A method for solving lower bounds of double-agent problems with release time flow shop
A technology that releases time and lower bounds. It is applied in the field of solving lower bounds of NP-hard problems. It can solve problems that are not suitable for large-scale data simulation and industrial production testing, do not conform to actual production conditions, and do not have industrial value and practicability.
Active Publication Date: 2020-10-16
NORTHEASTERN UNIV LIAONING
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[0004] At present, the double-agent problem in the flow shop is still a relatively new problem. In the literature related to the double-agent problem in the flow shop, the theoretical proof is based on the single-machine problem, and only a few literatures use two machines without release Taking the time model as an example to carry out theoretical research, only some unique properties of the double-agent problem in the flow shop are given from the level of theoretical proof. This model is too special and does not conform to the actual production situation, and is not suitable for the simulation of actual large-scale data. And industrial production test, does not have industrial value and practicability
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[0019] The specific implementation of the present invention will be described in detail below.
[0020] 1. Example calculation
[0021]
[0022] First, determine the priority of A and B. Obviously, the A set has a higher priority.
[0023] A complete assembly line model such as figure 2 Shown: (the sorting order of each machine is the same)
[0024] Therefore, the maximum completion time Cmax=32+39=71 can be calculated using this algorithm. That is to say, the objective function value obtained by this algorithm is 71.
[0025] The lower bound is calculated as follows:
[0026] From the processing time and release time given by the example, the R 1,1 A =10,R 1,2 A = 0, R 1,1 B =15,R 1,2 B = 4, R 1,3 B =9,R 2,1 A =10+4=14, R 2,2 A =0+3=3,R 2,1 B =15+3=18, R 2,2 B =4+5=9, R 2,3 B =9+6=15, R 3,1 A =14+5=19, R 3,2 A =3+4=7, R 3,1 B =18+2=20, R 3,2 B =9+3=12, R 3,3 B =15+3=18.
[0027] Depend on image 3 Can get LB1=14+22+7+5=48; LB2=19+24+3+...
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The invention belongs to the field of production scheduling and provides a method of solving a NP (non-deterministic polynomial)-hard problem lower bound, that is, a lower bound solving method for a double agent problem based on a flow shop with release time. The lower bound is the solution obtained by sorting when certain constraints are relaxed, sorting solution by the used algorithm obtains a feasible solution, that is, an upper bound, and the optimal solution of sorting is between the upper bound and the lower bound. The lower bound thus serves as an important means for evaluating the solution performance of the algorithm. The lower bound designed in the method of the invention uses a method based on a single machine problem, one lower bound is solved on each machine, and the maximum one is taken. An interruptible mode is adopted on each machine to relax the constraint conditions. As is known from a simulation result, the lower bound is convergent, that is, when the workpiece number tends to infinity, the lower bound is convergent at the optical solution. In a large-scale condition, an important meaning exists in evaluating the algorithm solution performance.
Description
technical field [0001] The invention belongs to the field of production scheduling and relates to a method for solving the lower bound of NP-hard problems. Background technique [0002] NP-hard, where NP refers to a non-deterministic polynomial (abbreviated as NP). The so-called non-determinism means that a certain number of operations can be used to solve problems that can be solved in polynomial time. Generally speaking, it is a problem that the correctness of the solution can be "easy to check". [0003] Assuming that two existing manufacturers want to process on a certain assembly line, and each manufacturer hopes to deliver their products as soon as possible, how should an assembly line factory arrange production to best meet the requirements of two customers? This is a very typical two-agent flow shop scheduling problem, assuming that the number of jobs in agent A is n A , the number of workpieces in agent B is n B , n A +n B =n. The objective function is min(Cma...
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IPC IPC(8): G06Q10/04G06Q10/06
CPCG06Q10/04G06Q10/06316
Inventor 付尧崔晓智刘冰倩唐梦倩白丹宇任涛
Owner NORTHEASTERN UNIV LIAONING