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This paper investigates the common due-window assignment scheduling problem with deteriorating jobs on a single machine in which the processing time of a job is a proportional function of its starting time. The goal is to minimize the maximum value of earliness and tardiness penalties, as well as due-window location cost, and size cost. Depending on whether the location and size of due-window are known, this paper studies three relevant cases, all of which are solvable in polynomial time.

This paper considers a group scheduling problem with shorten (i.e., a proportional linear shortening) job processing times and ready times on a single machine. If the jobs are in the same group, they have independent and constant ready times. The setup time of a group is independent constant setup time between each group. The goal is to determine the optimal group sequence and the job sequence within the groups such that the makespan (i.e., the maximum completion time) is minimized. For the general case of the problem, an initial heuristic algorithm (an upper bound) and some lower bounds are proposed, and then a branch-and-bound algorithm can be developed to solve the problem.

This paper studies the single machine scheduling problems with truncated logarithm processing times and exponential past-sequence-dependent delivery times. We prove that the makespan and total completion time minimizations are polynomially solvable. For the total weighted completion time minimization, we illustrate that it remains polynomially solvable under a special case; under the general case, this paper proposes heuristic, tabu search and branch-and-bound algorithms. Computational experiments indicate that the heuristic algorithm is more effective than tabu search algorithm.

In order to increase the efficiency of production in a deteriorating environment through competition amongst the individual agents, this study explores a two-agent scheduling problem with one deterioration rate for each job, where the processing time of a job is a function of the position-dependent workload, resource allocation, and deterioration rate (the range of the deterioration rate is non-negative). The optimal processing sequence and resource allocation for the jobs are found by giving an upper bound of an agent to minimize the maximum value of earliness, tardiness and decision variable of another agent under slack due-date assignment. It is verified that the problem cannot be solved in polynomial time, for which various heuristic algorithms and a branch-and-bound algorithm are proposed to simulate the data to find a better range in the deterioration rate parameter.

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

This paper addresses the single-machine scheduling with general truncated learning effects (GTLE) and delivery times that are past sequence dependent (DTpsd). The objective is to determine an optimal job schedule such that makespan, sum of the βth power of job completion times, and total weighted completion time are minimized, where β>0is a given constant. We proved that the makespan, the sum of the βth power of job completion times, and a special case of the total weighted completion time can be solved in polynomial time. For the general case of the total weighted completion time, we propose the heuristic, simulated annealing and branch-and-bound algorithms. Extensive numerical experiments validate the efficiency of the proposed solution algorithms on a set of randomly generated instances. Furthermore, the computational experiment is also conducted to show that the simulated annealing performs effectively and efficiently.

The structure stability, elastic property and electronic structure of α-FT supercell with La atom were investigated by first-principles, in which, generalized gradient approximation (GGA) with the Perdew Burke Ernzerhof (PBE) was used as exchange-correlation functional. α-Fe supercells with La atom include α-Fe supercell with La atom in octahedral interstitial solid solute (La-OISS), that with La atom in tetrahedral interstitial solid solute (La-TISS) and that with La atom in substitutional solid solute (La-SSS). The results show that the La-SSS α-Fe supercell is more stable than La-OISS one. The resistance to volume change, reversible deformation and stiffness of La-OISS α-Fe supercell are stronger than those of La-SSS one. Moreover, the degrees of anisotropy and ionization in La-SSS α-Fe supercell are both stronger than those in La-OISS one. The bonding strength between La atom and Fe atom in La-SSS α-FT supercell is larger than that in La-OISS one.

The structure stability, elastic property and electronic structure of α-Fe supercell with La atom were investigated by first-principles, in which, generalized gradient approximation (GGA) with the Perdew Burke Ernzerhof (PBE) was used as exchange-correlation functional. α-Fe supercells with La atom include α-Fe supercell with La atom in octahedral interstitial solid solute (La-OISS), that with La atom in tetrahedral interstitial solid solute (La-TISS) and that with La atom in substitutional solid solute (La-SSS). The results show that the La-SSS α-Fe supercell is more stable than La-OISS one. The resistance to volume change, reversible deformation and stiffness of La-OISS α-Fe supercell are stronger than those of La-SSS one. Moreover, the degrees of anisotropy and ionization in La-SSS α-Fe supercell are both stronger than those in La-OISS one. The bonding strength between La atom and Fe atom in La-SSS α-Fe supercell is larger than that in La-OISS one.

This paper addresses single-machine scheduling problems with truncated learning effects. The objective is to determine the optimal job schedule such that the makespan, the total weighted completion time and the maximum lateness are to be minimized. All the considered problems are NP-hard; hence, for each problem, we propose the heuristic and branch-and-bound algorithms. Extensive numerical experiments validate the efficiency of the proposed solution algorithms on a set of randomly generated instances.

This paper studies a single machine scheduling problem with rejection. Each job has a variable processing time and a rejection penalty. The objective function is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We show that the problem can be solved in polynomial time.

In this note, we consider the machine scheduling problems with the effects of learning and deterioration. In this model, job processing times are defined by functions dependent on their starting times and positions in the sequence. The scheduling objectives are makespan, sum of completion times. It is shown that even with the introduction of learning effect and deterioration jobs to job processing times, several flow shop problems remain polynomially solvable.

The paper deals with a single machine scheduling problem with deteriorating jobs and group technology (GT) assumption. By deteriorating jobs and group technology assumption, we mean that the group setup times and job processing times are both simple linear functions of their starting times. We show that the makespan minimization problem with release dates can be solved in polynomial time.

In this paper, a single-machine scheduling problem with simple linear deterioration was explored. By simple linear deterioration, we mean that the processing time of a job is a simple linear function of its execution starting time and its deterioration rate. The objective of this study was to find a schedule that minimizes the absolute value of maximum lateness, where the due date of jobs are a common due date. Given that the cases of common due date is a given constant and variable, we showed that the problem can be solved in polynomial time, respectively. Some extensions of the problem were also delineated.