scholarly journals On the route construction in changing environments using solutions of the eikonal equation

2021 ◽  
Vol 58 ◽  
pp. 59-72
Author(s):  
A.L. Kazakov ◽  
A.A. Lempert
Keyword(s):  
Integral Functional ◽  
Numerical Algorithms ◽  
Geometric Approach ◽  
Approximate Solutions ◽  
Central Feature ◽  
Routing Problem ◽  
Propagation Of Light ◽  
Proposed Model ◽  
Optically Inhomogeneous Medium ◽  
The Cost

The article deals with the vehicle routing problem in an environment with dynamically changing properties. The problem is relevant in current conditions when the delivery cost has a steady upward trend and is often comparable to the cost of the product itself. A central feature of the study is that the optimality criterion is the minimum delivery time, but not the distance traveled. The optical-geometric approach developed by the authors, based on the analogy between the propagation of light in an optically inhomogeneous medium and the minimization of the integral functional, is used as a research tool. We use exact and approximate solutions of the eikonal equations to describe wave fronts. Two original numerical algorithms for route construction are proposed and implemented as software. A computational experiment is performed that justified the effectiveness of the proposed model-algorithmic tools.

scholarly journals Inventory routing of industrial gases with stochastic demand

2021 ◽  
Author(s):  
Bhupeshkumar Gandhi
Keyword(s):  
Stochastic Demand ◽  
Total System ◽  
Inventory Routing ◽  
Routing Problem ◽  
Numerical Examples ◽  
Proposed Model ◽  
Industrial Gases ◽  
Number Of Visits ◽  
The Cost ◽  
Optimal Quantity

This report proposes a methodology to solve the inventory routing problem of industrial gases with stochastic demand. The gas tanker distributes gases from a depot to several dispersed customers in a route, and each customer has stochastic demand modeled by a Brownian motion. The proposed model determines the optimal quantity required to refill each customer by minimizing the cost associated with earliness, which increases number of visits per year, and lateness, which increases probability of stockout. Overall, the proposed model minimizes the total system cost, helps find the optimal tanker capacity for a given route, and improves supplier and customers' relationship. Numerical examples and sensitivity analysis are given to illustrate the proposed model.

scholarly journals Inventory routing of industrial gases with stochastic demand

2021 ◽  
Author(s):  
Bhupeshkumar Gandhi
Keyword(s):  
Stochastic Demand ◽  
Total System ◽  
Inventory Routing ◽  
Routing Problem ◽  
Numerical Examples ◽  
Proposed Model ◽  
Industrial Gases ◽  
Number Of Visits ◽  
The Cost ◽  
Optimal Quantity

This report proposes a methodology to solve the inventory routing problem of industrial gases with stochastic demand. The gas tanker distributes gases from a depot to several dispersed customers in a route, and each customer has stochastic demand modeled by a Brownian motion. The proposed model determines the optimal quantity required to refill each customer by minimizing the cost associated with earliness, which increases number of visits per year, and lateness, which increases probability of stockout. Overall, the proposed model minimizes the total system cost, helps find the optimal tanker capacity for a given route, and improves supplier and customers' relationship. Numerical examples and sensitivity analysis are given to illustrate the proposed model.

Fuzzy multi-objective location and routing problem

2020 ◽  
Vol 39 (3) ◽  
pp. 3259-3273
Author(s):  
Nasser Shahsavari-Pour ◽  
Najmeh Bahram-Pour ◽  
Mojde Kazemi
Keyword(s):  
Firefly Algorithm ◽  
High Reliability ◽  
Research Area ◽  
Nsga Ii ◽  
Location Routing Problem ◽  
Routing Problem ◽  
Location Allocation ◽  
Multi Objective ◽  
Location Routing ◽  
The Cost

