Joint pricing and lot-sizing for a production model under controllable deterioration and carbon emissions

Carbon emission regulations help firms to develop green inventory systems. Besides, lots of items perish because of deterioration. Therefore, controlling both carbon emissions and the deterioration of items becomes essential. Despite the importance of the contribution of these issues, a few works have attended the concepts simultaneously. To fill this gap, this paper proposes a production system considering carbon emissions and deterioration of items and utilises green and preservation technologies to control them, respectively. Moreover, as determining the selling price of items plays a crucial role in a production system, pricing is another issue that this paper concentrates on it. This paper determines the preservation technology investment and green technology investment with discrete values of the cycle length and selling price for an item which: (a) items deteriorate at a constant rate, and the investment in preservation technology is allowable to mitigate the number of deteriorated items, (b) carbon is emitted due to setup and holding the items and the manufacturer follows carbon cap-and-trade regulation and invests on emission reduction, (c) a price-dependent demand is utilised to evaluate the selling price in optimal value. To validate the mathematical model, numerical examples for all cases are exposed.