In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...

The problem addressed in this paper is scheduling jobs on unrelated parallel machines with sequence-dependent setup times to minimize the maximum completion time (i.e., the makespan). This problem is NP-hard even without including setup times. Adding sequence-dependent setup times adds another dimension of complexity to the problem and obtaining optimal solutions becomes very difficult especial...

Abstract This paper deals with a reentrant hybrid flow shop problem sequence-dependent setup time and limited buffers where there are multiple unrelated parallel machines at each stage. A mathematical model the minimization of total weighted completion is constructed for this problem. Considering complexity hand, an effective cooperative adaptive genetic algorithm (CAGA) proposed. In algorithm,...

In this paper, we address the problem of finding a permutation schedule of n jobs in an m machine flow-shop environment that minimizes the maximum completion time Cmax (Makespan) of all jobs. The jobs are available at time zero and have sequence-dependent setup times on each machine. All parameters, such as processing and setup times, are assumed to be known with certainty. This problem is clas...

In this study, we consider single-machine scheduling problems with past-sequence-dependent (denoted by psd) setup times in which the of jobs are proportional to length already processed jobs. Under common (CON) and slack (SLK) due-date assignment methods, prove that weighted sum earliness, tardiness minimization remains polynomially solvable. We also give some extensions for psd times.

This paper breaks new ground by modelling lot sizing and scheduling in a flexible flow line (FFL) simultaneously instead of separately. This problem, called the ‘General Lot sizing and Scheduling Problem in a Flexible Flow Line’ (GLSP-FFL), optimizes the lot sizing and scheduling of multiple products at multiple stages, each stage having multiple machines in parallel. The objective is to satisf...