Loading constraints for a multi-compartment vehicle routing problem

Abstract

Multi-compartment vehicles (MCVs) can deliver several product segments jointly. Separate compartments are necessary as each product segment has its own specific characteristics and segments cannot be mixed during transportation. The size and position of the compartments can be adjusted for each tour with the use of flexible compartments. However, this requires that the compartments can be accessed for loading/unloading. The layout of the compartments is defined by the customer and segment sequence, and it needs to be organized in a way that no blocking occurs during loading/unloading processes. Routing and loading layouts are interdependent for MCVs. This paper addresses such loading/unloading issues raised in the distribution planning when using MCVs with flexible compartments, loading from the rear, and standardized transportation units. The problem can therefore be described as a two-dimensional loading and multi-compartment vehicle routing problem (2L-MCVRP). We address the problem of obtaining feasible MCV loading with minimal routing, loading and unloading costs. We define the loading problem that configures the compartment setup. Consequently, we develop a branch-and-cut (B&C) algorithm as an exact approach and extend a large neighborhood search (LNS) as a heuristic approach. In both cases, we use the loading model in order to verify the feasibility of the tours and to assess the problem as a routing and loading problem. The loading model dictates the cuts to be performed in the B&C, and it is used as a repair mechanism in the LNS. Numerical studies show that the heuristic reaches the optimal solution for small instances and can be applied efficiently to larger problems. Additionally, further tests on large instances enable us to derive general rules regarding the influence of loading constraints. Our results were validated in a case study with a European retailer. We identified that loading constraints matter even for small instances. Feasible loading can often be achieved only through minor changes to the routing solution and therefore with limited additional costs. Further, the importance to integrate loading constraints grows as the problem size increases, especially when a heterogeneous mix of segments is ordered.

A Fuzzy Receding Horizon Control Strategy for Dynamic Vehicle Routing Problem

“…The equation (4) means that the total demands for all customers are less than the total capacities of all vehicles. The equations (5) and (6) ensure that there is only one travel route between any two customers. The equation (7) means that the demands of the customers in one vehicle do not exceed the maximum capacity of the vehicle.…”

Exact algorithms for the multi-compartment vehicle routing problem with flexible compartment sizes

“…Oppen and Løkketangen (2008) present a tabu search approach and Oppen et al (2010) introduce an exact column-generation based solution approach. A grocery distribution problem is presented by Ostermeier et al (2018) that includes the decision of using cost-different single-compartment or multi-compartment vehicles. The problem is solved by a large neighborhood search.…”

“…They present a large-neighborhood search with specialized removal and reinsert operators. Ostermeier et al (2018) include loading constraints to the problem, develop a branch-and-cut algorithm, and extend the large neighborhood search of Hübner and Ostermeier. Derigs et al (2010) consider the MCVRP with fixed and flexible compartment sizes and introduce a solver suite consisting of construction heuristics, improvement heuristics, and metaheuristics.…”

Retail operations

“…It also supports to improve the quality of decisions in retail and consumer goods industry. Each of the selected papers deal with planning problems in retail operations at the interfaces with customer management (Steiner et al 2018;Corsten et al 2017), store management (Wensing et al 2018;Turgut et al 2018), distribution planning (Klein et al 2017;Ostermeier et al 2018;Koch et al 2018;Soriano et al 2018) and warehousing and picking (Schubert et al 2018;Boysen et al 2017). In particular, this special issue addresses the following topics: Flexible estimation of time-varying effects for frequently purchased retail goods: A modeling approach based on household panel data Steiner et al (2018) develop an innovative approach for demand estimation.…”

“…However, this requires that the compartments and each particular order can be accessed for loading at the warehouse and unloading at the customer stop. Ostermeier et al (2018) develop a model that determines the loading sequence of customer orders to each compartment and the vehicle routing. A hybrid algorithm for the vehicle routing problem with backhauls, time windows and three-dimensional loading constraints Retail stores are usually supplied by a central warehouse, and they wish to return packaging material.…”