Multi-choice and stochastic programming for transportation problem involved in supply of foods and medicines to hospitals with consideration of logistic distribution

2020 ◽  
Vol 54 (4) ◽  
pp. 1119-1132
Author(s):  
Deshabrata Roy Mahapatra ◽  
Shibaji Panda ◽  
Shib Sankar Sana
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Transportation Problem ◽  
Programming Model ◽  
Logistic Distribution ◽  
Programming Approach ◽  
Binary Variables ◽  
Cost Coefficient ◽  
Aspiration Levels ◽  
Stochastic Constraints

The objective of the proposed article is to minimize the transportation costs of foods and medicines from different source points to different hospitals by applying stochastic mathematical programming model to a transportation problem in a multi-choice environment containing the parameters in all constraints which follow the Logistic distribution and cost coefficients of objective function are also multiplicative terms of binary variables. Using the stochastic programming approach, the stochastic constraints are converted into an equivalent deterministic one. A transformation technique is introduced to manipulate cost coefficients of objective function involving multi-choice or goals for binary variables with auxiliary constraints. The auxiliary constraints depends upon the consecutive terms of multi-choice type cost coefficient of aspiration levels. A numerical example is presented to illustrate the whole idea.

Solving Solid Transportation Problems With Multi-Choice Cost and Stochastic Supply and Demand

2018 ◽  
pp. 137-170 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Deshabrata Roy Mahapatra
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solid Transportation Problem ◽  
New Approach ◽  
Non Linear Programming ◽  
The Cost

In this chapter, the authors propose a new approach to analyze the Solid Transportation Problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming, which is incorporated in three constraints, namely sources, destinations, and capacities constraints, followed by Cauchy's distribution for solid transportation problem. The multi-choice programming and stochastic programming are combined into a solid transportation problem, and this new problem is called Multi-Choice Stochastic Solid Transportation Problem (MCSSTP). The solution concepts behind the MCSSTP are based on a new transformation technique that will select an appropriate choice from a set of multi-choice, which optimize the objective function. The stochastic constraints of STP converts into deterministic constraints by stochastic programming approach. Finally, the authors construct a non-linear programming problem for MCSSTP, and by solving it, they derive an optimal solution of the specified problem. A realistic example on STP is considered to illustrate the methodology.

Solving Solid Transportation Problem with Multi-Choice Cost and Stochastic Supply and Demand

2014 ◽  
Vol 5 (3) ◽  
pp. 1-26 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Deshabrata Roy Mahapatra
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solid Transportation Problem ◽  
New Approach ◽  
Non Linear Programming ◽  
The Cost

This paper proposes a new approach to analyze the solid transportation problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming which is incorporated in three constraints namely sources, destinations and capacities constraints followed by Cauchy's distribution for solid transportation problem. The multi-choice programming and stochastic programming are combined into solid transportation problem and this new problem is called multi-choice stochastic solid transportation problem (MCSSTP). The solution concepts behind the MCSSTP are based on a new transformation technique which will select an appropriate choice from a set of multi-choice which optimizes the objective function. The stochastic constraints of STP convert into deterministic constraints by stochastic programming approach. Finally, the authors have constructed a non-linear programming problem for MCSSTP and have derived an optimal solution of the specified problem. A realistic example on STP is considered to illustrate the methodology.

Solving Solid Transportation Problems with Multi-Choice Cost and Stochastic Supply and Demand

2015 ◽  
pp. 397-428
Author(s):  
Sankar Kumar Roy ◽  
Deshabrata Roy Mahapatra
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solid Transportation Problem ◽  
New Approach ◽  
Non Linear Programming ◽  
The Cost

In this chapter, the authors propose a new approach to analyze the Solid Transportation Problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming, which is incorporated in three constraints, namely sources, destinations, and capacities constraints, followed by Cauchy's distribution for solid transportation problem. The multi-choice programming and stochastic programming are combined into a solid transportation problem, and this new problem is called Multi-Choice Stochastic Solid Transportation Problem (MCSSTP). The solution concepts behind the MCSSTP are based on a new transformation technique that will select an appropriate choice from a set of multi-choice, which optimize the objective function. The stochastic constraints of STP converts into deterministic constraints by stochastic programming approach. Finally, the authors construct a non-linear programming problem for MCSSTP, and by solving it, they derive an optimal solution of the specified problem. A realistic example on STP is considered to illustrate the methodology.

