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Abstract:The aim of the paper is to present a heuristic method for decision-making regarding an NP-hard scheduling problem with limitations related to tasks and the resources dependent on the current state of the process. The presented approach is based on the algebraic-logical meta-model (ALMM), which enables making collective decisions in successive process stages, not separately for individual objects or executors. Moreover, taking into account the limitations of the problem, it involves constructing only an acceptable solution and significantly reduces the amount of calculations. A general algorithm based on the presented method is composed of the following elements: preliminary analysis of the problem, techniques for the choice of decision at a given state, the pruning non-perspective trajectory, selection technique of the initial state for the trajectory final part, and the trajectory generation parameters modification. The paper includes applications of the presented approach to scheduling problems on unrelated parallel machines with a deadline and machine setup time dependent on the process state, where the relationship between tasks is defined by the graph. The article also presents the results of computational experiments.

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The Dynamic Vehicle Routing Problem (DVRP) is one of the most important problems in the area of enterprise logistics. DVRP problems involve these dynamics: the appearance of customers, travel times, service times, or vehicle availability. One of the most often considered aspects of the DVRP is the availability of customers, in which a part or all of the customers are revealed dynamically during the design or execution of the routes. A classification of the DVRP problem due to various elements causing dynamism is proposed. The aim of the paper is to distinguish dynamic VRP, which takes into account the dynamic appearance of customers to serve during the design or execution of the routes. In particular, the difference between the predictive and unexpected aspects of the customer’s availability is considered. Above all, the variant of customer’s availability which is predicted according to an appropriate general rule is modeled using the algebraic-logical meta-model (ALMM). It is a methodology which enables making collective decisions in successive process stages, not separately for individual vehicles. The algebraic-logical model of the dynamic vehicle routing problem with predicted consumer availability is proposed. The paper shows the possibilities of applying the ALMM approach to dynamic problems both with predicted and unexpected customer availability.

The article deals with a formal approach to solving manufacturing problem with defects removal and presents the application of this approach to flow-shop system with defects. The defects are detected during quality control and thus they are unexpected events. Moreover, a job processing time is not predetermined, and it may contain the unknown time needed to repair. Therefore, stochastic uncertainties are considered, but in addition, we model the process of decision making. The algebraic-logical meta-model methodology constitutes the basis for our approach. A hybrid algorithm for constructing a solution based on the process simulation using special local optimizing task and algebraic-logical models switching when defect detection occurs is presented. In particular, the following elements of the presented approach are shown: disturbances type analyzing, definition of switching states set, definition of subproblems, algebraic-logical metamodels creating for all subproblems, switching types determining, determination of the switching rules, the switching function, and components of special local criterion definition. The article shows results of computer experiments.

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