Discrete production workstation with two types of imperfect items: determining the optimal promise time

This paper presents a discrete production system where units are manufactured and reworked, if needed, one at a time using the same resources. Examples of these systems include products that involve extensive manual operations such as welding or manual assembly of intricate items. This industrial setting is not discussed in the literature. The major difficulty in studying these systems is the huge number of possible sequences of conforming and non-conforming units. This paper presents a very efficient approach to analyse these systems. We generate the system statistics for short production periods. In order to study the long-term behaviour of system statistics, we introduce renewal cycles. A major issue facing a manufacturer using these systems is determining the time it takes to produce a given customer order which is called promise time. This paper aims to find the optimal promise time that maximises the expected profit. Numerical experiments show that the expected profit is inversely proportional to the processing times. In addition, the expected profit is sensitive to the parameters; a change of +/- 0.05 in the probability of having a conforming unit may result in a 25% change in the expected profit.