An integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment

Brand substitution is common observed phenomenon in daily life. It the decision makers’ economic understanding and potential scheme for business-industries. Also, it provides flexibility management increases ability to control production. This works proposes an integrated supplier–retailer inventory model substitutable products. Two suppliers work not with two different brand products their corresponding demand are involved one retailer sells each of To nullify complexities joint optimization problem, we first develop a deterministic three cases: no substitution, partial full then go its fuzzification. Keeping financial constraint producer, have studied over elasticity cost parameters by means triangular dense fuzzy lock set approach locking unlocking property final making. Finally, sensitivity analysis graphical illustrations made justify model.