Integrating prepayment installment, pricing and replenishment decisions for growing items with power demand pattern and non-linear holding cost under carbon regulations

Increasingly strict carbon regulations enforced by regulators are encouraging companies to seek better ways to manage inventories with a desire to reduce carbon emissions from their operations. This work investigates joint prepayment installment, pricing and replenishment decisions for a growing item under cap-and-price, cap-andtrade and carbon tax regulations with the goal of maximizing a livestock farming company's profit while simultaneously reducing total carbon emissions. To investigate the work in a more general perspective, the consumption structure of the slaughtered growing items is considered as a power pattern in both price and storage time, while the cumulative holding cost to hold a weight unit up to any time is a non-linear function of storage time under an imposed prepayment mechanism. This study examines, for the first time, the best prepayment installment decision for a growing item after characterizing its properties theoretically under carbon regulations. Integrating all possible cases of the optimal solutions from theoretical outcomes, an algorithm is suggested to achieve joint optimal decisions for the farm. Five different numerical examples are solved to examine the working performance of the algorithm and finally, several management insights are provided by investigating the changing pattern of the optimal strategies for variation of the system parameters. The derived outcomes highlight that the cap-and-price policy performs well both economically and environmentally for the livestock farming company when the penalty is less than or equal to the reward for each unit of carbon emissions. Furthermore, increased customer demand in the early stages of the cycle compels the farm to purchase a higher number of growing items amid a higher number of prepayment installments and set a lower selling price for the slaughtered growing items for increasing profit. The farming company should try to finish the prepayment using multiple payments in small amounts when the prepayment portion, the rate of interest charged and the authorized time period for prepayment are all high.