Inverse scheduling: two machine flow shop problem

We study an inverse counterpart of the two-machine flow-shop scheduling problem that arises in the context of inverse optimization. While in the forward scheduling problem all parameters are given and the objective is to find job sequence(s) for which the value of the makespan is minimum, in the inverse scheduling the exact values of processing times are unknown and they should be selected within given boundaries so that pre-specified job sequence(s) become optimal. We derive necessary and sufficient conditions of optimality of a given solution for the general case of the flow-shop problem when the job sequences on the machines can be different. Based on these conditions we prove that the inverse flow-shop problem is NP-hard even in the case of the same job sequence on both machines and produce a linear programming formulation for a special case which can be solved efficientl

Flow shop scheduling with earliness, tardiness and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding) and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two di erent, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two di erent lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with di erent types of strongly NP-hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs

Applying Machine Based Decomposition in 2-Machine Flow Shops

The Shifting Bottleneck (SB) heuristic is among the most successful approximation methods for solving the Job Shop problem. It is essentially a machine based decomposition procedure where a series of One Machine Sequencing Problems (OMSPs) are solved. However, such a procedure has been reported to be highly ineffective for the Flow Shop problems (Jain and Meeran 2002). In particular, we show that for the 2-machine Flow Shop problem, the SB heurisitc will deliver the optimal solution in only a small number of instances. We examine the reason behind the failure of the machine based decomposition method for the Flow Shop. An optimal machine based decomposition procedure is formulated for the 2-machine Flow Shop, the time complexity of which is worse than that of the celebrated Johnsons Rule. The contribution of the present study lies in showing that the same machine based decomposition procedures which are so successful in solving complex Job Shops can also be suitably modified to optimally solve the simpler Flow Shops.

Improving local search heuristics for some scheduling problems - I

Local search techniques like simulated annealing and tabu search are based on a neighborhood structure defined on a set of feasible solutions of a discrete optimization problem. For the scheduling problems $P2||C_{max}, 1|prec|\sum C_i$ and $1||\sum T_i$ we replace a simple neighborhood by a neighborhood on the set of all locally optimal solutions. This allows local search on the set of solutions that are locally optimal

Spatial-temporal data modelling and processing for personalised decision support

The purpose of this research is to undertake the modelling of dynamic data without losing any of the temporal relationships, and to be able to predict likelihood of outcome as far in advance of actual occurrence as possible. To this end a novel computational architecture for personalised ( individualised) modelling of spatio-temporal data based on spiking neural network methods (PMeSNNr), with a three dimensional visualisation of relationships between variables is proposed. In brief, the architecture is able to transfer spatio-temporal data patterns from a multidimensional input stream into internal patterns in the spiking neural network reservoir. These patterns are then analysed to produce a personalised model for either classification or prediction dependent on the specific needs of the situation. The architecture described above was constructed using MatLab© in several individual modules linked together to form NeuCube (M1). This methodology has been applied to two real world case studies. Firstly, it has been applied to data for the prediction of stroke occurrences on an individual basis. Secondly, it has been applied to ecological data on aphid pest abundance prediction. Two main objectives for this research when judging outcomes of the modelling are accurate prediction and to have this at the earliest possible time point. The implications of these findings are not insignificant in terms of health care management and environmental control. As the case studies utilised here represent vastly different application fields, it reveals more of the potential and usefulness of NeuCube (M1) for modelling data in an integrated manner. This in turn can identify previously unknown (or less understood) interactions thus both increasing the level of reliance that can be placed on the model created, and enhancing our human understanding of the complexities of the world around us without the need for over simplification. Read less Keywords Personalised modelling; Spiking neural network; Spatial-temporal data modelling; Computational intelligence; Predictive modelling; Stroke risk predictio

Spatial-temporal data modelling and processing for personalised decision support

The purpose of this research is to undertake the modelling of dynamic data without losing any of the temporal relationships, and to be able to predict likelihood of outcome as far in advance of actual occurrence as possible. To this end a novel computational architecture for personalised ( individualised) modelling of spatio-temporal data based on spiking neural network methods (PMeSNNr), with a three dimensional visualisation of relationships between variables is proposed. In brief, the architecture is able to transfer spatio-temporal data patterns from a multidimensional input stream into internal patterns in the spiking neural network reservoir. These patterns are then analysed to produce a personalised model for either classification or prediction dependent on the specific needs of the situation. The architecture described above was constructed using MatLab© in several individual modules linked together to form NeuCube (M1). This methodology has been applied to two real world case studies. Firstly, it has been applied to data for the prediction of stroke occurrences on an individual basis. Secondly, it has been applied to ecological data on aphid pest abundance prediction. Two main objectives for this research when judging outcomes of the modelling are accurate prediction and to have this at the earliest possible time point. The implications of these findings are not insignificant in terms of health care management and environmental control. As the case studies utilised here represent vastly different application fields, it reveals more of the potential and usefulness of NeuCube (M1) for modelling data in an integrated manner. This in turn can identify previously unknown (or less understood) interactions thus both increasing the level of reliance that can be placed on the model created, and enhancing our human understanding of the complexities of the world around us without the need for over simplification. Read less Keywords Personalised modelling; Spiking neural network; Spatial-temporal data modelling; Computational intelligence; Predictive modelling; Stroke risk predictio

Parallel machine scheduling with precedence constraints and setup times

This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. Limited discrepancy search methods mixed with local search principles, dominance conditions and specific lower bounds are proposed. The proposed methods are evaluated on a set of randomly generated instances and compared with previous results from the literature and those obtained with an efficient commercial solver. We conclude that our propositions are quite competitive and our results even outperform other approaches in most cases

Project scheduling under undertainty – survey and research potentials.

The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, that is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, stochastic GERT network scheduling, fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling projects under uncertainty.Management; Project management; Robustness; Scheduling; Stability;