Enhancing S-Graph Framework to Address Scheduling Under Uncertainty

4 Enhancing S-Graph Framework to Address Scheduling Under Uncertainty 

In this section, the framework proposed for solving stochastic scheduling problems is described. It basically consists in a systematic search strategy based on the schedule generator (S-graph) and the expected performance evaluator (LP Model). The algorithm flowsheet is presented in Fig. 8.4. 

The first step of the algorithm is to define the search space. This consists of the set of nodes corresponding to different combinations of production routes for each final product. Routes are those different realistic ways to process a product or combination of products. Then, a node N could be described by a S P dimensional integer matrix, where each component Np r represents the number of batches of product p to produce from route r. The procedure followed to define the search space is the same described in Sect. 8.3.2. In general, this procedure finds the maximum product p number of batches that each route r can process over the time horizon of interest (Np, .) (see Sect. 8.3.2.1). Here, toTest is defined as the set of nodes that have not been tested yet but still have an opportunity to result in a higher expected profit. The initial search space is used to initialize toTest. 

The schedule resulting with the higher expected profit is selected from the nodes found during the definition of the search space (N , .). Such schedule is used to initialize cb value and cb schedule which represent the best expected profit currently found and its corresponding schedule, respectively. 

If toTest is empty, cb value is the expected profit corresponding to the optimal solution stored in cb schedule. Otherwise, the iterative part of the algorithm is repeated as described above. 

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