scholarly journals Multi-choice stochastic transportation problem involving weibull distribution

2013 ◽  
Vol 4 (1) ◽  
pp. 45-55 ◽  
Author(s):  
Deshabrata Roy Mahapatra
Keyword(s):  
Objective Function ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Real Life ◽  
Solution Procedure ◽  
Binary Variables ◽  
Real Life Situation ◽  
Stochastic Transportation Problem ◽  
Stochastic Constraints ◽  
Additional Constraints

A solution procedure for multi-choice stochastic transportation problem is presented herewith some stochastic constraints containing parameters as supply and demand of Weibull distributionand cost coecients of objective function have multi-choice in nature of real life situation. At rst, allstochastic constraints are transformed into deterministic constraints by using the stochastic approach.A transformation technique is introduced for manipulation of multi-choice cost coecients of objectivefunction into equivalent deterministic form in terms of binary variables with additional restrictions.The auxiliary and additional constraints involving binary variables depend upon the set of consecutiveterms of cost coecients of the objective function whose sum is equal or nearer to the aspiration levels.Finally, a numerical example is presented to illustrate the solution procedure of the specied proposedmodel.

A Stochastic Programming Approach for Locating and Dispatching Two Types of Ambulances

2021 ◽  
Vol 55 (2) ◽  
pp. 275-296
Author(s):  
Soovin Yoon ◽  
Laura A. Albert ◽  
Veronica M. White
Keyword(s):  
Stochastic Programming ◽  
Large Scale ◽  
Simulation Analysis ◽  
Programming Model ◽  
Prehospital Care ◽  
Programming Approach ◽  
Solution Technique ◽  
Solution Approach ◽  
Stochastic Solution ◽  
Problem Instances

Emergency Medical Service systems aim to respond to emergency calls in a timely manner and provide prehospital care to patients. This paper addresses the problem of locating multiple types of emergency vehicles to stations while taking into account that vehicles are dispatched to prioritized patients with different health needs. We propose a two-stage stochastic-programming model that determines how to locate two types of ambulances in the first stage and dispatch them to prioritized emergency patients in the second stage after call-arrival scenarios are disclosed. We demonstrate how the base model can be adapted to include nontransport vehicles. A model formulation generalizes the base model to consider probabilistic travel times and general utilities for dispatching ambulances to prioritized patients. We evaluate the benefit of the model using two case studies, a value of the stochastic solution approach, and a simulation analysis. The case study is extended to study how to locate vehicles in the model extension with nontransport vehicles. Stochastic-programming models are computationally challenging for large-scale problem instances, and, therefore, we propose a solution technique based on Benders cuts.

An Integer Programming Approach to Optimize the Plantation in Order to Reduce Global Warming

2012 ◽  
Vol 548 ◽  
pp. 767-771 ◽  
Author(s):  
C. Vanlisuta ◽  
Suksan Prombanpong
Keyword(s):  
Mathematical Model ◽  
Linear Programming ◽  
Objective Function ◽  
Programming Model ◽  
Programming Approach ◽  
Profit Function ◽  
Carbon Credit ◽  
Integer Linear Programming Model ◽  
The Mathematical Model

The objective of this paper is to determine the number and species of trees to be planted in order to maximize a profit through an integer linear programming model. The mathematical model is developed in terms of the profit function. This objective function is therefore, a difference between carbon credit revenue and costs of plantation. The economical plants are only considered in the model. Consequently, fourteen different tree species are to be investigated. The objective function is subjected to several constraints i.e. planting area, carbon sequestration and so on. The planting envelope of each tree is assigned 4 by 4 meters. In this paper, the Eastern part of Thailand is considered the case study. It is found that three kinds of plants, Copper pod, Cananga, and Bullet wood are suitable for planting. A number of trees to be planted in 1600 square meter are twenty, thirty, and fifty plants respectively. The profit earned is of 12,112 $ per year in the next fifth year.

