The job scheduling problem (JSP) is considered as one of the most complex combinatorial optimization problems. JSP is not an independent task, but is rather a part of a company business case. In this paper, we have studied JSPs under sudden machine breakdown scenarios that introduce a risk of not completing the jobs on time. We have first solved JSPs using an improved memetic algorithm and extended the algorithm to deal with the disruption situations, and then developed a simulation model to analyze the risk of using a job order and delivery scenario. This paper deals with job scheduling under ideal conditions and rescheduling under machine breakdown, and provides a risk analysis for a production business case. The extended algorithm provides better understanding and results than existing algorithms, the rescheduling shows a good way of recovering from disruptions, and the risk analysis shows an effective way of maximizing return under such situations.

We study a service system in which, in each service period, the server performs the current set B of tasks as a batch, taking time s(B), where the function s(·) is subadditive. A natural definition of ‘traffic intensity under congestion’ in this setting is ρ := limt→∞t-1Es (all tasks arriving during time [0,t]). We show that ρ > 1 and a finite mean of individual service times are necessary and sufficient to imply stability of the system. A key observation is that the numbers of arrivals during successive service periods form a Markov chain {An}, enabling us to apply classical regenerative techniques and to express the stationary distribution of the process in terms of the stationary distribution of {An}.