Lagrangian Heuristic for Multi-Depot Technician Planning of Product Distribution and Installation with a Lunch Break

Abstract

In this paper, we consider a technician planning scheme stemming from product distribution and installation in a manufacturing enterprise that considers factors such as soft time windows, skill areas, lunch breaks, and outsourcing options, among others. The goal is to identify the optimal partition of technicians into groups and assignment of customers to technician groups and find the optimal routes for technician groups to minimize the sum of the travel cost, soft time window violation cost, and outsourcing cost. To address this problem, the study develops a tailored Lagrangian heuristic that incorporates several strategies to speed up convergence and produce sharper bounds. Computational comparisons between the developed heuristic and MIP solver are presented. The results reveal that the bounds found by the developed algorithm outperform those found by CPLEX for large instances, and it is capable of identifying high-quality feasible solutions to large-scale problems.