New solution procedures for the order picker routing problem in U-shaped pick areas with a movable depot

This paper develops new solution procedures for the order picker routing problem in U-shaped order picking zones with a movable depot, which has so far only been solved using simple heuristics. The paper presents the first exact solution approach, based on combinatorial Benders decomposition, as well as a heuristic approach based on dynamic programming that extends the idea of the venerable sweep algorithm. In a computational study, we demonstrate that the exact approach can solve small instances well, while the heuristic dynamic programming approach is fast and exhibits an average optimality gap close to zero in all test instances. Moreover, we investigate the influence of various storage assignment policies from the literature and compare them to a newly derived policy that is shown to be advantageous under certain circumstances. Secondly, we investigate the effects of having a movable depot compared to a fixed one and the influence of the effort to move the depot.

Routing algorithms as tools for integrating social distancing with emergency evacuation

One of the lessons from the COVID-19 pandemic is the importance of social distancing, even in challenging circumstances such as pre-hurricane evacuation. To explore the implications of integrating social distancing with evacuation operations, we describe this evacuation process as a Capacitated Vehicle Routing Problem (CVRP) and solve it using a DNN (Deep Neural Network)-based solution (Deep Reinforcement Learning) and a non-DNN solution (Sweep Algorithm). A central question is whether Deep Reinforcement Learning provides sufficient extra routing efficiency to accommodate increased social distancing in a time-constrained evacuation operation. We found that, in comparison to the Sweep Algorithm, Deep Reinforcement Learning can provide decision-makers with more efficient routing. However, the evacuation time saved by Deep Reinforcement Learning does not come close to compensating for the extra time required for social distancing, and its advantage disappears as the emergency vehicle capacity approaches the number of people per household.

Penyelesaian Multiple Trip Heterogeneous Fix Fleet Vehicle Routing Problem (MTHFFVRP) Menggunakan Algoritma Sweep untuk Mendapatkan Optimasi Rute Distribusi LPG 3 kg di PT. Gending Gemilang

ABSTRAKDistibusi merupakan suatu kegiatan menyalurkan produk dari satu tempat ke tempat lainnya. PT. Gending Gemilang merupakan suatu perusahaan yang bergerak dibidang distributor Liquefied Petroleum Gas (LPG) 3 kg, setiap harinya perusahaan diharuskan untuk memenuhi permintaan ke 29 pangkalan yang dimiliki perusahaan. Perusahaan memiliki 2 jenis armada yaitu truk sebanyak 4 unit dan L300 sebanyak 3 unit dengan kapasitas setiap jenis armada berbeda beda dan setiap pangkalan memiliki alamat yang berbeda sehingga permasalahan penentuan rute masuk kedalam Multiple Trips Heterogeneous Fix Fleet Routing Problem (MTHFFVRP). Salah satu penentuan rute yang mampu meminimumkan ongkos pengirimanan adalah dengan menggunakan algoritma sweep, algoritma ini bekerja dengan cara melakukan proses clustering berdasarkan urutan sudut polar setiap pangkalan, pada penelitian ini jenis algoritma sweep yang digunakan adalah backward sweep sehingga untuk pembuatan cluster dimulai dari pangkalan yang memiliki sudut polar terbesar menuju pangkalan yang memliki sudut polar terkecil. Dari hasil penelitian menunjukan pembuatan rute menggunakan algoritma sweep mampu melakukan penghematan secara signifikan terhadap rute perusahaan saat iniKata kunci: Distribusi, Vehicle Routing Problem, Multiple Trips Heterogenous Fix Fleet Routing Problem (MTHFFVRP), Algoritma sweep ABSTRACTDistribution is an activity to distribute products from one place to another. PT. Gending Gemilang is a company engaged in the distribution of 3 kg of liquefied petroleum gas or it can be called (LPG) 3 kg, every day the company is required to fulfill requests from 29 bases owned by the company. The company has 2 types of fleets, namely 4 unit trucks and 3 unit L300 with different capacities for each type of fleet and each base has a different address so that the problem of determining routes enters the Multiple Trips Heterogeneous Fix Fleet Routing Problem (MTHFFVRP). Determination to minimize the shipping cost of the route used is the sweep algorithm, this algorithm works to carry out the clustering process based on the order of the polar angles of each base, in this study the type of sweep algorithm used is backward sweep so that clustering starts from the base with the largest polar angle towards the base that has the smallest polar angle. The research results show that route creation using the sweep algorithm is able to make significant savings on current company routesKeywords: Distribution; Vehicle Routing Problem; Multiple Trips Heterogenous Fix Fleet Routing Problem (MTHFFVRP); Sweep Algorithm

