A dynamic model and an algorithm for short-term supply chain scheduling in the smart factory industry 4.0

State-of-the art in short-term, medium-term, and reactive scheduling for large-scale batch and continuous processes

In this paper we introduce a geometric analysis of reservoir dynamics in the short-term operation of hydroelectric plants with both run-off-river and storage reservoirs. Based on minimum and maximum limits on water release, we calculate upper bounds on the evolution of reservoir storage levels over a given planning horizon. The resulting analytical framework will function as a general use tool to determine the necessity for representation of water continuity equations in short-term hydropower scheduling models. We present a numerical application of our framework to the Brazilian power system. We show that the vast majority of these plants do not require the representation of water continuity equations in their short-term scheduling models, given the insignificant sensitivity of reservoir storage and reservoir elevation levels in one-day horizons for practical assumptions.

The artificial intelligence-assisted short-term optimal scheduling of a cascade hydro-photovoltaic complementary system with hybrid time steps

A design pattern-based approach for automatic choice of semi-partitioned and global scheduling algorithms

Dynamic job shop scheduling (JSS) problems with dynamic job arrivals have been studied extensively in the literature due to their applicability to real-world manufacturing systems, such as semiconductor manufacturing. In a dynamic JSS problem with dynamic job arrivals, jobs arrive on the shop floor unannounced that need to be processed by the machines on the shop floor. A job has a sequence of operations that can only processed on specific machines, and machines can only process one job at a time. Many effective genetic programming based hyper-heuristic (GP-HH) approaches have been proposed for dynamic JSS problems with dynamic job arrivals, where high quality dispatching rules are automatically evolved by GP to handle the dynamic JSS problem instances. However, research that focus on handling multiple dynamic events simultaneously are limited, such as both dynamic job arrivals and machine breakdowns. A machine breakdown event results in the affected machine being unable to process any jobs during the repair time. It is likely that machine breakdowns can significantly affect the effectiveness of the scheduling procedure unless they are explicitly accounted for. Therefore, this paper develops new machine breakdown terminals for a GP approach and evaluates their effectiveness for a dynamic JSS problem with both dynamic job arrivals and machine breakdowns. The results show that the GP approaches with the machine breakdown terminals do show improvements. The analysis shows that the machine breakdown terminals may indirectly contribute in the evolution of high quality rules, but occur infrequently in the output rules evolved by the machine breakdown GP approaches.

Unit-specific event-based continuous time models have gained significant attention in the past decade for their advantages of requiring less number of event points, smaller problem size, and hence, a better computational performance. In the literature, different models had been proposed for short-term scheduling problems involving with and without resource constraints using unit-specific event-based formulations. For scheduling problems involving no resource constraints, generally the unit-specific event-based models do not allow tasks to continue over multiple events unlike in models that account for resource constraints explicitly. In this work, we emphasize the necessity for allowing tasks to take place over multiple event points even for simpler scheduling problems involving no resource constraints. We propose a novel short-term scheduling model using three-index binary and continuous variables that efficiently merges both the problems involving resources and no resource constraints into a unified, generic common framework. The proposed approach is based on state-task-network (STN) representation and is suitable for both batch and continuous plants, although we focus only on batch plants in this paper. Detailed computational case studies are presented to demonstrate the efficacy of the proposed model.

This paper presents a compact aggregated unit model (CAUM) for short-term hydro power generation scheduling. The CAUM, which is obtained based on optimal piecewise linear approximation, represents the relationship between the maximum power generation level of the plant, total water discharge and the average storage of the reservoir. Different from the real-time optimal dispatch of the hydropower system, the CAUM is an off-line optimization. Meanwhile, the aggregation of the individual unit simplifies the short-term hydro power generation scheduling since all the individual unit related constraints are removed. By using the CAUM, the optimal power generation level can be rapidly determined and the short-term hydro power generation scheduling would be greatly simplified. Numerical testing results demonstrate that the method is effective.

Short-term load distribution model for giant cascade serial diversion-type hydropower stations

Short-term production scheduling in open pit mines usually generates a scheme to enable mining operations to deliver the budgeted tonnes and grades to the mill while following the long-term mine plan. The goal of this paper is to develop and test an optimisation model for short-term open pit mine production scheduling. A multidestination mixed integer linear programming (MILP) model is proposed, which minimises the overall cost of mining operations including mining, processing, haulage, rehandling and rehabilitation costs. The model is solved by branch-and-cut algorithm using TOMLAB/CPLEX optimiser. The model incorporates buffer and blending stockpiles, horizontal directional mining, and decisions on ramps while controlling technical constraints. A monthly production schedule in an iron ore mine is developed over 12 months to illustrate the practicality of the developed model. Three scenarios with different mining horizontal directions are considered. The scenario with minimum number of drop-cuts is selected as the best practical schedule.

This paper proposes a random fuzzy optimization (RFO) model for short-term hydropower scheduling, in order to avoid frequent unit switches owing to uncertainty of the power load. The cascade hydropower stations of Qing River in China are firstly introduced for research, and the power load error of the cascade is described. Defined as a random fuzzy variable, the error is analyzed and its distribution is derived to signify the uncertainty. Then random fuzzy programming is integrated into short-term hydropower scheduling to develop the RFO model, with more attention payed to unit spare capacity, while satisfying the demand of power grids. Meanwhile, an applicable solution searching strategy is proposed to solve the model. Simulation results of random fuzzy optimization of the cascade prove that the strategy is practical and the developed model is effective to avoid frequent unit switches. The method also can provide available references for other cascade dispatching center and hydropower stations with the same plight.

Production scheduling of a large-scale industrial continuous plant: Short-term and medium-term scheduling

Production scheduling of a large-scale industrial continuous plant: Short-term and medium-term scheduling

An optimization framework for multi-timescale operations of pumped storage systems: Balancing stability and economy

Scheduling in Industry 4.0 systems belongs to a class of problems that have mixed structural-temporal-logical constraints. In other words, a strong coupling is considered when product and process are created simultaneously. As a result of the proven NP-hardness of such problems, solution methods have extensively utilized different decomposition principles. The known decomposition methods in discrete optimization are founded on the difficulties in deriving analytical properties. The existing solutions in continuous optimization are based on the maximum principle and yield a dynamic process decomposition using the natural logic of time. By combining the advantages of continuous and discrete optimization, this chapter develops a decomposition method for shop floor scheduling in Industry 4.0 manufacturing systems. Technically, this study proposes to decompose dynamically the large-scale assignment matrix according to the precedence relations between the operations of the jobs and considers only the operations that satisfy these precedence relations at a given time point in small-dimensional, discrete optimization models. Continuous optimization is used to generate a schedule from the assignments found in the discrete optimization models at each time point by extremizing the Hamiltonian function at this time point subject to scheduling objective(s). In addition, the execution of the operations in time can be accurately modeled in continuous time as a continuous state variable; the machine availability and capacity disturbances at the machines are also considered. The method developed provides further insights into decomposition methods for scheduling and is supported by an analytical analysis and an algorithmic realization.

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