The bi-objective location-allocation-routing problem in the post-disaster phase considering inter-depot routes and time windows

The periodic vehicle routing problem (PVRP) is an extension of the well-known vehicle routing problem. In this paper, the PVRP with time windows and time spread constraints (PVRP-TWTS) is addressed, which arises in the high-value shipment transportation area. In the PVRP-TWTS, period-specific demands of the customers must be delivered by a fleet of heterogeneous capacitated vehicles over the several planning periods. Additionally, the arrival times to a customer should be irregular within its time window over the planning periods, and the waiting time is not allowed for the vehicles due to the security concerns. This study, proposes novel mixed-integer linear programming (MILP) and constraint programming (CP) models for the PVRP-TWTS. Furthermore, we develop several valid inequalities to strengthen the proposed MILP and CP models as well as a lower bound. Even though CP has successful applications for various optimization problems, it is still not as well-known as MILP in the operations research field. This study aims to utilize the effectiveness of CP in solving the PVRP-TWTS. This study presents a CP model for PVRP-TWTS for the first time in the literature to the best of our knowledge. Having a comparison of the CP and MILP models can help in providing a baseline for the problem. We evaluate the performance of the proposed MILP and CP models by modifying the well-known benchmark set from the literature. The extensive computational results show that the CP model performs much better than the MILP model in terms of the solution quality.

In this work, we consider the Vehicle Routing Problem with Simultaneous Delivery and Pickup, and constrained by time windows, to improve the performance and responsiveness of the supply chain by transporting goods from one location to another location in an efficient manner. In this class of problem, each customer demands a quantity to be delivered as a part of the forward supply service and another quantity to be picked up as a part of the reverse recycling service, and the complete service has to be done simultaneously in a single visit of a vehicle, and the objective is to minimize the total cost, which includes the traveling cost and dispatching cost for operating vehicles. We propose a Mixed Integer Linear Programming (MILP) model for solving this class of problem. In order to evaluate the performance of the proposed MILP model, a comparison study is made between the proposed MILP model and an existing MILP model available in the literature, with the consideration of heterogeneous vehicles. Our study indicates that the proposed MILP model gives tighter lower bound and also performs better in terms of the execution time to solve each of the randomly generated problem instances, in comparison with the existing MILP model. In addition, we also compare the proposed MILP model (assuming homogeneous vehicles) with the existing MILP model that also considers homogeneous vehicles. The results of the computational evaluation indicate that the proposed MILP model gives much tighter lower bound, and it is competitive to the existing MILP model in terms of the execution time to solve each of the randomly generated problem instances.

Collaborative multicenter vehicle routing problem with time windows and mixed deliveries and pickups

The heterogeneous fixed fleet open vehicle routing problem with time windows is a very significant type of the vehicle routing problem (VRP) that aims to find the minimum fixed and variable cost of transportation for a heterogeneous fleet with a fixed number in which the capacity of every vehicle and usage of the vehicles should not be ignored. Also, in this problem, each customer has a special time window for servicing and each vehicle starts its route from the warehouse and ends up in one of the customers. We propose a mixed integer linear programming model of this problem. Since this problem, as well as open VRP and VRP with fixed heterogeneous fleet are hard NP problem, an improved tabu search algorithm is proposed to solve the problem. Our proposed algorithm uses a modified sweep algorithm to generate some initial solutions. Besides, a variable tabu list and some new mechanisms for intensification and diversification mechanisms are used. Numerical results are presented to show the correctness of our model and finally, the efficiency of the proposed algorithm is compared with an exact algorithm, classic tabu search and simulated annealing. The obtained results prove the efficiency of the proposed algorithm.

