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Managing a sustainable integrated inventory model for imperfect production process with type one and type two errorsThis study develops a sustainable integrated inventory model for controllable lead time with defective items, errors in inspection, and variable lead-time. The research investigates the effect of controlling lead time and capital investment in the setup cost.We assume that the buyer receives a lot size that may contain some defective items with a known defective probability. The buyer's inspector conducts a 100% quality inspection and may incorrectly classify a non-defective item as a defective item (type one (I) error), or incorrectly classify a defective item as a non-defective item (type two (II) error). The mathematical inventory model considering carbon emission cost is developed, and the solution procedure is designed to derive the optimal solution.Finally, numerical examples and sensitivity analysis are given to illustrate the results.

This study develops a sustainable integrated inventory model for controllable lead time with defective items, errors in inspection, and variable lead-time. The research investigates the effect of controlling lead time and capital investment in the setup cost. We assume that the buyer receives a lot size that may contain some defective items with a known defective probability. The buyer’s inspector conducts a 100% quality inspection and may incorrectly classify a non-defective item as a defective item (type one (I) error), or incorrectly classify a defective item as a non-defective item (type two (II) error). The mathematical inventory model considering carbon emission cost is developed, and the solution procedure is designed to derive the optimal solution. Finally, numerical examples and sensitivity analysis are given to illustrate the results.