learning mechanism is proposed to effectively guide the update of the probability model. Fourth, a local intensification based on maximum likelihood is used to exploit better solutions. The effect of critical parameters on the performances of the proposed algorithm is investigated by the Taguchi design of the experimental method. To demonstrate the effectiveness of the proposed algorithm, we carry out extensive offline experiments on real-world historical data. Besides, we employ the GMMs obtained by our algorithm in a real-world on-demand food delivery platform, Meituan, to assist decision-making for order dispatching. The results of rigorous online A/B tests verify the practical value of introducing the uncertainty model into the real-life application.

Workload Balancing Among Heathcare Workers Under Uncertain Service Time Using Distributionally Robust Optimization

Healthcare systems are facing serious challenges in balancing their human resources to cope with volatile service demand, while at the same time providing necessary job satisfaction to the healthcare workers. In this paper, we propose a distributionally robust optimization formulation to generate a task assignment plan that promotes the fairness in allocation, attained by reducing the difference in the total working time among workers, under uncertain service time. The proposed joint chance constraint model is conservatively approximated by a worst-case Conditional Value-at-Risk, and we devise a sequential algorithm to solve the finite-dimensional reformulations which are linear (mixed-binary) optimization problems. We also provide explicit formula in the situation where the support set of the random vectors is a hyperrectangle. The experiment with both synthetic and real data indicates promising results for our distributionally robust optimization approach.

Routing optimization of shared autonomous electric vehicles under uncertain travel time and uncertain service time

The emerging autonomous electric vehicles have facilitated the implementation of the shared autonomous electric vehicle (SAEV) service. In real-life applications, the operations of SAEVs may be affected by various uncertain factors, such as uncertain travel time caused by traffic congestion and uncertain service time caused by unpredictable customer delay. It is essential to consider uncertain factors to design conservative and robust routes for SAEVs. In this paper, we study a routing optimization problem of SAEVs, where the charging schedules, uncertain travel time, and uncertain service time are considered. The objective of the problem is to minimize the total operational cost that consists of fixed cost and travel cost of SAEVs. A branch-and-price algorithm is developed to solve the problem. Specifically, a tailored label setting algorithm is introduced to identify the robust feasible routes with accessible charging schedules for the pricing subproblem. The proposed algorithm is tested on a set of generated instances. The computational results indicate that the proposed algorithm outperforms the commercial solver CPLEX in terms of both solution quality and computational time. Besides, based on the sensitivity analyses, we show the impact of the budgets of uncertainty, maximum deviations of uncertain parameters, battery capacity, fixed cost, and charging speed on the SAEV service. This work can also provide inspirations of both models and algorithms for many other application areas, such as urban logistics.

A deep reinforcement learning based hyper-heuristic for combinatorial optimisation with uncertainties

In the past decade, considerable advances have been made in the field of computational intelligence and operations research. However, the majority of these optimisation approaches have been developed for deterministically formulated problems, the parameters of which are often assumed perfectly predictable prior to problem-solving. In practice, this strong assumption unfortunately contradicts the reality of many real-world problems which are subject to different levels of uncertainties. The solutions derived from these deterministic approaches can rapidly deteriorate during execution due to the over-optimisation without explicit consideration of the uncertainties. To address this research gap, a deep reinforcement learning based hyper-heuristic framework is proposed in this paper. The proposed approach enhances the existing hyper-heuristics with a powerful data-driven heuristic selection module in the form of deep reinforcement learning on parameter-controlled low-level heuristics, to substantially improve their handling of uncertainties while optimising across various problems. The performance and practicality of the proposed hyper-heuristic approach have been assessed on two combinatorial optimisation problems: a real-world container terminal truck routing problem with uncertain service times and the well-known online 2D strip packing problem. The experimental results demonstrate its superior performance compared to existing solution methods for these problems. Finally, the increased interpretability of the proposed deep reinforcement learning hyper-heuristic has been exhibited in comparison with the conventional deep reinforcement learning methods.

A robust home health care routing-scheduling problem with temporal dependencies under uncertainty

Inspiring by real-world assumptions, this paper aims to present a robust optimization model for a home health care routing-scheduling problem with uncertain service and travel times. The constraints include temporal precedence and synchronization constraints, timing constraints for the transferring biological samples, and constraints associated with the multiple deployments of caregivers to provide the possibility of visiting one patient multiple times in the one-day planning horizon. Also, the existing uncertainty in service and travel times arising from an increase in customer-oriented service strategies is another crucial issue that should be appropriately addressed. Due to the complexity of this problem, three meta-heuristic algorithms (i.e., simulated annealing, genetic algorithm, and memetic algorithm) are proposed to solve the developed model. A series of experiments are implemented and shown that the memetic algorithm outperforms other proposed algorithms for large-sized problems. Furthermore, a detailed analysis of the results achieved by solving deterministic and robust models demonstrates the advantage of using the robust model. Finally, the dynamic version of this problem is proposed, and two dispatching policies are used to address this problem.

