A multi-periods production–inventory model with capacity constraints for multi-manufacturers – A global optimality in intuitionistic fuzzy environment

The paper deals with a managerial issue of a production plant having multi-manufacturers. The plant has its own multiple shop/delivery system and different machines which run in several periods. For a long lasting commodities, the total demand at each shop are taking into a vital role in the whole entire process of the plant. The plant needs to increase production level (hiring), reducing production level (layoff) and over-time scheduling has on the basis of forecasted demands at different periods of different shops. Main objective of the plant is to determine optimal regular and overtime production lots per periods under limited capacities by minimizing cost function that consists of regular and overtime production costs, inventory cost, hiring and layoff costs. A crisp model of the concerned linear programming problem (L.P.P.) with multiple constraints has been discussed first. Then, the cost function is optimized for three different fuzzy as well as intuitionistic fuzzy assumptions. Score function followed by ranking index method is used to optimize the function. Moreover, a comparison between general fuzzy optimization (GFO) and intuitionistic fuzzy optimization (IFO) has been done by some numerical examples. Finally, sensitivity analysis and graphical illustrations are made to justify the proposed model.