Probabilistic Formulation for Emergency Facility Location in a Divided Area

2013 ◽  
Vol 845 ◽  
pp. 527-531
Author(s):  
Seyed Ali Mirzapour ◽  
Kuan Yew Wong ◽  
Seyedeh Sabereh Hosseini ◽  
Saber Shiripour
Keyword(s):  
Facility Location ◽  
Emergency Situation ◽  
Mixed Integer ◽  
Border Crossings ◽  
Location Allocation ◽  
Normal Probability ◽  
Minlp Model ◽  
Service Response Time ◽  
Normal Probability Distribution ◽  
Fixed Line

Capacitated minimax facility location-allocation (LA) is a type of facility problem which is of prime importance for emergency situation, since it directly affects the service response time to customers. Capacitated minimax LA problem is concerned with locating some new facilities and allocating their capacity to customers when the maximum travelled distance from customers to facilities is minimized. This study involves a fixed line barrier in a region with some border crossings along it which divides the area into two subregions. Although several studies have recently been done on this problem in which the customer locations are known with certainty, much less attention has been devoted to developing a comprehensive mathematical model for the probabilistic extension of customer locations when there are some restrictions in the region. In order to fill this gap, a Mixed Integer Nonlinear Programming (MINLP) model is proposed for facility LA when customer locations are randomly distributed according to a bivariate normal probability distribution. Finally, the BARON solver in the GAMS software is used to solve the model, and a numerical example is provided to demonstrate its efficiency.

scholarly journals Evaluation of a facility location for a food assistance supply chain. The case of Bienestarina in Colombia

2020 ◽  
Vol 39 (3) ◽  
pp. 50-61
Author(s):  
Feizar Javier Rueda-Velasco ◽  
Wilson Adarme-Jaimes ◽  
Angélica Garzón-Luna ◽  
Jhonatan Marroquín-Ávila ◽  
Gabriel Parada-Caro
Keyword(s):  
Supply Chain ◽  
Facility Location ◽  
Programming Model ◽  
Food Assistance ◽  
Social Program ◽  
Policy Implications ◽  
Mixed Integer ◽  
Current Configuration ◽  
Location Allocation ◽  
The Government

The evaluation of the strategic supply chain configuration is considered one of the strategic logistics decisions, especially in food assistance supply chains focused on generating better nutritional conditions in vulnerable populations. In Colombia, there is a social program called Bienestarina, which aims to promote food and nutritional security in a vulnerable population. Although the government supports the program for improving nutritional support, there are currently inconsistencies in freight flows, lack of coverage in some areas, and delivery delays. Therefore, this work aims to evaluate the current configuration of the supply chain and propose improvements related to the facility location. Such advances would enable the increase in the efficacy of the network and the reduction of malnutrition in the country. For this purpose, a mixed-integer mathematical programming model is presented, which considers the weighted distance criterion for different demand scenarios and supports the location-allocation decision in a social assistance supply chain. The current network configuration was compared with the optimal proposed structure. The comparisons show highly potential improvements in freight flow allocation, suggests several variations in the existing warehouses emplacement, and generates public policy implications to reduce the logistic cost in the system, prioritizing in turn the demand covering.

scholarly journals Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xuejie Bai ◽  
Ying Liu
Keyword(s):  
Facility Location ◽  
Value At Risk ◽  
Structural Characteristics ◽  
Fuzzy Variable ◽  
Mixed Integer ◽  
Minimum Risk ◽  
Fuzzy Variables ◽  
Location Allocation ◽  
The Impact

Facility location decision is basically viewed as a long-term strategy, so the inherited uncertainty of main parameters ought to be taken into account in order to make models applicable. In this paper, we examine the impact of uncertain transportation costs and customers’ demands on the choice of optimal location decisions and allocation plans. This leads to the formulation of the facility location-allocation (FLA) problem as a fuzzy minimum risk programming, in which the uncertain parameters are assumed to be characterized by type-2 fuzzy variables with known type-2 possibility distributions. Since the inherent complexity of type-2 fuzzy FLA may be troublesome, existing methods are no longer effective in handling the proposed problems directly. We first derive the critical value formula for possibility value-at-risk reduced fuzzy variable of type-2 triangular fuzzy variable. On the basis of formula obtained, we can convert original fuzzy FLA model into its equivalent parametric mixed integer programming form, which can be solved by conventional numerical algorithms or general-purpose software. Taking use of structural characteristics of the equivalent optimization, we design a parameter decomposition method. Finally, a numerical example is presented to highlight the significance of the fuzzy FLA model. The computational results show the credibility and superiority of the proposed parametric optimization method.

scholarly journals A Capacitated Location-Allocation Model for Flood Disaster Service Operations with Border Crossing Passages and Probabilistic Demand Locations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Seyed Ali Mirzapour ◽  
Kuan Yew Wong ◽  
Kannan Govindan
Keyword(s):  
Programming Model ◽  
Border Crossing ◽  
Mixed Integer ◽  
Allocation Model ◽  
Safe Place ◽  
Location Allocation ◽  
Proposed Model ◽  
Flood Disasters ◽  
Nonlinear Programming Model ◽  
Fixed Line

