Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S2969 - S2982|
|Published online||02 March 2021|
An optimization of solid transportation problem with stochastic demand by Lagrangian function and KKT conditions
Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723104, India
* Corresponding author: firstname.lastname@example.org
Accepted: 20 November 2020
In this paper, a stochastic solid transportation problem (SSTP) is constructed where the demand of the item at the destinations are randomly distributed. Such SSTP is formulated with profit maximization form containing selling revenue, transportation cost and holding/shortage cost of the item. The proposed SSTP is framed as a nonlinear transportation problem which is optimized through Karush–Kuhn–Tucker (KKT) conditions of the Lagrangian function. The primary model is bifurcated into three different models for continuous and discrete demand patterns. The concavity of the objective functions is also presented here very carefully. Finally, a numerical example is illustrated to stabilize the models.
Mathematics Subject Classification: 49Q22 / 90B06 / 90C08
Key words: Solid transportation problem / stochastic demand / Lagrangian / KKT condition
© EDP Sciences, ROADEF, SMAI 2021
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