Service scheduling to minimise the risk of missing appointments

Abstract

This paper introduces the risk minimisation objective in the Stochastic Vehicle Routing Problem (SVRP). In the studied variant of SVRP, technicians drive to customer sites to provide service. The service times and travel times are stochastic, and a time window is required for the start of the service for each customer. Most previous research uses a chance-constrained approach to the problem. Some consider the probability of journey duration exceeding the threshold of the driver's workload while others set restrictions on the probability of individual time window constraints being violated. Their objectives are related to traditional routing costs whilst a different approach was taken in this paper. The risk of missing a task is defined as the probability that the technician assigned to the task arrives at the customer site later than the time window. The problem studied in this paper is to generate a schedule that minimises the maximum risk and sum of risks of the tasks. Each task duration may be considered as following a known normal distribution. However the distribution of the start time of the service at a customer site will not be normally distributed due to time window constraints. Therefore a multiple integral expression of the risk was derived, and this expression works whether task distribution is normal or not. Additionally a deterministic heuristic searching method was applied to solve the problem. Experiments are carried out to test the method. Results of this work have been applied to an industrial case of SVRP where field engineering individuals drive to customer sites to provide time-constrained services. This original approach allows organisations to pay more attention to increasing customer satisfaction and become more competitive in the market. Keywords-vehicle routing with time windows; stochastic service time; risk minimisation I.

Scheduling on-site service deliveries to minimise the risk of missing appointment times

“…We use Monte Carlo method for integrals of more than 5-dimensions for better computational efficiency, while using Simpson's rule for integrals for 5-dimensions or lower for better accuracy. For the details of the approach please refer to Ji et al (2018).…”

Incorporating Risk in Field Services Operational Planning Process

“…The risk in the problem is defined as the probability that the arrival time is after the upper limit of the time window [14]. More specifically, as it is shown in the Fig.1, given a schedule, with a sequence of tasks { 1 , 2 , 3 , ⋯ } allocated to technician , 1 , 2 , 3 … are the task duration times, 0 1 is the travel time from the depot of technician to his first task, 1 2 , 2 3 , 3 4 are the travel times between tasks ( .…”

“…Moreover, an important property is that the risk increases simultaneously as it propagates for each technician, it is reasonable because the uncertainty aggregates as there is more uncertainty of the travel time and task time. In addition, from a previous study [14], the mathematical expression of risks can be derived as…”

“…Constraints (13) indicate that each customer is served by one technician. Constraints (14) and 15make sure that the task list of each technician is consecutive. Constraints (16) show that for each technician the arrival time of the current task is the previous task start time combined with the previous task duration and the travel time to the current task.…”