The location-routing problem is a research area that simultaneously solves location-allocation and vehicle routing issues. It is critical to delivering emergency goods to customers with high reliability. In this paper, reliability in location and routing problems was considered as the probability of failure in depots, vehicles, and routs. The problem has two objectives, minimizing the cost and maximizing the reliability, the latter expressed by minimizing the expected cost of failure. First, a mathematical model of the problem was presented and due to its NP-hard nature, it was solved by a meta-heuristic approach using a NSGA-II algorithm and a discrete multi-objective firefly algorithm. The efficiency of these algorithms was studied through a complete set of examples and it was found that the multi-objective discrete firefly algorithm has a better Diversification Metric (DM) index; the Mean Ideal Distance (MID) and Spacing Metric (SM) indexes are only suitable for small to medium problems, losing their effectiveness for big problems.

scholarly journals An Optimized Mathematical Model for Items Supplies Planning of a Logistic System

2016 ◽  
Vol 10 (10) ◽  
pp. 133
Author(s):  
Mohammad Ali Nasiri Khalili ◽  
Mostafa Kafaei Razavi ◽  
Morteza Kafaee Razavi
Keyword(s):  
Mathematical Model ◽  
Mixed Integer ◽  
Logistics System ◽  
Proposed Model ◽  
Multiple Objective Decision Making ◽  
System Requirements ◽  
Purchasing Logistics ◽  
The Cost ◽  
The Mathematical Model ◽  
First Time

Items supplies planning of a logistic system is one of the major issue in operations research. In this article the aim is to determine how much of each item per month from each supplier logistics system requirements must be provided. To do this, a novel multi objective mixed integer programming mathematical model is offered for the first time. Since in logistics system, delivery on time is very important, the first objective is minimization of time in delivery on time costs (including lack and maintenance costs) and the cost of purchasing logistics system. The second objective function is minimization of the transportation supplier costs. Solving the mathematical model shows how to use the Multiple Objective Decision Making (MODM) can provide the ensuring policy and transportation logistics needed items. This model is solved with CPLEX and computational results show the effectiveness of the proposed model.

A Multi-Period Evacuation Vehicle Routing Problem Model

2014 ◽  
Vol 931-932 ◽  
pp. 578-582
Author(s):  
Sunarin Chanta ◽  
Ornurai Sangsawang
Keyword(s):  
Vehicle Routing ◽  
Public Transportation ◽  
Vehicle Routing Problem ◽  
Programming Model ◽  
High Water ◽  
Mixed Integer ◽  
Routing Problem ◽  
Problem Model ◽  
Proposed Model ◽  
Evacuation Routing

In this paper, we proposed an optimization model that addresses the evacuation routing problem for flood disaster when evacuees trying to move from affected areas to safe places using public transportation. A focus is on the situation of evacuating during high water level when special high vehicles are needed. The objective is to minimize the total traveled distance through evacuation periods where a limited number of vehicles is given. We formulated the problem as a mixed integer programming model based on the capacitated vehicle routing problem with multiple evcuation periods where demand changing by the time. The proposed model has been tested on a real-world case study affected by the severe flooding in Thailand, 2011.

scholarly journals A Heuristics-Based Parthenogenetic Algorithm for the VRP with Potential Demands and Time Windows

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Chenghua Shi ◽  
Tonglei Li ◽  
Yu Bai ◽  
Fei Zhao
Keyword(s):  
Genetic Algorithm ◽  
Time Windows ◽  
Computation Time ◽  
Routing Problem ◽  
Split Delivery ◽  
Soft Time Windows ◽  
Comparison Results ◽  
Potential Demand ◽  
The Cost

We present the vehicle routing problem with potential demands and time windows (VRP-PDTW), which is a variation of the classical VRP. A homogenous fleet of vehicles originated in a central depot serves customers with soft time windows and deliveries from/to their locations, and split delivery is considered. Also, besides the initial demand in the order contract, the potential demand caused by conformity consuming behavior is also integrated and modeled in our problem. The objective of minimizing the cost traveled by the vehicles and penalized cost due to violating time windows is then constructed. We propose a heuristics-based parthenogenetic algorithm (HPGA) for successfully solving optimal solutions to the problem, in which heuristics is introduced to generate the initial solution. Computational experiments are reported for instances and the proposed algorithm is compared with genetic algorithm (GA) and heuristics-based genetic algorithm (HGA) from the literature. The comparison results show that our algorithm is quite competitive by considering the quality of solutions and computation time.