scholarly journals A Stochastic Programming Approach for Resilient Hub Location in Power Projection Network considering Random Hub Failures

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Xu-Tao Zhang ◽  
Hai-Ling Bi ◽  
Yun Wang
Keyword(s):  
Stochastic Programming ◽  
Programming Model ◽  
Programming Approach ◽  
Hub Location ◽  
Hub Location Problem ◽  
Power Projection ◽  
Critical Facilities ◽  
Resilient Networks ◽  
The Impact ◽  
Projection Network

Hubs are critical facilities in the power projection network. Due to the uncertainty factors such as terrorism threats, severe weather, and natural disasters, hub facilities may be disrupted randomly, which could lead to excessive cost or loss in practice. One of the most effective ways to withstand and reduce the impact of disruptions is designing more resilient networks. In this paper, a stochastic programming model is employed for the hub location problem in the presence of random hub failures. A heuristic algorithm based on Monte Carlo method and tabu search is put forward to solve the model. The proposed approach is more general if there are numbers of hubs that would fail even with different failure probability. Compared with the benchmark model, the model which takes the factor of stochastic failure of hubs into account can give a more resilient power projection network.

scholarly journals A fuzzy optimization approach to strategic organ transplantation network design problem: A real case study

2021 ◽  
Vol 10 (3) ◽  
pp. 195-216
Author(s):  
Samira Rouhani ◽  
Mir Saman Pishvaee ◽  
Naeme Zarrinpoor
Keyword(s):  
Programming Model ◽  
Organ Transplant ◽  
Real Case ◽  
Programming Approach ◽  
Optimization Approach ◽  
Primary Role ◽  
Model Based ◽  
Aspiration Levels ◽  
Possibilistic Programming

Designing an efficient supply chain for organ transplant networks which is intimately related to humans’ life plays a primary role in improving the network’s performance. This research is focused on proposing a new multi-period location-allocation modeling approach to make appropriate strategic decisions for designing organ transplant networks under supply and budget uncertainties. To serve this purpose, a bi-objective possibilistic programming model is formulated the aim of which is to maximize network responsiveness and minimize the total cost. A fuzzy goal programming approach is adopted to solve multiple objective function models and control their deviations from the corresponding aspiration levels. As an important contribution of this study, the chance of success of transplantation processes is taken into consideration by proposing appropriate utility functions according to transportation criteria. Moreover, for the purpose of coping with the inherent uncertainty of the input parameters, a possibilistic programming model based on Me measure converted to three optimistic, realistic and pessimistic models is developed. Three new formulations have also been developed to tackle equality chance constraints. Finally, the optimal solutions of the developed models are analyzed through conducting a real case study in Iran. According to the results, for the considered organ transplant network, the possibilistic programming model based on the realistic measure is better than the optimistic and pessimistic measure in most confidence levels.

scholarly journals A Multi-Stage Stochastic Programming Approach to Epidemic Resource Allocation with Equity Considerations

2021 ◽  
Author(s):  
Xuecheng Yin ◽  
İ. Esra Büyüktahtakın
Keyword(s):  
Resource Allocation ◽  
Stochastic Programming ◽  
Ebola Virus ◽  
Programming Model ◽  
Virus Disease ◽  
Programming Approach ◽  
Multiple Time ◽  
Allocation Policy ◽  
Multi Stage ◽  
Constraints Model

AbstractExisting compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected number of new infections and funerals. We define two new equity metrics, namely infection and capacity equity, and explicitly consider equity for allocating treatment funds and facilities over multiple time stages. We also study the multistage value of the stochastic solution (VSS), which demonstrates the superiority of the proposed stochastic programming model over its deterministic counterpart. We apply the proposed formulation to control the Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia of West Africa to determine the optimal and fair resource-allocation strategies. Our model balances the proportion of infections over all regions, even without including the infection equity or prevalence equity constraints. Model results also show that allocating treatment resources proportional to population is sub-optimal, and enforcing such a resource allocation policy might adversely impact the total number of infections and deaths, and thus resulting in a high cost that we have to pay for the fairness. Our multi-stage stochastic epidemic-logistics model is practical and can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations.

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