Abstract
Given automated order systems, detailed characteristics of items and vehicles enable the detailed planning of deliveries including more efficient and safer loading of distribution vehicles. Many vehicle routing approaches ignore complex loading constraints. This paper focuses on the comprehensive evaluation of loading constraints in the context of combined Capacitated Vehicle Routing Problem and 3D Loading (3L-CVRP) and its extension with time windows (3L-VRPTW). To the best of our knowledge, this paper considers the currently largest number of loading constraints meeting real-world requirements and reducing unnecessary loading efforts for both problem variants. We introduce an approach for the load bearing strength of items ensuring a realistic load distribution between items. Moreover, we provide a new variant for the robust stability constraint enabling better performance and higher stability. In addition, we consider axle weights of vehicles to prevent overloaded axles for the first time for the 3L-VRPTW. Additionally, the reachability of items, balanced loading and manual unloading of items are taken into account. All loading constraints are implemented in a deepest-bottom-left-fill algorithm, which is embedded in an outer adaptive large neighbourhood search tackling the Vehicle Routing Problem. A new set of 600 instances is created, published and used to evaluate all loading constraints in terms of solution quality and performance. The efficiency of the hybrid algorithm is evaluated by three well-known instance sets. We outperform the benchmarks for most instance sets from the literature. Detailed results and the implementation of loading constraints are published online.
Highlights
In recent years, sales in online trading have risen steadily
This paper considers the Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP) and its extension with Time Windows (3L-VRPTW), which represent a combination of the Vehicle Routing Problem (VRP) and 3D Loading constraints
For the analysis of the loading constraints, we use our new instance set to enable comparison concerning the number of customers (n), items (m) and item types
Summary
Sales in online trading have risen steadily. Forecasts for the coming years predict significant growth. This paper considers aspects for manual unloading, reachability, the axle weights of vehicles and a balanced loading For the latter, we introduce formulas to illustrate our implementation approach. Our evaluations consist of over 30,000 results, and we provide all results online and in detail (e.g. routing and packing plans with the position of all items) to ensure extraordinary transparency. On this basis, we give recommendations about which constraints are reasonable based on their impact on algorithmic performance and solution quality.
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