A GRASP-Tabu Heuristic Approach to Territory Design for Pickup and Delivery Operations for Large-Scale Instances

Abstract

We address a logistics districting problem faced by a parcel company whose operations consist of picking up and delivering packages over a service region. The districting process aims to find a partition of the service region into delivery and collection zones that may be served by a single vehicle that departs from a central depot. Criteria to be optimized are to balance workload content among the districts and to create districts of compact shape. A solution approach based on a hybrid procedure that combines elements of GRASP and Tabu Search (TS) is proposed to solve large-scale instances. Numerical experimentation is performed considering different instance sizes and types. Results show that the proposed solution approach is able to solve large-scale instances in reasonable computational times with good quality of the solutions obtained. To determine the quality of the solutions, results are compared with CPLEX solutions and with the current real solution to highlight the benefits of the proposed approach. Conclusions and recommendations for further research are provided.

A Districting Application with a Quality of Service Objective

“…Within the different applications, we can find both in the areas already mentioned, that is, the design of political territories [15][16][17] and that of sales territories [18][19][20], as in other areas, such as the design of service areas, in settings as diverse as home health care [21,22], police patrolling [23,24], the design of school districts [25], the design of energy distribution networks [26], or waste collection [27,28]. Finally, and of special interest for this work are the applications related to the design of distribution territories [29,30], which is the area in which this work is focused. The design of distribution territories consists of designing zones for the pick up and/or delivery of products to customers residing in the zone.…”

Multiobjective Genetic Algorithms for Reinforcing Equal Population in Congressional Districts

“…where P max and P min represent the population of the largest and smallest districts, respectively, and P m is the average district population. Equations (5) and (6) measure the level of population deviation among the districts. e lower the value for f 1 , or f 2 , the better population equality.…”

“…e lower the value for f 1 , or f 2 , the better population equality. In an ideal case, the number of inhabitants in each district is equal to the average district population, and in this case, equations (5) and (6) reach their lowest possible value of zero.…”

“…Input parameters: N (archive size), T (maximum number of generations) Output: A (Pareto front approximation) (1) t ⟵ 0 (2) Generate an initial population, P t , and external archive, P t (3) while t < T do (4) Calculate fitness values of individuals in P t and P t (5) Copy all nondominated individuals in P t and P t to P t+1 (6) if…”

“…e criteria can be the construction of zones with a specific shape and the same amount of clients or services among others. e zone design problem has a broad range of applications such as land use [1], commercial territory design [2], school districting [3], police districting [4], and service and maintenance zones [5]. Due to its complexity, which has shown to be NP-hard [6], there have been several heuristic approaches such as genetic algorithms [7], tabu search [8], and GRASP [9] to fulfill its objectives in reasonable time.…”