A production planning problem with lost sales and nonlinear convex production cost function under carbon emission restrictions

Abstract

In this paper, a finite-horizon production planning problem with possible lost sales under several carbon emission restrictions is investigated. The studied model is deterministic with known demands which may not necessarily be met as lost sales are also allowed to provide reasonable flexibility with carbon emission restrictions. The problem is modeled as mixed integer nonlinear programming which has been reformulated in conic-quadratic form for convex cases. The problem is numerically investigated with respect to the costs incurred, the amount of carbon emissions and the magnitude of resulting demand losses. These issues are considered under different carbon restriction policies imposed over several block of periods over the planning horizon. Different carbon cap policies are defined and examined to with wide range of parameter sets to observe how different policies affect the amount of emission, cost and lost sales as the main KPI's set in this study. Numerical examples and their corresponding observations and managerial insights are provided accordingly.