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This paper may provide an alternative to the problem of a two-stage assembly system with imperfect processes in a single manufacturer-retailer and two-level integrated supply chain. A mathematical model is developed based on the following scenarios: (a) the manufacturer and the retailer are in different countries where the exchange rate is uncertain; (b) the fixed and variable carbon emission costs are incorporated into current environmental issues; (c) shortage is allowed, and the unsatisfied demand is completely backlogged. In the light of these concerns, our model is to determine the production run time, the shortage time period and defective rate of manual stage. The optimal solutions are computed by our proposed algorithm. Finally, a numerical example and sensitivity analysis are carried out to illustrate the model.

Two-stage assembly system with imperfect items for a coordinated two-level integrated supply chain under carbon emission constraints