EOQ model with backorders under linear combination of possibility and necessity measure (Q1635443)

Summary: This paper considers an EOQ model with backorders and imprecise holding cost, ordering cost and shortage cost under linear combination of possibility measure and necessity measure. The objective function of this model is to minimise fuzzy total annual cost, which includes fuzzy annual holding cost, fuzzy annual ordering cost and fuzzy annual shortage penalty cost. Making use of \(m_\lambda\)-measure, a linear combination of possibility measure and necessity measure, two fuzzy chance-constrained programming models are constructed to determine optimistic and pessimistic values of the objective function. An objective function is optimised with some predefined degree of \(m_\lambda\)-measure and accordingly the problem is transferred to an equivalent crisp problem. An analytical approach is developed to resolve the reduced models. To analyse the characteristics of the proposed model and to find the optimal decision under different situations, numerical illustrations are presented along with a sensitivity analysis.