A Robust Expected Makespan for Permutation Flow Shop Scheduling Depending on Machine Failure Rate

The environment of Flow Shop Scheduling Problems (FSSPs) to minimize the makespan of n jobs that have to be performed on m machines is considered. In real-world manufacturing systems nowadays, the uncertain circumstances to execute these jobs have an essential effect on the final scheduling scheme. This paper puts forward an integrated optimization heuristics that combine two distinct factors in flow shop scheduling. These factors are the variation in the processing times and the machine's reliability (machine failure rate), which must be considered to obtain optimal scheduling under stochastic assumptions. Two new approaches have been proposed in this work to achieve a robust expected makespan in the stochastic environment. The procedure is to add buffer time depending on the machine failure rate. Hence, the first procedure is to add buffer time to each operation in the mission according to the reliability of all machines (system reliability). The second one is to add buffer time to each operation depending on the reliability of each machine (machine reliability). For solving this problem with consideration to minimizing the expected makespan and maximizing the robustness simultaneously, the well-known (NEH) heuristic is implemented to schedule a set of jobs. Computational simulations are carried out with some well-studied problems taken from the OR-Library. Experimental results show that the proposed methods provide robust and efficient solutions. Moreover, the effects of some parameters on the optimization performance are discussed.

Stochastic Load Balancing on Unrelated Machines

We consider the problem of makespan minimization on unrelated machines when job sizes are stochastic. The goal is to find a fixed assignment of jobs to machines, to minimize the expected value of the maximum load over all the machines. For the identical-machines special case when the size of a job is the same across all machines, a constant-factor approximation algorithm has long been known. Our main result is the first constant-factor approximation algorithm for the general case of unrelated machines. This is achieved by (i) formulating a lower bound using an exponential-size linear program that is efficiently computable and (ii) rounding this linear program while satisfying only a specific subset of the constraints that still suffice to bound the expected makespan. We also consider two generalizations. The first is the budgeted makespan minimization problem, where the goal is to minimize the expected makespan subject to scheduling a target number (or reward) of jobs. We extend our main result to obtain a constant-factor approximation algorithm for this problem. The second problem involves q-norm objectives, where we want to minimize the expected q-norm of the machine loads. Here we give an [Formula: see text]-approximation algorithm, which is a constant-factor approximation for any fixed q.

Shortening Project Makespan in the Case of Resource Constraints and Activity Durations Uncertainty

Shortening project expected makespan in the case of resource constraints is the most popular problem in project scheduling. But in practice activity durations is not determined. So the problem is to find a policy which could define which activity should be started at decision points to minimize expected project makespan. This problem usually called SRCPSP. In this paper we define key research tasks of such a problem and propose extended activity-based policy XABP. Computational results show us the high efficiency of this policy.