Multithreading Parallel Robust Approach for the VRPTW with Uncertain Service and Travel Times

The objective of this paper is to consider the vehicle routing problem with time windows under two uncertainties: service and travel times. We introduce new resolution approaches for the robust problem and an efficient parallel procedure for the generation of all possible scenarios. The best robust solution of each scenario can be achieved by using a parallel adaptive large neighborhood search metaheuristic. Through our analysis, we expect to find the best compromise between the reduced running time and a best good solution, which leads to four distinct combinations of parallel/sequential approaches. The computational experiments are performed and tested on Solomon’s benchmark and large randomly generated instances. Furthermore, our results can be protected against delay in service time in a reasonable running time especially for large instances.

Surgery scheduling in outpatient procedure centre with re-entrant patient flow and fuzzy service times

To meet the increase in demand for outpatient surgical services, surgery scheduling for outpatient procedure centres (OPCs) has recently attracted considerable attention in both the healthcare industry and the academic community. This paper considers a novel OPC daily surgery scheduling problem (ODSSP) to minimise the average recovery completion time of all patients. To satisfy the OPC surgical practice, patient intake and recovery are applied in the same area for more resource flexibility, and uncertain service times for intake, surgical procedures and recovery are considered. Owing to the similarities shared between healthcare delivery systems and production systems, ODSSP is formulated as a two-stage no-wait re-entrant hybrid flow shop scheduling problem with fuzzy service times. Considering the NP-hardness of such scheduling problem, a new hybrid meta-heuristic (GA-BAVNS) is employed to obtain detailed daily OPC surgery schedules. To achieve greater balance between exploration and exploitation in the search space, GA-BAVNS hybridises a genetic algorithm (GA) and a variable neighbourhood search (VNS) to schedule outpatients for surgical services. To improve the local search performance of the VNS, six novel block-based neighbourhood structures are employed to generate neighbourhood solutions. Moreover, an adaptive neighbourhood change procedure (ANCP) is employed to systematically change the search order of neighbourhood structures for better solutions. Computational results on a set of test problems indicate the superiority of the proposed GA-BAVNS.

A robust approach for solving a vehicle routing problem with time windows with uncertain service and travel times

A robust approach for solving a vehicle routing problem with time windows with uncertain service and travel times

Surgical case scheduling problem with fuzzy surgery time: An advanced bi-objective ant system approach

We address the bi-objective surgical case scheduling problem under uncertain service times. The goal is to simultaneously minimize (i) makespan and (ii) number of unscheduled surgical cases. We optimize two decisions in our surgical case scheduling problem: the allocation of the resources to the surgical cases and their starting times. We formulate our problem as a novel bi-objective no-wait multi-resource flexible job shop problem. We use fuzzy numbers to represent the inherent stochasticity in the length-of-stays of patients in different stages of an operating theater. Due to the intractability of the problem even for small instances, we develop a novel bi-objective ant system: Fuzzy Pareto Envelope-based Selection Ant System. The performance of the new algorithm on all test instances is compared to a basic bi-objective ant system under the fuzzy condition: Pareto strength ant colony optimization. Finally, we demonstrate computationally that our approach outperforms the state-of-the-art algorithm in literature in terms of both efficiency and effectiveness.

The resampling M/G/1 non-preemptive LIFO queue and its application to systems with uncertain service time

We introduce and analyse the M∕G∕1 resampling queue with non-preemptive LIFO policy, then we use it to provide bounds on the performance characteristics of an M∕G∕1 processor sharing queue with inaccurate service time information.

Optimal and Fast Real-Time Resource Slicing With Deep Dueling Neural Networks

Effective network slicing requires an infrastructure/network provider to deal with the uncertain demands and real-time dynamics of the network resource requests. Another challenge is the combinatorial optimization of numerous resources, e.g., radio, computing, and storage. This paper develops an optimal and fast real-time resource slicing framework that maximizes the long-term return of the network provider while taking into account the uncertainty of resource demands from tenants. Specifically, we first propose a novel system model that enables the network provider to effectively slice various types of resources to different classes of users under separate virtual slices. We then capture the real-time arrival of slice requests by a semi-Markov decision process. To obtain the optimal resource allocation policy under the dynamics of slicing requests, e.g., uncertain service time and resource demands, a Q-learning algorithm is often adopted in the literature. However, such an algorithm is notorious for its slow convergence, especially for problems with large state/action spaces. This makes Q-learning practically inapplicable to our case, in which multiple resources are simultaneously optimized. To tackle it, we propose a novel network slicing approach with an advanced deep learning architecture, called deep dueling, that attains the optimal average reward much faster than the conventional Q-learning algorithm. This property is especially desirable to cope with the real-time resource requests and the dynamic demands of the users. Extensive simulations show that the proposed framework yields up to 40% higher long-term average return while being few thousand times faster, compared with the state-of-the-art network slicing approaches.

