Scheduling problems

This suggests that in otganizing the assessment task, you may want to identify as broad a group of qualified individuals as possible, and be prepared to provide them with detailed guidance. This may help you accommodate last-minute scheduling problems while assuring consistent quality. 

Problem of approximation, 52 Product ensemble, 198 Production scheduling problem, 297 Profit maximization, 286 Programming, dynamic, 305 Programming, linear (see Linear programming)... 

To solve the flowshop scheduling problem, or indeed most problems with significant discrete structure, we are forced to adopt some form of... 

The next section will highlight these features of the branch-and-bound framework, within the context of the flowshop scheduling problem. Then we will give an abstract description of the algorithm, followed by the... 

In addition to the elimination of partial solutions on the basis of their lower-bound values, we can provide two mechanisms that operate directly on pairs of partial solutions. These two mechanisms are based on dominance and equivalence conditions. The utility of these conditions comes from the fact that we need not have found a feasible solution to use them, and that the lower-bound values of the eliminated solutions do not have to be higher than the objective function value of the optimal solution. This is particularly important in scheduling problems where one may have a large number of equivalent schedules due to the use of equipment with identical processing characteristics, and many batches with equivalent demands on the available resources. 

The intuitive notion behind a dominance condition, D, is that by comparing certain properties of partial solutions x and y, we will be able to determine that for every solution to the problem y(y) we will be able to find a solution to Yix) which has a better objective function value (Ibaraki, 1977). In the flowshop scheduling problem several dominance conditions, sometimes called elimination criteria, have been developed (Baker, 1975 Szwarc, 1971). We will state only the simplest ... 

At this point the lower-bounding scheme consists of solving a single machine scheduling problem where for each job i, the release time is the due date is, and the processing time is This nonbottleneck scheme can be further simplified in two steps. First, we can assume that for a/8 =. ., avoiding the need to consider release times of and due dates of, which turns an NP-complete problem, into one solvable in polynomial time. If only one of these were to be relaxed, the schedule can still be foimd in polynomial time by Jackson s rule (Jackson, 1955). Second, we can avoid the computation of completely, by assuming that the maximum is obtained at / = m for all values of i. 

This section details the different aspects of the representation we have adopted to describe the problem solutions and the new control knowledge generated by the learning mechanism. Throughout the section we will continue to use the flowshop scheduling problem as an illustration. The section starts by discussing the motives for selecting the horn clause form of first-order predicate calculus, and then proceeds to show how the representation supports both the synthesis of problem solutions and their analysis. The section concludes with a description of how the sufficient... 

Figure 8 shows the trace of the application of Axiom- , Axiom-2, Rule-l, Rule-2, Rule-3, and Rule-4 in our specific scheduling problem. The trace consists of a repeated pattern of rule applications Rule-4 followed by either Rule-2 or Rule-3. At each step the intrasituational rule converts an end-time to a start-time, and then the start-time is matched to the... 

Optimal schedules are given in Table 7.4-20. Clearly, for cleaning times of five hours, single-product campaigns are the best solution of the scheduling problem, while for zero cleaning times (theoretical case) mixed-product campaigns would be best. 

The scheduling problem that is considered in this chapter can be stated as follows. Given ... 

In addition to their ability to capture the multidimensionality of batch operations, another advantage of mathematical programming techniques is the flexibility and adaptability of the performance index, i.e. the objective function. In a design problem, the objective function can take a form of a capital cost investment function. In a scheduling problem it can be minimization of makespan, maximization of throughput, maximization of revenue, etc. In this chapter, the objective function will either... 

A natural progression from the scheduling of zero effluent operations is the derivation of a formulation that synthesises batch plants operating in the zero effluent mode of operation. The problem to be solved is slightly different to the general scheduling problem addressed in the formulation presented previously. 

Choice of the optimum production order is a scheduling problem. Like the problem of the traveling gourmet, a GA solution for the flowshop consists of an ordered list. In the flowshop, this list specifies the order in which chemicals are to be made ... 

There is a need for advanced discrete-continuous optimization tools that can handle mixed-integer, discrete-logic, and quantitative-qualitative equations to model synthesis and planning and scheduling problems. 

Catoni, 0. (1998) Solving scheduling problems by simulated annealing. SIAM J Contr Optim, 36, 1539-1575. 

Cavalieri, S. and Gaiardelli, P. (1998) Hybrid genetic algorithms for a multiple-objective scheduling problem. 

Another special aspect of the production process considered here is that there is only one unique end product - copper anodes with a final copper content of 99.6%. This changes the problem focus compared to other typical scheduling problems, where different properties of various products have to be taken into account in determining a production sequence, as well as cleaning requirements and product-equipment compatibility, to name a few. Here we do not have, e.g.,... 

During normal operation of the copper plant, there are a number of regular maintenance jobs that need to be planned. They are included in the scheduling problem as additional jobs that have given release dates and due dates. These maintenance jobs can mostly be performed only when a unit is empty and not in use. The optimization approach finds the best location for each maintenance job with the least impact on production throughput and, furthermore, modifies the batch recipes such that there will be a suitable break in the operation for the equipment that must be maintained. 

The solution developed is able to solve the scheduling problem very efficiently, resulting in good and realistic schedules. Of course, the solution quality depends to a great deal on how well the parameter estimation matches with the production process. More illustrations on the solution can be found in [5]. 

V. et al. (2003) A solution to the copper smelter scheduling problem, in The Hermann Schwarze Symposium on Copper Pyrometallurgy, vol. IV, Pyrometallurgy of Copper (eds C. Diaz,... 

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