The distribution of goods to a set of geographically dispersed customers is a common problem faced by carrier companies, well-known as the Vehicle Routing Problem (VRP). The VRP consists of finding an optimal set of routes that minimizes total travel times for a given number of vehicles with a fixed capacity. Given the demand of each customer and a depot, the optimal set of routes should adhere to the following conditions: ?? Each customer is visited exactly once by exactly one vehicle. ?? All vehicle routes start and end at the depot. ?? Every route has a total demand not exceeding the vehicle capacity. The travel times between any two potential locations are given as input to the problem. Consequently, the total travel is computed by summing up the travel time over the chosen routes. In reality, carrier companies are faced with a number of other issues not conveyed in the VRP. The research in this thesis introduces a number of realistic variants of the VRP. These variants consider the VRP as a core component and incorporate additional features. By definition the VRP is NP-hard. Throughout the years a vast amount of research was aimed at developing both exact and heuristic solution procedures. Building on this established literature, solution procedures are developed to fit the variants proposed in this thesis. The standard VRP considers that the travel time between any pair of locations is constant throughout the day. However, congestion is present in most road networks. Considering traffic congestion results in time-dependent travel times, where the travel time between two location depends not only on the distance between them but also on the time of day one chooses to traverse this distance. Time-dependent travel times are considered in Chapters 2 and 3 of this thesis. Thus, in these Chapters we incorporate the time dimension into the VRP. The standard VRP does not take into account any customer service aspect. The customers are presumed to be available to receive their goods upon arrival of the vehicles. However, a number of carrier companies quote their expected arrival time to their customers. We introduce the concept of self-imposed time windows (SITW). SITW reflect the fact that the carrier company decides on when to visit the customer and communicates this to the customer. Once a time window is quoted to a customer the carrier company strives to provide service within this time window. SITW differ from time windows in the widely studied VRP with time windows (VRPTW), as the latter are exogenous constraints. In Chapters 4 and 5 SITW are endogenous decisions in stochastic environments. Thus, in addition to the sequencings decisions required by the VRP further timing decisions are needed. This thesis extends the VRP in two major dimensions: time-dependent travel times and self-imposed time windows. In reality carrier companies are faced with various uncertainties. The presented models incorporated some of these uncertainties by addressing three stochastic aspects: (I) In Chapter 3 stochastic service times are considered. (II) In Chapter 4, stochasticity in travel time is modeled to describes variability caused by random events such as car accidents or vehicle break down. (III) Finally, in Chapter 5 the objective was to construct a long term plan for providing consistent service to reoccurring customers. Stochasticity in this thesis is treated in an a priori manner. The plan, consisting of routes and timing decisions where necessary, is determined beforehand and is not modified according to the realization of the random events. Chapter 2 addresses environmental concerns by studying CO2 emissions in a timedependent vehicle routing problem environment. In addition to the decisions required for the assignment and scheduling of customers to vehicles, the vehicle speed limit is considered. The emissions per kilometer as a function of speed, is a function with a unique minimum speed v*. However, we show that limiting vehicle speed to this v* might be sub-optimal, in terms of total emissions. We adapted a Tabu search procedure for the proposed model. Furthermore, upper and lower bounds on the total amount of emissions that may be saved are presented. Quantifying the tradeoff between minimizing travel time as opposed to CO2 emissions is an important contribution. Another important contribution lies in incorporating fuel costs in the optimization. As fuel costs are correlated with CO2 emissions, Chapter 2 shows that even in today’s cost structure limiting vehicle speeds is beneficial. Chapter 3 defines the perturbed time-dependent VRP (P-TDVRP) model which is designed to handle unexpected delays at the various customer locations. A solution method that combines disruptions in a Tabu Search procedure is proposed. In Chapter 3 we identify situations capable of absorbing delays. i.e. where inserting a delay will lead to an increase in travel time that is less than the delay length itself. Based on this, assumptions with respect to the solution structure of P-TDVRP are formulated and validated. Furthermore, most experiments showed that the additional travel time required by the P-TDVRP, when compared to the travel time required by the TDVRP, was justified. In Chapter 4 the notion of self imposed time windows is defined and embedded in the VRP-SITW model. The objective of this problem is to minimize delay costs (caused by late arrivals at customers) as well as traveling time. The problem is optimized under various disruptions in travel times. The basic mechanism of dealing with these disruptions is allocating time buffers throughout the routes. Thus, additional timing decisions are taken. The time buffers attempt to reduce potential damage of disruptions. The solution approach combines a linear programming model with a local search heuristic. In Chapter 4, two main types of experiments were conducted: one compares the VRP with VRP-SITW while the other compares VRPTW with VRPSITW. The first set of experiments assessed the increase in operational costs caused by incorporating SITW in the VRP. The second set of experiments enabled evaluating the savings in operational costs by using flexible time windows, when compared to the VRPTW. Chapter 5 extends the customer service dimension by considering the consistent vehicle routing problem. Consistency is defined by having the same driver visiting the same customers at roughly the same time. As such, two main dimensions of consistency are identified in the literature, driver- and temporal consistency. In Chapter 5, driver consistency is imposed by having the same driver visit the same customers. Furthermore, we impose temporal consistency by SITW. A stochastic programming formulation is presented for the consistent VRP with stochastic customers. An exact solution method is proposed by adapting the 0-1 integer L- shaped algorithm to the problem. The method was able to solve the majority of test instances to optimality.

Mixed Integer Linear Programming Model for Vehicle Routing Problem for Hazardous Materials Transportation

In this paper a model‐based heuristic approach for a typical distribution problem is presented. In order to be cost‐effective, the distribution process for many customers, each of them with orders of considerable volume, should be dealt with like a combination of two well‐known problems: the vehicle routing problem (VRP) and the container loading problem (CLP). This paper studies a particular integration of these two problems called the vehicle routing and loading problem (VRLP). The VRLP is an operational problem that must be solved daily by many production and distribution companies. Like the two original problems (VRP and 3D‐CLP), the VRLP is NP‐hard. In this work, regardless of the complexity of this problem, a mixed integer linear programming (MILP) model that characterizes the VRLP with time windows is presented and it is also used to solve the problem optimally. Then, a model‐based heuristic that improves the computational time, when bigger instances need to be solved, is also presented. In order to prove the viability of the approach and the developed MILP model, tests with the benchmark instances of the VRLP were made and the results compared with other published works. Despite the long computational time needed to solve bigger instances, the VRLP model could be used to compute optimal solutions or at least good lower bounds, in order to have a base of comparison when nonexact methods are applied to the VRLP.

