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

• 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.

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.