A robust possibilistic programming model for production-routing problem in a three-echelon supply chain

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Ali Beheshtinia ◽  
Narjes Salmabadi ◽  
Somaye Rahimi
Keyword(s):  
Supply Chain ◽  
Real Life ◽  
Model Parameters ◽  
Pickup And Delivery ◽  
Distribution Centers ◽  
Routing Problem ◽  
Remarkable Feature ◽  
Content Type ◽  
Proposed Model ◽  
Production Routing

Purpose This paper aims to provide an integrated production-routing model in a three-echelon supply chain containing a two-layer transportation system to minimize the total costs of production, transportation, inventory holding and expired drugs treatment. In the proposed problem, some specifications such as multisite manufacturing, simultaneous pickup and delivery and uncertainty in parameters are considered. Design/methodology/approach At first, a mathematical model has been proposed for the problem. Then, one possibilistic model and one robust possibilistic model equivalent to the initial model are provided regarding the uncertain nature of the model parameters and the inaccessibility of their probability function. Finally, the performance of the proposed model is evaluated using the real data collected from a pharmaceutical production center in Iran. The results reveal the proper performance of the proposed models. Findings The results obtained from applying the proposed model to a real-life production center indicated that the number of expired drugs has decreased because of using this model, also the costs of the system were reduced owing to integrating simultaneous drug pickup and delivery operations. Moreover, regarding the results of simulations, the robust possibilistic model had the best performance among the proposed models. Originality/value This research considers a two-layer vehicle routing in a production-routing problem with inventory planning. Moreover, multisite manufacturing, simultaneous pickup of the expired drugs and delivery of the drugs to the distribution centers are considered. Providing a robust possibilistic model for tackling the uncertainty in demand, costs, production capacity and drug expiration costs is considered as another remarkable feature of the proposed model.

An M/M/C/K queueing system in an inventory routing problem considering congestion and response time for post-disaster humanitarian relief: a case study

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mahdieh Masoumi ◽  
Amir Aghsami ◽  
Mohammad Alipour-Vaezi ◽  
Fariborz Jolai ◽  
Behdad Esmailifar
Keyword(s):  
Sensitivity Analyses ◽  
Inventory Routing ◽  
Humanitarian Relief ◽  
Exact Methods ◽  
Routing Problem ◽  
Content Type ◽  
Inventory Routing Problem ◽  
The People ◽  
Proposed Model

PurposeDue to the randomness and unpredictability of many disasters, it is essential to be prepared to face difficult conditions after a disaster to reduce human casualties and meet the needs of the people. After the disaster, one of the most essential measures is to deliver relief supplies to those affected by the disaster. Therefore, this paper aims to assign demand points to the warehouses as well as routing their related relief vehicles after a disaster considering convergence in the border warehouses.Design/methodology/approachThis research proposes a multi-objective, multi-commodity and multi-period queueing-inventory-routing problem in which a queuing system has been applied to reduce the congestion in the borders of the affected zones. To show the validity of the proposed model, a small-size problem has been solved using exact methods. Moreover, to deal with the complexity of the problem, a metaheuristic algorithm has been utilized to solve the large dimensions of the problem. Finally, various sensitivity analyses have been performed to determine the effects of different parameters on the optimal response.FindingsAccording to the results, the proposed model can optimize the objective functions simultaneously, in which decision-makers can determine their priority according to the condition by using the sensitivity analysis results.Originality/valueThe focus of the research is on delivering relief items to the affected people on time and at the lowest cost, in addition to preventing long queues at the entrances to the affected areas.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

BIOMATH ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2106147
Author(s):  
Debkumar Pal ◽  
D Ghosh ◽  
P K Santra ◽  
G S Mahapatra
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Treatment Control ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
The Cost ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

Sign in / Sign up

Export Citation Format

Share Document