Adaptive large neighborhood search for the pickup and delivery problem with time windows, profits, and reserved requests

This paper studies the distribution of emergency relief for electric vehicles (EVs), which considers energy saving, multi-depot, and vehicle routing problems with time windows, and the named energy saving-oriented multi-depot vehicle routing problem with time windows (ESMDVRPTW). Our aim is to find routes for EVs such that all the shelter demands are fulfilled during their time windows and the total cost traveled by the fleet is minimized. To this end, we formulate the ESMDVRPTW as a mixed-integer linear programming model. Since the post-disaster transportation network contains a large number of vertices and arcs composed of vertices, we propose a two-stage approach to solve the ESMDVRPTW. The first stage is to obtain the minimal travel cost between any two vertices in real-time on a post-disaster transportation network using the proposed Floyd algorithm combined with the neighboring list (Floyd-NL algorithm). In the second stage, we develop the genetic algorithm (GA) incorporating large neighborhood search (GA-LNS), which determines the delivery scheme of shelters. Simulation results of the MDVRPTW benchmark illustrate that the performance of the GA-LNS is better than GA, simulated annealing (SA) and tabu search (TS). Finally, case studies are constructed on two real cases acquired from the OpenStreetMap (OSM) generated by the Quantum Geographic Information System (QGIS) in Ichihara city, Japan, and the test results of case studies show the effectiveness of the proposed two-stage approach.

Vehicle routing problem with time window (VRPTW) has been investigated by many researchers, in which the vehicle number is fixed in advance. In fact, the vehicle number can't be determined beforehand for practical problems. Because the fixed cost of a vehicle is much more than the running cost, and it is effective to cut down the total cost to seek the minimum number of vehicles in VRPTW. So, both the number and the routes of vehicles should be objectives of the VRPTW, which are described here. This paper presents a mathematical model of vehicle routing problem with time window with uncertain vehicle number. An improved chromosome representation that expresses the various vehicle numbers is proposed on the basis of customers. It is proved by an experiment that the genetic algorithm can search for the optimal solution for both route length and vehicle number.

Development of energy consumption optimization model for the electric vehicle routing problem with time windows

In this paper, the green vehicle routing problem with time windows constraint is studied in the presence of a heterogeneous fleet of vehicles and filling stations. In addition, the number of vehicles and their fuel tank capacity are both limited. The main contribution of this study is the simultaneous consideration of these features, which makes the problem more practical. For this purpose, a mixed integer linear programming model that minimises the transportation costs and (or carbon dioxide) emissions, is proposed. Furthermore, a genetic algorithm and a population-based simulated annealing are developed to find high-quality solutions for large-scale instances. To validate the proposed model and algorithms, 28 instances are generated using a benchmark database. The computational results demonstrate that both algorithms provide efficient solutions regarding the objective function value and CPU time. Finally, a comprehensive sensitivity analysis is carried out to show the importance of features mentioned above. [Received: 7 October 2016; Revised: 27 December 2018; Accepted: 13 January 2019]

The vehicle routing problem with simultaneous deliveries and pickups (VRPSDP) has attracted much research interest because of the potential to provide cost savings to transportation and logistics operators. Several extensions of VRPSDP exist. Of these extensions, the simultaneous deliveries and pickups with split loads problem (SDPSLP) has been proposed to eliminate vehicle capacity constraints, as well as allow the deliveries or pickups for a customer to be split into multiple visits. Although delivery and pickup activities are often constrained by time windows, few studies have considered such constraints when SDPSLP has been addressed. To fill the gap, this paper formulates the vehicle routing problem of simultaneous deliveries and pickups with split loads and time windows (VRPSDPSLTW) as a mixed-integer programming problem. A hybrid heuristic algorithm was developed to solve this problem. Solomon data sets with minor modifications were applied to test the effectiveness of the solution algorithm. The results of a computational experiment demonstrated that use of the proposed algorithms to solve VRPSDPSLTW had advantages for minimization of the total travel cost, number of vehicles, and loading rate. The proposed formulation and solution algorithm for VRPSDPSLTW may serve as a general analytical tool for the optimization of vehicle routing in practice.

The distribution of vegetables in Indonesia is still constrained by the guarantee of continuity between product quality, the minimum amount of supply, and the timeliness of delivery. Time is a very crucial factor in the distribution of vegetables because vegetables are commodities that experience a rapid decline in quality, so they must reach consumers at the right time. PT ABC is a company engaged in the distribution of fresh fruit and vegetables. The problem faced by PT ABC in distribution activities lies in the delay in delivery. This delay problem can be minimized by optimizing the distribution network so that delivery delays do not occur again. The characteristic of the problem contained in this final project is Vehicle Routing Problem with Heterogeneous Fleet and Time Window. The model that will be used to solve this problem is the Mixed Integer Linear Programming model with the main objective to minimize transportation costs and minimize delivery delays. Problem solving was carried out using the Python programming language and Gurobi Solve. The final result obtained is a reduction in the percentage of delays by 5% and a minimization of transportation costs by 4%.

A new MILP model and fast heuristics for the variable-sized bin packing problem with time windows