EPQ model with learning consideration, imperfect production and partial backlogging in fuzzy random environment

The article scrutinises the learning effect of the unit production time on optimal lot size for the uncertain and imprecise imperfect production process, wherein shortages are permissible and partially backlogged. Contextually, we contemplate the fuzzy chance of production process shifting from an ‘in-control’ state to an ‘out-of-control’ state and re-work facility of imperfect quality of produced items. The elapsed time until the process shifts is considered as a fuzzy random variable, and consequently, fuzzy random total cost per unit time is derived. Fuzzy expectation and signed distance method are used to transform the fuzzy random cost function into an equivalent crisp function. The results are illustrated with the help of numerical example. Finally, sensitivity analysis of the optimal solution with respect to major parameters is carried out.

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