An imperfect multi-item production system is considered against time dependent demands for a finite time horizon. Here production is defective. Following [Khouja and Mehrez J. Oper. Res. Soc. 45 (1994) 1405–1417], unit production cost depends on production, raw-material and maintenance costs. Produced items have same fixed life-time. Warehouse capacity is limited and used as a constraint. Available space, production, stock and different costs are assumed as crisp or imprecise. With the above considerations, crisp and fuzzy constrained optimal control problems are formulated for the minimization of total cost consisting of raw-material, production and holding costs. These models are solved using conventional and fuzzy variational principles with equality constraint condition and no-stock as end conditions. For the first time, the inequality space constraint is converted into an equality constraint introducing a pseudo state variable following Bang Bang control. [Roul et al., J. Intell. Fuzzy Syst. 32 (2017) 565–577], as stock is mainly controlled by production, for the control problems production is taken as the control variable and stock as state variable. The reduced optimal control problem is solved by generalised reduced gradient method using Lingo-11.0. The models are illustrated numerically. For the fuzzy model, optimum results are obtained as fuzzy numbers expressed by their membership functions. From fuzzy results, crisp results are derived using α-cuts.
Mots-clés : Fuzzy variational principle, finite time horizon, imperfect production, space constraint, imprecise inventory cost
@article{RO_2019__53_3_1061_0, author = {Roul, Jotindra Nath and Maity, Kalipada and Kar, Samarjit and Maiti, Manoranjan}, title = {Multi-item {Optimal} control problem with fuzzy costs and constraints using {Fuzzy} variational principle}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {1061--1082}, publisher = {EDP-Sciences}, volume = {53}, number = {3}, year = {2019}, doi = {10.1051/ro/2019022}, zbl = {1428.49006}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2019022/} }
TY - JOUR AU - Roul, Jotindra Nath AU - Maity, Kalipada AU - Kar, Samarjit AU - Maiti, Manoranjan TI - Multi-item Optimal control problem with fuzzy costs and constraints using Fuzzy variational principle JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 1061 EP - 1082 VL - 53 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2019022/ DO - 10.1051/ro/2019022 LA - en ID - RO_2019__53_3_1061_0 ER -
%0 Journal Article %A Roul, Jotindra Nath %A Maity, Kalipada %A Kar, Samarjit %A Maiti, Manoranjan %T Multi-item Optimal control problem with fuzzy costs and constraints using Fuzzy variational principle %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 1061-1082 %V 53 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2019022/ %R 10.1051/ro/2019022 %G en %F RO_2019__53_3_1061_0
Roul, Jotindra Nath; Maity, Kalipada; Kar, Samarjit; Maiti, Manoranjan. Multi-item Optimal control problem with fuzzy costs and constraints using Fuzzy variational principle. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 3, pp. 1061-1082. doi : 10.1051/ro/2019022. http://www.numdam.org/articles/10.1051/ro/2019022/
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