The surgical case scheduling problem with fuzzy duration time: An ant system algorithm

In this paper, we address the surgical case scheduling problem in multi operating theater environment with uncertain service times in order to minimize makespan. In surgical case scheduling, not only the hospital resources are allocated to surgical cases but also the start time of performing surgeries is determined based on sequence of cases in a short-term time horizon. We consider fuzzy numbers for duration times of all stages and hereafter the problem called fuzzy surgical case scheduling. Since the operational environment in the problem is similar to no-wait multi-resource fuzzy flexible job shop problem, we consider constraints of that for formulating and solving problem. This problem is strongly an NP-hard optimization problem, hence we employ ant system algorithm to tackle problem. The proposed approach is illustrated by detailed examples of three test cases, and numerical computational experiments. Therefore, the performance of proposed algorithm is compared with a schedule constructed by first-come-first-service rule on all test instances. Also, a real case is provided from Isfahan’s hospital to evaluate proposed algorithm. Consequently, computational experiments state that algorithm outperforms results obtained by hospital planning as well as fuzzy rule, and these indicate efficiency and capability of our algorithm for optimizing the makespan.

Mitigating Delays and Unfairness in Appointment Systems

We consider an appointment system where heterogeneous participants are sequenced and scheduled for service. Because service times are uncertain, the aims are to mitigate the unpleasantness experienced by the participants in the system when their waiting times or delays exceed acceptable thresholds and to address fairness in the balancing of service levels among participants. To evaluate uncertain delays, we propose the Delay Unpleasantness Measure, which takes into account the frequency and intensity of delays above a threshold, and introduce the concept of lexicographic min-max fairness to design appointment systems from the perspective of the worst-off participants. We focus our study in the healthcare industry in balancing physicians’ overtime and patients’ waiting times in which patients are distinguished by their service time characterizations. The model can be adapted in the robust setting when the underlying probability distribution is not fully available. To capture the correlation between uncertain service times, we suggest using the mean absolute deviations as the descriptive statistics in the distributional uncertainty set to preserve the linearity of the model. The optimal sequencing and scheduling decisions can be derived by solving a sequence of mixed-integer programming problems, and we report the insights from our computational studies.This paper was accepted by Yinyu Ye, optimization.

Speed optimization and bunkering in liner shipping in the presence of uncertain service times and time windows at ports

Recent studies in maritime shipping have concentrated on environmental and economic impacts of ships. In this regard, fuel is considered as one of the important factors for such impacts. In particular, the sailing speed of the vessels affects the fuel consumption directly. In this study, we consider a speed optimization problem in liner shipping, which is characterized by stochastic port times and time windows. The objective is to minimize the total fuel consumption while maintaining the schedule reliability. We develop a dynamic programing model by discretizing the port arrival times to provide approximate solutions. A deterministic model is presented to provide a lower bound on the optimal expected cost of the dynamic model. We also work on the effect of bunker prices on the liner service schedule. We propose a dynamic programing model for bunkering problem. Our numerical study using real data from a European liner shipping company indicates that the speed policy obtained by proposed dynamic model performs significantly better than the ones obtained by benchmark methods. Moreover, our results show that making speed decisions considering the uncertainty of port times will noticeably decrease fuel consumption cost.

Application of a fuzzy ant colony system to solve the dynamic vehicle routing problem with uncertain service time

Service management has been an important issue for many companies, especially for service-based companies. This paper studies a routing problem that is usually faced by on-site service companies. This type of company continuously receives orders during its working hours. In order to maximize the number of customers served and minimize the customer waiting time, the service team is responsible for determining which orders should be served during the ongoing working period and which orders should be served in the following working period. This paper represents this problem as a dynamic vehicle routing problem (DVRP). The proposed DVRP model also considers the uncertain service time using fuzzy theory. Furthermore, an algorithm using an improved fuzzy ant colony system (ACS) is proposed in order to solve the proposed model. The proposed algorithm embeds a cluster insertion algorithm into the ACS algorithm. The proposed algorithm is validated using some benchmark datasets. The results show that the proposed algorithm performs better than the previous fuzzy-ACS algorithm without cluster insertion algorithm. In addition, further sensitivity analysis is also presented to derive more information about the model and the proposed algorithm for application to real-world problems.

Dynamic arc routing problem in road maintenance service with uncertain travel and service times

This paper describes a dynamic arc routing problem motivated by daily maintenance operations on road networks to improve the maintenance efficiency. Uncertain service and travel times on road segments are considered and defined using discrete stochastic distribution. An algorithm based on the multiple scenario approach (MSA) is developed to deal with the uncertainty of the network. The MSA scheme is triggered to update the maintenance routing by an event-driven mechanism. The computational experiments demonstrate the effectiveness of the algorithm.