Minimizing makespan in flowshop with time lags

We consider the problem of minimizing the makespan in a flowshop involving maximal and minimal time lags. Time lag constraints generalize the classical precedence constraints between operations. We assume that such constraints are only defined between operations of the same job. We propose a solution method and present several extensions.Comment: 2 pages. Also available at http://hal.inria.fr/inria-0000014

Polynomial-time approximation schemes for scheduling problems with time lags

We identify two classes of machine scheduling problems with time lags that possess Polynomial-Time Approximation Schemes (PTASs). These classes together, one for minimizing makespan and one for minimizing total completion time, include many well-studied time lag scheduling problems. The running times of these approximation schemes are polynomial in the number of jobs, but exponential in the number of machines and the ratio between the largest time lag and the smallest positive operation time. These classes constitute the first PTAS results for scheduling problems with time lags

Heuristics for scheduling a two-stage hybrid flow shop with parallel batching machines: application at a hospital sterilisation plant

The model of a two-stage hybrid (or flexible) flow shop, with sequence-independent uniform setup times, parallel batching machines and parallel batches has been analysed with the purpose of reducing the number of tardy jobs and the makespan in a sterilisation plant. Jobs are processed in parallel batches by multiple identical parallel machines. Manual operations preceding each of the two stages have been dealt with as machine setup with standardised times and are sequence-independent. A mixed-integer model is proposed. Two heuristics have been tested on real benchmark data from an existing sterilisation plant: constrained size of parallel batches and fixed time slots. Computation experiments performed on combinations of machines and operator numbers suggest balancing the two stages by assigning operators proportionally to the setup time requirements

Mathematical models for planning support

In this paper we describe how computer systems can provide planners with active planning support, when these planners are carrying out their daily planning activities. This means that computer systems actively participate in the planning process by automatically generating plans or partial plans. Active planning support by computer systems requires the application of mathematical models and solution techniques. In this paper we describe the modeling process in general terms, as well as several modeling and solution techniques. We also present some background information on computational complexity theory, since most practical planning problems are hard to solve. We also describe how several objective functions can be handled, since it is rare that solutions can be evaluated by just one single objective. Furthermore, we give an introduction into the use of mathematical modeling systems, which are useful tools in a modeling context, especially during the development phases of a mathematical model. We finish the paper with a real life example related to the planning process of the rolling stock circulation of a railway operator.optimization;mathematical models;modeling process;planning support;Planning

A Comparative Representation Approach to Modern Heuristic Search Methods in a Job Shop

The job shop problem is among the class of NP- hard combinatorial problems. This Research paper addresses the problem of static job shop scheduling on the job-based representation and the rule based representations. The popular search techniques like the genetic algorithm and simulated annealing are used for the determination of the objectives like minimizations of the makespan time and mean flow time. Various rules like the SPT, LPT, MWKR, and LWKR are used for the objective function to attain the results. The summary of results from this paper gives a conclusion that the genetic algorithm gives better results in the makespan time determination on both the job based representation and the rule based representation and the simulated annealing algorithm gives the better results in the mean flow time in both the representations

An exact method for solving the two-machine flow-shop problem with time delays

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