A construction heuristic for finding initial solution to a very large-scale capacitated vehicle routing problem

In this paper, a deterministic heuristic method is developed for obtaining an initial solution to an extremely large-scale capacitated vehicle routing problem (CVRP) having thousands of customers. The heuristic has three main objectives. First, it should be able to withstand the computational and memory problems normally associated with extremely large-scale CVRP. Secondly, the outputs should be reasonably accurate and should have a minimum number of vehicles. Finally, it should be able to produce the results within a short duration of time. The new method, based on the sweep algorithm, minimizes the number of vehicles by loading the vehicles nearly to their full capacity by skipping some of the customers as and when necessary. To minimize the total traveled distance, before the sweeping starts the customers are ordered based on both the polar angle and the distance of the customer from the depot. This method is tested on 10 sets of standard benchmark instances found in the literature. The results are compared with the results of the CW 100 method by Arnold et al. (2019a). The results indicate that the new modified sweep algorithm produces an initial solution with a minimum number of vehicles and with reasonable accuracy. The deviation of the output from the best-known solution (BKS) is within a reasonable limit for all the test instances. When compared with the CW 100 the modified sweep provides a better initial solution than CW 100 whenever the capacity of the vehicle is more and the depot is located eccentrically. The heuristic does not face any memory problems normally associated with the solving of an extremely large-scale CVRP.

Routing Algorithms as Tools for Integrating Social Distancing with Emergency Evacuation

We explore the implications of integrating social distancing with emergency evacuation, as would be expected when a hurricane approaches a city during the COVID-19 pandemic. Specifically, we compare DNN (Deep Neural Network)-based and non-DNN methods for generating evacuation strategies that minimize evacuation time while allowing for social distancing in emergency vehicles. A central question is whether a DNN-based method provides sufficient extra routing efficiency to accommodate increased social distancing in a time-constrained evacuation operation. We describe the problem as a Capacitated Vehicle Routing Problem and solve it using a non-DNN solution (Sweep Algorithm) and a DNN-based solution (Deep Reinforcement Learning). The DNN-based solution can provide decision-makers with more efficient routing than the typical non-DNN routing solution. However, it does not come close to compensating for the extra time required for social distancing, and its advantage disappears as the emergency vehicle capacity approaches the number of people per household.

In-Memory Interval Joins

The interval join is a popular operation in temporal, spatial, and uncertain databases. The majority of interval join algorithms assume that input data reside on disk and so, their focus is to minimize the I/O accesses. Recently, an in-memory approach based on plane sweep (PS) for modern hardware was proposed which greatly outperforms previous work. However, this approach relies on a complex data structure and its parallelization has not been adequately studied. In this article, we investigate in-memory interval joins in two directions. First, we explore the applicability of a largely ignored forward scan (FS)-based plane sweep algorithm, for single-threaded join evaluation. We propose four optimizations for FS that greatly reduce its cost, making it competitive or even faster than the state-of-the-art. Second, we study in depth the parallel computation of interval joins. We design a non-partitioning-based approach that determines independent tasks of the join algorithm to run in parallel. Then, we address the drawbacks of the previously proposed hash-based partitioning and suggest a domain-based partitioning approach that does not produce duplicate results. Within our approach, we propose a novel breakdown of the partition-joins into mini-joins to be scheduled in the available CPU threads and propose an adaptive domain partitioning, aiming at load balancing. We also investigate how the partitioning phase can benefit from modern parallel hardware. Our thorough experimental analysis demonstrates the advantage of our novel partitioning-based approach for parallel computation.