Scheduling is a decision making process that concerns with allocation of limited resources (machines, material handling equipment, operators, tools, etc.) to competing tasks (operations of jobs) over time with the goal of optimizing one or more objectives. The output of this process is time/machine/operation assignments. In the scheduling theory, the objective is generally to optimize one or more regular performance measures such as makespan, flow-time, and tardiness. Recently, two new measures have been also used in scheduling applications: "robustness" and "stability". In this paper, we develop a new surrogate measure to achieve robustness and stability. This measure is embedded in a tabu search algorithm to generate schedules in a single machine environment subject to random machine breakdowns. The results of extensive computational experiments indicate that the proposed method performs better than the average slack method used in the literature.