Mixed integer programming for vehicle routing problem with time windows

Aggarwal, Divya; Kumar, Vijay

doi:10.1504/ijista.2019.097744

Cited by 9 publications

(7 citation statements)

References 19 publications

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“…Tasar et al (2019) determined the optimal number of vehicles to minimize the fixed and fuel costs. Similarly, Aggarwal and Kumar (2019) established the objective to drop their transportation cost and cost for the availability of vehicles and determine the optimal vehicle number. Unlike introduced studies, Afifi et al (2016) and Pérez-Rodríguez, Hernández-Aguirre (2019) focused on reducing time and distance in their problem, respectively.…”

Section: Literature Reviewmentioning

confidence: 99%

Clustering Algorithm for a Vehicle Routing Problem With Time Windows

Nguyen

Oláh

et al. 2022

Transport

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The demand for daily food purchases has increased dramatically, especially during the Covid-19 pandemic. This requires suppliers to face a huge and complex problem of delivering products that meet the needs of their customers on a daily basis. It also puts great pressure on managers on how to make day-to-day decisions quickly and efficiently to both satisfy customer requirements and satisfy capacity constraints. This study proposes a combination of the cluster-first –route-second method and k-means clustering algorithm to deal with a large Vehicle Routing Problem with Time Windows (VRPTW) in the logistics and transportation field. The purpose of this research is to assist decision-makers to make quick and efficient decisions, based on optimal costs, the number of vehicles, delivery time, and truck capacity efficiency. A distribution system of perishable goods in Vietnam is used as a case study to illustrate the effectiveness of our mathematical model. In particular, perishable goods include fresh products of fish, chicken, beef, and pork. These products are packed in different sizes and transferred by vehicles with 1000 kg capacity. Besides, they are delivered from a depot to the main 39 customers of the company with arrival times following customers’ time window. All of the data are collected from a logistics company in Ho Chi Minh city (Vietnam). The result shows that the application of the clustering algorithm reduces the time for finding the optimal solutions. Especially, it only takes an average of 0.36 s to provide an optimal solution to a large Vehicle Routing Problem (VRP) with 39 nodes. In addition, the number of trucks, their operating costs, and their utilization are also shown fully. The logistics company needs 11 trucks to deliver their products to 39 customers. The utilization of each truck is more than 70%. This operation takes the total costs of 6586215.32 VND (Vietnamese Dong), of which, the transportation cost is 1086215.32 VND. This research mainly contributes an effective method for enterprises to quickly find the optimal solution to the problem of product supply.

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Section: Literature Reviewmentioning

confidence: 99%

Clustering Algorithm for a Vehicle Routing Problem With Time Windows

Nguyen

Oláh

et al. 2022

Transport

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“…Mixed-integer programming is used popularly in formulating a model of the VRP. For example, Aggarwal, D., and Kumar, V. (2019) and Tasar, B., et al (2019) used an MIP to model their problems with a large number of nodes. For more complexity in the constraints and variables of the VRP, MIP also develops into Mixed-Integer Linear Programming (MILP).…”

Section: Literature Reviewmentioning

confidence: 99%

“…In addition to forming mathematical models, previous studies have applied or developed an efficient algorithm to search for solutions quickly. To find optimal solutions, algorithms include the following: an estimation of distribution, heuristic, artificial bee colony, local search, response surface method, biased random-key genetic, exact branch-price-andcut algorithm, tabu search, and simulated annealing (Qi and Hu, 2020;Kantawong and Pravesjit, 2020;Londoño et al, 2020;Aggarwal and Kumar, 2019;Pérez-Rodríguez and Hernández-Aguirre, 2019;Tasar et al, 2019;Setamanit, 2019Zhu andHu, 2019;Ruiz et al, 2019;Zhang et al, 2017;Huang et al, 2017;Afifi et al, 2016;Spliet and Desaulniers, 2015).…”

Section: Literature Reviewmentioning

confidence: 99%

“…For instance, customer A always receives cargo from 9:00 a.m. to 11:00 a.m. every day. Hence, vehicles can arrive before 9:00 a.m. or after 11:00 a.m. but they have to wait until the time window starts (Aggarwal and Kumar, 2019) In this study, a paired pickup and delivery vehicle routing problem considering hard time windows is presented. This network is two echelons of a distribution network including three members: a logistics company, a group of 35 depots/ports, and a group of 106 customers.…”

Section: Introductionmentioning

confidence: 99%

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Optimal vehicle route schedules in picking up and delivering cargo containers considering time windows in logistics distribution networks: A case study

Nguyen

Oláh

et al. 2020

Production Engineering Archives

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This study describes a pickup and delivery vehicle routing problem, considering time windows in reality. The problem of tractor truck routes is formulated by a mixed integer programming model. Besides this, three algorithms - a guided local search, a tabu search, and simulated annealing - are proposed as solutions. The aims of our study are to optimize the number of internal tractor trucks used, and create optimal routes in order to minimize total logistics costs, including the fixed and variable costs of an internal vehicle group and the renting cost of external vehicles. Besides, our study also evaluates both the quality of solutions and the time to find optimal solutions to select the best suitable algorithm for the real problem mentioned above. A novel mathematical model is formulated by OR tools for Python. Compared to the current solution, our results reduced total costs by 18%, increased the proportion of orders completed by internal vehicles (84%), and the proportion of orders delivered on time (100%). Our study provides a mathematical model with time constraints and large job volumes for a complex distribution network in reality. The proposed mathematical model provides effective solutions for making decisions at logistics companies. Furthermore, our study emphasizes that simulated annealing is a more suitable algorithm than the two others for this vehicle routing problem.

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“…; and 2) inter-route heuristics such as λ-interchange [20], cyclic exchanges [21], edge exchange schemes [22], ejection chains [23]- [25], very Large Neighbor Search (VLNS) [26], Adaptive Large Neighbor Search (ALNS) [27], etc. In addition, many other optimization techniques have also been applied in recent research on VRPTW, such as lagrangian relaxation [28], [29], integer programming [30], etc.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Swarm Intelligence Algorithm for Vehicle Routing Problem With Time Windows

et al. 2020

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The Vehicle Routing Problem with Time Windows (VRPTW) has drawn considerable attention in the last decades. The objective of VRPTW is to find the optimal set of routes for a fleet of vehicles in order to serve a given set of customers within capacity and time window constraints. As a combinatorial optimization problem, VRPTW is proved NP-hard and is best solved by heuristics. In this paper, a hybrid swarm intelligence algorithm by hybridizing Ant Colony System (ACS) and Brain Storm Optimization (BSO) algorithm is proposed, to solve VRPTW with the objective of minimizing the total distance. In the BSO procedure, both inter-route and intra-route improvement heuristics are introduced. Experiments are conducted on Solomon's 56 instances with 100 customers benchmark, the results show that 42 out of 56 optimal solutions (18 best and 24 competitive solutions) are obtained, which illustrates the effectiveness of the proposed algorithm. INDEX TERMS Ant colony system, brain storm optimization, heuristics, swarm intelligence, vehicle routing problem with time windows.

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Mixed integer programming for vehicle routing problem with time windows

Cited by 9 publications

References 19 publications

Clustering Algorithm for a Vehicle Routing Problem With Time Windows

Clustering Algorithm for a Vehicle Routing Problem With Time Windows

Optimal vehicle route schedules in picking up and delivering cargo containers considering time windows in logistics distribution networks: A case study

A Hybrid Swarm Intelligence Algorithm for Vehicle Routing Problem With Time Windows

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