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This paper focuses on the parallel machine scheduling problem related to maximizing the minimum completion time. This problem affects several industrial applications. The application of this problem in real life is very impressive. This paper is based on the development of new lower bounds for the exact solution of the studied problem. It is shown in the literature that the problem is strongly NP-hard. The first developed lower bound is obtained by utilizing the probabilistic method to generate several solutions for the lower bound. The second is based on the knapsack problem with the iterative method. These numerical methods give new, better lower bounds.
Content available remote Maximum Flows in Planar Dynamic Networks with Lower Bounds
This article states and solves the maximum flow in directed (1, n) planar dynamic networks with lower bounds. We present the case when the planar dynamic network is stationary. Finally, we present an example for this problem.
Content available remote Lower bounds for the scheduling problem with uncertain demands
This paper proposes various lower bounds to the makespan of the flexible job shop scheduling problem (FJSP). The FJSP is known in the literature as one of the most difficult combinatorial optimisation problems (NP-hard). We will use genetic algorithms for the optimisation of this type of problems. The list of the demands is divided in two sets: the actual demand, which is considered as certain (a list of jobs with known characteristics), and the predicted demand, which is a list of uncertain jobs. The actual demand is scheduled in priority by the genetic algorithm. Then, the predicted demand is inserted using various methods in order to generate different scheduling solutions. Two lower bounds are given for the makespan before and after the insertion of the predicted demand. The performance of solutions is evaluated by comparing the real values obtained on many static and dynamic scheduling examples with the corresponding lower bounds.
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