The machine breakdown paradox: How random shifts in the production rate may increase company profits

Highlights

• The literature on machine breakdowns is summarized and structured in three main streams.

• We identify a paradox related to machine breakdowns in an existing inventory model.

• 7 Test problems are analyzed and used to show where the paradox occurs.

• We explain it with a differentiation between technical efficiency and economic rationality.

• We identify common assumptions in modeling the inventory system which lead to the paradox.

Abstract

The causes and effects of machine breakdowns have frequently been investigated in the past. One popular stream of research studies technical errors in production and analyzes their impact on the inventory policy of the company. In this paper, we show that random shifts in the production rate of a machine, which may occur, for example, due to technical defects, may lead to a reduction in total cost and therewith to an increase in profit. This obvious paradox may lead to situations where it is economically rational for the company to sustain a technically inefficient situation, or even to take measures to intentionally induce a shift in the production rate, for example by damaging the machine on purpose. In this paper, we illustrate this paradox by referring to an existing inventory model, and trace it back to common assumptions made in the literature.

Introduction

Cost, quality and time have often been described as the three most important factors in generating customer value. Companies that succeed in producing a product at a high quality and at low costs and that are able to react to customer requirements quickly create superior customer value and differentiate themselves from their competitors (see, e.g., Chandler, 1990).

At the level of production, the reliability of the production process is of major importance in realizing these strategic goals. If production is unreliable and errors occur frequently in processing a product, this may result in an increase in manufacturing costs (e.g., because scrap is generated, which needs to be reworked or disposed of), a decrease in quality (e.g., because defective products are delivered to the customer) and/or an increase in delivery time (e.g., because production processes have to be interrupted and restored frequently). To assist companies in increasing the reliability of production and in improving customer value, management researchers have analyzed management concepts that help companies to improve along the three strategic dimensions introduced above (see, e.g., the total quality management concept (Hackman and Wageman, 1995, Powel, 1995)).

In production management, the causes and effects of machine breakdowns have frequently been the subjects of research. Researchers in this area have studied how the run time of a machine influences the probability of a breakdown (e.g., Khouja, 2005, Lee and Rosenblatt, 1987), how a machine breakdown influences product quality or the production rate (e.g., Ben-Daya et al., 2008, Salameh and Jaber, 2000), and how inventory policies should be adjusted if production processes are prone to errors (e.g., Groenevelt et al., 1992, Meyer et al., 1979), among others. The basic statement of these works is that machine breakdowns lead to technically and economically inefficient production processes which need to be restored to ensure that the company generates customer value and maximizes its profit.

In this paper, we show that random shifts in the production rate of a machine, which may, for example, occur due to technical defects, may lead to a reduction in total cost and therewith to an increase in profit. This obvious paradox, which is in contradiction to the tenor of the works cited above, may lead to situations where it is economically rational for the company to sustain a technically inefficient situation, or even to take measures to intentionally induce a shift in the production rate, for example by damaging the machine on purpose. In this paper, we illustrate this paradox by referring to an existing inventory model, and trace it back to common assumptions made in the literature. We conclude that if these assumptions are adjusted, we can avoid that this paradox occurs and that inefficient decisions are made in practice.

The remainder of this paper is structured as follows: The next section gives an overview of works that study machine breakdowns and their effects on inventory policies. Section 3 introduces an inventory model where random shifts in the production rate may occur, and Section 4 identifies and explains this paradox by differentiating between technical efficiency and economical rationality. Section 5 summarizes and concludes the paper.