Rule-based scheduling of multi-stage multi-product batch plants with parallel units

A novel rule-based model for multi-stage multi-product scheduling problem(MMSP)in batch plants with parallel units is proposed.The scheduling problem is decomposed into two sub-problems of order assignment and order sequencing.Firstly,hierarchical scheduling strategy is presented for solving the former sub-problem,where the multi-stage multi-product batch process is divided into multiple sequentially connected single process stages,and then the production of orders are arranged in each single stage by using forward order assignment strategy and backward order assignment strategy respectively according to the feature of scheduling objective.Line-up competition algorithm(LCA)is presented to find out optimal order sequence and order assignment rule,which can minimize total flow time or maximize total weighted process time.Computational results show that the proposed approach can obtain better solutions than those of the literature for all scheduling problems with more than 10 orders.Moreover,with the problem size increasing,the solutions obtained by the proposed approach are improved remarkably.The proposed approach has the potential to solve large size MMSP.

A new simplified ordered upwind method for calculating quasi-potential

We present a new method for calculation of quasi-potential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the finite difference upwind scheme,the first-order line integral is used as its update rule.With sufficient accuracy,the new simplified method can greatly speed up the computational time.Once the quasi-potential has been computed,the minimum action path(MAP)can also be obtained.Since the MAP is of concern in most stochastic situations,the effectiveness of this new method is checked by analyzing the accuracy of the MAP.Two cases of isotropic diffusion and anisotropic diffusion are considered.It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time.Meanwhile anisotropy will affect the accuracy of the computed MAP.

Orderly Algorithm to Enumerate Central Groupoids and Their Graphs

A graph has the unique path property UPPn if there is a unique path of length n between any ordered pair of nodes. This paper reiterates Royle and MacKay＇s technique for constructing orderly algorithms. We wish to use this technique to enumerate all UPP2 graphs of small orders 3^2 and 4^2. We attempt to use the direct graph formalism and find that the algorithm is inefficient. We introduce a generalised problem and derive algebraic and combinatoric structures with appropriate structure. Then we are able to design an orderly algorithm to determine all UPP2 graphs of order 3^2, which runs fast enough. We hope to be able to determine the UPP2 graphs of order 4^2 in the near future.

Numerical study on the gas-kinetic high-order schemes for solving Boltzmann model equation

The high-order compact finite difference technique is introduced to solve the Boltzmann model equation, and the gas-kinetic high-order schemes are developed to simulate the different kinetic model equations such as the BGK model, the Shakhov model and the Ellipsoidal Statistical (ES) model in this paper. The methods are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the inner flows of normal shock wave for different Mach numbers, and the two-dimensional flows past a circular cylinder and a NACA 002 airfoil to verify the reliability of the present high-order algorithm and simulate gas transport phenomena covering various flow regimes. The computed results are found in good agreement both with the theoretical prediction from continuum to rarefied gas dynamics, the related DSMC solutions, and with the experimental results. The numerical effect of the schemes with the different precision and the different types of Boltzmann collision models on the computational efficiency and computed results is investigated and analyzed. The numerical experience indicates that an approach developing and applying the gas-kinetic high-order algorithm is feasible for directly solving the Boltzmann model equation.