Integrated Supply Chain Model for Imperfect and Deteriorating Items with Inflation and Delay in Payments Under Carbon Emission Constraint

In a competitive commercial market, when an order is made, a retailer has the privilege to decide on the number of deliveries. The optimal number of deliveries received only from the retailer's point of view may not be the most profitable for the manufacturer. However, considering both their perspectives, an overall joint profit can be achieved. So this article develops an integrated single manufacturer and single retailer production-inventory model for imperfect quality items considering carbon emission. Permissible delay in payment is also considered for retailer if outstanding amount is repaid within the given credit period. Now, since not all customers are willing to wait for backlogged during the shortage period, shortages are also allowed in this model considered as partially backlogged. The objective of this study is to decide retailer's optimal number of deliveries so as to maximize the total profit of the integrated supply chain. To illustrate the proposed model, a numerical example is presented and sensitivity analysis is also performed to see the impact on the optimal solutions with respect to major parameters is carried out using Mathematica-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$-$$\end{document}12.0 software.