Analysis of a production system of green products considering single-level trade credit financing via a parametric approach of intervals and meta-heuristic algorithms

Abstract

The use of chemicals and preservatives during the production of most daily-used products has increased rapidly over the last few decades. In turn, manufacturers, to improve the sustainability of a manufacturing unit in the current highly competitive market, are obliged to provide various facilities to their customers. However, estimating the best optimal decision for manufacturing companies seems like a daunting task amid highly uncertain market conditions. By shedding more light on these facts and considering the gaps in the existing literature on production inventory, this work aims to incorporate a production model which is concerned with the factors mentioned above, so that it can be beneficial for a manufacturer. This work involves the demonstration of an imperfect green production system under single-layer full-trade credit financing and partial backlog shortages using interval flexibility. Based on the credit period lengths provided by the manufacturer to the consumers, three distinct cases have arisen and for each case, the average profit of the system appears to be an interval valued optimal control problem, and several theorems are evaluated to obtain analytical forms of respective objective functions of each case. Additionally, to test the effect of different credit lengths on optimal policy and to examine the feasibility of each case, a numerical example is solved using the Equilibrium Optimizer (EO) algorithm. Finally, a sensitivity experiment is performed and the results obtained from the simulation are shown graphically to gain some managerial insights.