Effects of variable prepayment installments on pricing and inventory decisions with power demand pattern and non-linear holding cost under carbon cap-and-price regulation

Regulators' increasingly stringent carbon rules to protect the environment are encouraging practitioners to modify their operational activities that are accountable for releasing emissions into the atmosphere. Thereby, practitioners dealing with product inventory planning are seeking proper management strategies not only to increase profits but also to reduce released carbons from operations. In addition, increasing uncertainty in supply operations has motivated suppliers to impose prepayment mechanisms in recent decades. This study examines the best prepayment installment policy for a practitioner for the first time, where the consumption behavior of consumers changes as a result of the combined effects of unit selling price and storage time. Moreover, to make the present inventory planning more realistic, the unit holding cost function is adopted as a power function of the inventory unit's storage period. The goal of this study is to provide the best combined installment for advance payment, price, and replenishment strategies for a practitioner under cap-and-price, cap-and-trade, and carbon tax environmental guidelines by ensuring maximum profit. For this purpose, an algorithm is created by combining all derived theoretical results from the analytical study, whereas the efficacy of the algorithm is assessed through the examination of five illustrative numerical instances. A plethora of noteworthy management insights for the practitioner are obtained by investigating the dynamic shifts in optimal strategies resulting from fluctuations in system parameters. The results reveal that if the demand is low in the nascent phases of the business cycle, then the prudent approach for the practitioner entails procuring a comparatively smaller lot-size using a modest number of payment frequencies and then setting a relatively small unit selling price to increase profits.