Scheduling theory in light of lean manufacturing

A central implicit axiom in classic deterministic scheduling theory is that the manufacturing resource, i.e., the machines, yields perfect and zero waste products throughout its life span. In this paper, we aim to challenge this hypothesis, as it is well known that there is always a non-zero percentage of defective products and raw material waste in real-life situations. Thus, we are trying to combine scheduling theory with the current and essential initiatives of Zero Waste Manufacturing (ZWM) and Zero Defect Manufacturing (ZDM), which aim to reduce waste and avoid failures and imperfections during production, respectively. Given this effort, we revisit and analyze several classic single-machine scheduling problems given ZWM. We assume the machine's performance deteriorates and tends to increase waste or produce faulty products. Therefore, a Calibration and Preventive Maintenance Activity (CPMA) is essential to guarantee optimal performance in the planning horizon. To this end, we postulate that each product is penalized with a job-dependent waste cost. Consequently, we seek to minimize a scheduling measure subject to an upper bound on the permitted total waste cost or, alternatively, an upper bound on the defective products’ fixing (repairing) cost. First, we address the fixed time CPMA interval and then the floating time interval. The researched scheduling measures are the makespan and the total weighted completion time. As these problems are known to be ordinary NP-hard, even without the new constraints, we introduce pseudo-polynomial dynamic programming (DP) algorithms. Furthermore, we demonstrate the procedure of mapping the set of Pareto-optimal solutions, establishing that all the studied problems are ordinary NP-hard.