This paper studies the slack due-window assignment scheduling problem with deterioration effects and a deterioration maintenance activity on a single-machine. The machine deteriorates during the machining process, and at a certain moment performs a deterioration maintenance activity, that is, the duration time of the maintenance activity is a linear function of the maintenance starting time. It is needed to make a decision on when to schedule the deteriorating maintenance activity, the optimal common flow allowances and the sequence of jobs to minimize the weighted penalties for the sum of earliness and tardiness, weighted number of early and delayed, and weighted due-window starting time and size. This paper proposes a polynomial time algorithm to solve this problem.

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.

Walking robot has complicate structure and strong ability to adapt ground conditions, and it is difficult to control. To realize dynamic walking of the humanoid robot, we have to establish robot dynamic models, design the control algorithm for gait and the stability postures. In this paper, study dynamic model and control system of a 7-links biped robot, build parameterized simulation model of biped walking robot, proceed gait planning and simulation experiments in the simulation surrounding, and get some experiment results. Compare the experiment data with the theoretic stable region and confirm that the biped walking robot as leg mechanism has good stability of static walking, and provide theoretic and data information for further work.

We focus on a single-machine scheduling problem with common and slack due-window assignment methods. Both the job sequence and due-windows are decision variables to be determined by the decision maker. We consider the following performance criterion: the total weighted number of early and late jobs plus the total weighted of earliness, tardiness and due-window assignment cost, where the weights depend on the position in which a job is scheduled. Some properties are established, and it is shown that the problem can be solved in [Formula: see text] time, where [Formula: see text] is the number of jobs. The extensions of the model are to cases of general position-dependent processing times and time-dependent processing times.

<abstract><p>This article deals with common due-window assignment and single-machine scheduling with proportional-linear shortening processing times. Objective cost is a type of minmax, that is, the maximal cost among all processed jobs is minimized. Our goal is to determine an optimal schedule, the optimal starting time, and size of due-window that minimize the worst cost, which consist of four parts: earliness, tardiness, starting time and length of the due-window. Optimal properties of the problem are given, and then an optimal polynomial algorithm is proposed to solve the problem.</p></abstract>