Multi-choice and stochastic programming for transportation problem involved in supply of foods and medicines to hospitals with consideration of logistic distribution
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 4, pp. 1119-1132.

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.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ro/2019050
Classification : 90B05
Mots-clés : Multi-choice programming, stochastic programming, Logistic distribution, transportation problem, transformation technique, mixed-integer programming 
@article{RO_2020__54_4_1119_0,
     author = {Mahapatra, Deshabrata Roy and Panda, Shibaji and Sana, Shib Sankar},
     title = {Multi-choice and stochastic programming for transportation problem involved in supply of foods and medicines to hospitals with consideration of logistic distribution},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1119--1132},
     publisher = {EDP-Sciences},
     volume = {54},
     number = {4},
     year = {2020},
     doi = {10.1051/ro/2019050},
     mrnumber = {4107502},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2019050/}
}
TY  - JOUR
AU  - Mahapatra, Deshabrata Roy
AU  - Panda, Shibaji
AU  - Sana, Shib Sankar
TI  - Multi-choice and stochastic programming for transportation problem involved in supply of foods and medicines to hospitals with consideration of logistic distribution
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2020
SP  - 1119
EP  - 1132
VL  - 54
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2019050/
DO  - 10.1051/ro/2019050
LA  - en
ID  - RO_2020__54_4_1119_0
ER  - 
%0 Journal Article
%A Mahapatra, Deshabrata Roy
%A Panda, Shibaji
%A Sana, Shib Sankar
%T Multi-choice and stochastic programming for transportation problem involved in supply of foods and medicines to hospitals with consideration of logistic distribution
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2020
%P 1119-1132
%V 54
%N 4
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2019050/
%R 10.1051/ro/2019050
%G en
%F RO_2020__54_4_1119_0
Mahapatra, Deshabrata Roy; Panda, Shibaji; Sana, Shib Sankar. Multi-choice and stochastic programming for transportation problem involved in supply of foods and medicines to hospitals with consideration of logistic distribution. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 4, pp. 1119-1132. doi : 10.1051/ro/2019050. http://www.numdam.org/articles/10.1051/ro/2019050/

[1] J.C. Ahuja and S.W. Nash, The generalized gompertz-verhulst family of distribution. Sankhya Ser. A 29 (1967) 141–156. | MR | Zbl

[2] N. Balakrishnan, Handbook of Logistic Distribution. Dekker, New York, NY (1991). | DOI | MR | Zbl

[3] M.P. Biswal and S. Acharya, Transformation of a Multi-choice linear programming problem. Appl. Math. Comput. 210 (2009) 182–188. | MR | Zbl

[4] C.-T. Chang, Multi-choice goal programming. Omega Int. J. Manage. Sci. 35 (2007) 389–396. | DOI

[5] C.-T. Chang, Binary fuzzy programming. Eur. J. Oper. Res. 180 (2007) 29–37. | DOI | MR | Zbl

[6] C.-T. Chang, Revised multi-choice goal programming. Appl. Math. Model. 32 (2008) 2587–2595. | DOI | MR | Zbl

[7] G.B. Dantzig, Linear Programming and Extensions, Princeton University Press, Princeton, NJ (1963). | MR | Zbl

[8] A. Goicoechea, D.R. Hansen and L. Duckstein, Multi-objective Decision Analysis with Engineering and Business Application. John Wiley and Sons, New York, NY (1982). | Zbl

[9] F.L. Hitchcock, The distribution of a product from several sources to numerous localities. J. Math. Phys. 20 (1941) 224–230. | DOI | JFM | MR | Zbl

[10] D.R. Mahapatra, S.K. Roy and M.P. Biswal, Computation of multi-ojective stochastic transportation problem involving normal distribution. J. Math. 19 (2011) 865–763.

[11] S. Mohapatra, Better healthcare at reduced cost through electronic integration of patient care data. Int. J. Electr. Healthc. 5 (2009) 87–98. | DOI

[12] S. Mohapatra, Using integrated information system for patient benefits: a case study in India. Int. J. Healthc. Manage. 8 (2015) 262–271. | DOI

[13] S. Mohapatra and S. Murarka, Improving patient care in hospital in India by monitoring influential parameters. Int. J. Healthc. Manage. 9 (2016) 83–101. | DOI

[14] A.K. Olapade, On extended Type-1 generalised logistic distribution. Int. J. Math. Sci. 57 (1991) 3069–3074. | MR | Zbl

[15] A. Rabindran, D.T. Philips and J.J. Solberg, Operations Research: Principles and Practice, 2nd edition. John Wiley and Sons, New York, NY (1987). | MR | Zbl

[16] S.K. Roy, D.R. Mahapatra and M.P. Biswal, Multi-choice stochastic transportation problem with exponential distribution. J. Uncertain Syst. 19 (2011) 865–763.

[17] L. Schrage, Optimiazation Modeling with Lingo, 6th edition. Lindo System, Chicago, III, USA (2006).

Cité par Sources :