Skill Vehicle Routing Problem With Time Windows Considering Dynamic Service Times and Time-Skill-Dependent Costs

Abstract

Service processes in modern logistic systems tend to be highly specialized and intellectualized. However, some casual and unexpected behavior may occur, causing specific dynamic interactions among their many constituents. As such, the optimization and modeling of complex problems have become increasingly tough. Besides, technicians typically need to possess appropriate skills that match assigned tasks. Faced with real service scenarios, however, employees inevitably suffer from an increasing level of fatigue attributed to continuous work, resulting in a gradual decrease in the efficiency of workers over time. In this situation, the service time for a given task can no longer be treated as a constant, but instead, it should be treated as dynamic. Moreover, highly skilled technicians are usually paid higher than the junior ones with basic or lower skill level, which introduces new challenges in the optimization of service task schedules' problem. In this paper, we first present the skill vehicle routing problem considering dynamic service times and time-skill-dependent costs, in which the efficiencies of the workers are dynamically affected by their fatigue levels, and the costs, i.e., salaries paid to the employees, are related to skill levels and continuous work time. Furthermore, we develop a comprehensive and general mixed-integer linear programming dynamicbased model to formulate the proposed problem, which is directly solvable by MIP solvers for small-sized problems. We also initiate an iteratively dynamic neighborhood search (IDNS) algorithm that combines iterative partial optimization with dynamic neighborhood search to efficiently solve large-sized problems with near-optimal solutions. The comprehensive computational experiments were performed on the problems of different sizes to test the effectiveness and efficiency of the proposed model and solution approach. Some useful managerial insights were obtained from the computational results that can help decision-makers to determine cost-effective service routes and schedules in complex transportation-related issues. INDEX TERMS Skill vehicle routing problem, dynamic service times, time-skill-dependent costs, dynamic-based modeling, iteratively dynamic neighborhood search algorithm.

Matheuristics and Column Generation for a Basic Technician Routing Problem

“…This results in a multi-objective extension and minimizing routing costs conjointly with the maximization of route balance for better equity and robustness relative to uncertainty [28]. Recently, an extension of skill VRPTW was proposed by taking into account that intervention time depends on the skill levels [29].…”

“…Note that, here, elementarity is not a necessary condition; it is implied by the optimality with triangle inequality and not necessary for the validity of the MILP formulation contrary to previous compact MILP formulations. Constraints (29) enforce that at most one route is chosen for each technician, and it is possible to have only zeros for technicians that are not leaving their depots.…”

“…This negativity question among a non-enumerable set is formulated as an optimization problem, minimizing the reduced costs of the columns that are not in ∪ i C i . These negativity questions are decomposed for all technicians, RC * = min i RC * i , where RC * i is the minimization problem over the possible routes for technician i, and RC * 0 ensures that the RMP gives the LP relaxation of ( 27)- (29). The computations of RC * i are independent for the technicians and can be formulated using MILP formulations of Section 4.…”

“…Constraints (28) are written with inequalities, and the MILP model is still valid with equalities instead. One could also have equalities in (29), defining explicitly empty routes. Using inequalities induces a better stability of the column generation algorithm, with signed dual variables π, σ [11].…”

Node and Edge Drone Surveillance Problem With Consideration of Required Observation Quality and Battery Replacement

“…We list only the #alt2 values. The last term is used to assess the workload balance of the drones [52] that is related to the makespan minimization. Gaps of the z values are defined as (z ARTS − z Firefly )/z Firefly × 100, whereas the gaps of other KPIs are defined as (z ARTS − z Firefly ).…”