A sustainable economic production model: effects of quality and emissions tax from transportation

Abstract

Faced with pressure from the public, governments, and environmental agencies, it is becoming essential for manufacturing firms to identify and implement sustainable operations aiming at reducing the negative social and environmental impacts while enhancing the firm’s public image and increasing its economic performance. This paper investigates a production model that incorporates the quality of different types of components/raw material parts used in the production process along with their transportation emissions tax. It is assumed that the various types of components contain both perfect and imperfect quality items. The percentage of perfect quality components of a particular type is a random variable having a known probability distribution. Based on results regarding the probability distribution and the expected value of the minimum of a set of random variables, a mathematical model is developed and the total production/inventory cost is obtained. A closed form formula approximating the optimal solution is derived in terms of the expected value of the minimum of a set of random variables related to the percentages of perfect quality components. The case in which the percentages of perfect quality components are uniformly distributed is investigated and a numerical example is given to illustrate this case. The accuracy of the approximated solution is assessed via a simulation algorithm that can also be used to approximate the optimal lot size in the case when the percentages of perfect quality components are not all uniformly distributed.