Potential consequences of flood disasters, including severe loss of life and property, induce emergency managers to find the appropriate locations of relief rooms to evacuate people from the origin points to a safe place in order to lessen the possible impact of flood disasters. In this research, a p-center location problem is considered in order to determine the locations of some relief rooms in a city and their corresponding allocation clusters. This study presents a mixed integer nonlinear programming model of a capacitated facility location-allocation problem which simultaneously considers the probabilistic distribution of demand locations and a fixed line barrier in a region. The proposed model aims at minimizing the maximum expected weighted distance from the relief rooms to all the demand regions in order to decrease the evacuation time of people from the affected areas before flood occurrence. A real-world case study has been carried out to examine the effectiveness and applicability of the proposed model.

scholarly journals MINLP formulations for continuous piecewise linear function fitting

2021 ◽  
Author(s):  
Noam Goldberg ◽  
Steffen Rebennack ◽  
Youngdae Kim ◽  
Vitaliy Krasko ◽  
Sven Leyffer
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Function Fitting ◽  
Computational Performance ◽  
Integer Nonlinear Programming ◽  
Minlp Model ◽  
Necessary Constraints ◽  
Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

A Note on a Conceptual Framework for Dynamic Location—Allocation Analysis

1976 ◽  
Vol 8 (4) ◽  
pp. 443-446
Author(s):  
W G Truscott
Keyword(s):  
Conceptual Framework ◽  
Integer Program ◽  
Original Version ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Location Allocation ◽  
Dynamic Location

This note examines a previously published model for dynamic location—allocation analysis. The usefulness of this model is enhanced by reformulating the problem as an operational zero-one, mixed-integer program while retaining the intent of the original version.

Feeder Bus Timetable Design and Vehicle Size Setting in Peak Hour Demand Conditions

2019 ◽  
Vol 2673 (10) ◽  
pp. 321-332 ◽  
Author(s):  
Xueping Dou ◽  
Qiang Meng
Keyword(s):  
Mixed Integer ◽  
Arrival Times ◽  
Non Linear Programming ◽  
Bee Colony ◽  
Proposed Model ◽  
Feeder Bus ◽  
Minlp Model ◽  
Failure Cost ◽  
Set Up ◽  
The Given

This study proposes a solution to the feeder bus timetabling problem, in which the terminal departure times and vehicle sizes are simultaneously determined based on the given transfer passengers and their arrival times at a bus terminal. The problem is formulated as a mixed integer non-linear programming (MINLP) model with the objective of minimizing the transfer waiting time of served passengers, the transfer failure cost of non-served passengers, and the operating costs of bus companies. In addition to train passengers who plan to transfer to buses, local passengers who intend to board buses are considered and treated as passengers from virtual trains in the proposed model. Passenger attitudes and behaviors toward the waiting queue caused by bus capacity constraints in peak hour demand conditions are explicitly embedded in the MINLP model. A hybrid artificial bee colony (ABC) algorithm is developed to solve the MINLP model. Various experiments are set up to account for the performance of the proposed model and solution algorithm.

scholarly journals Simultaneous Synthesis of Heat Exchanger Networks Considering Steam Supply and Various Steam Heater Locations

Energies ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1467 ◽  
Author(s):  
Yao Sheng ◽  
Linlin Liu ◽  
Yu Zhuang ◽  
Lei Zhang ◽  
Jian Du
Keyword(s):  
Heat Exchanger ◽  
Rankine Cycle ◽  
Mixed Integer ◽  
Total Annual Cost ◽  
Process Industries ◽  
Structural Improvement ◽  
Utility Systems ◽  
Utility System ◽  
Heat Exchanger Networks ◽  
Minlp Model

In process industries, the heating gap in heat exchanger networks (HENs) is normally compensated by the steam generated from a utility system, thus these two mutually influencing systems should be designed as a whole through establishing structural interrelationships. In this work, an improved stage-wise superstructure of HENs is proposed to integrate with a Rankine cycle-based utility system. Inner- and inter-stage heaters are considered in the new structure. Furthermore, the selection of steam in different levels is also investigated, extending the possibilities of steam utilization in HENs and generation in utility systems. The presented methodology is able to realize the optimal design of HENs by considering the supply and utilization of steam. Heaters’ allocations, matches of streams, steam distribution and utilization are optimized accompanying with the trade-off amongst equipment investment, fuel consumption and power generation in objective, which is highly related to the final structure of the system. The optimization problem is formulated into a mixed-integer non-linear programming (MINLP) model and solved towards the lowest total annual cost (TAC) of the entire system. Finally, a case study with two scenarios is studied. The detailed results are given and analyzed to demonstrate the benefit from structural improvement.

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