Improved Quantum Genetic Algorithm in Application of Scheduling Engineering Personnel

Table 2

Total time of completion of every process.

Work	Process
	Process 1	Process 2	Process 3	⋯	Process 𝑖
1	0+𝑋^(1)(𝑜1)1	𝑀^(1)(𝑜1)1+𝑋^(2)(𝑝1)1	𝑀^(2)(𝑝1)1+𝑋^(3)(𝑞1)1	⋯	𝑀^(𝑖−1)(𝑦1)1+𝑋^(𝑖)(𝑧1)1
2	𝑀^(1)(𝑜1)1+𝑋^(1)(𝑜2)2	max𝑀𝑜^(1)22,𝑀𝑝^(2)11+𝑋^(2)(𝑝2)2	max𝑀𝑝^(2)22,𝑀𝑞^(3)11+𝑋^(3)(𝑞2)2	⋯	max𝑀𝑦^(𝑖−1)22,𝑀𝑧^(𝑖)11+𝑋^(𝑖)(𝑧2)2
3	𝑀^(1)(𝑜2)2+𝑋^(1)(𝑜3)3	max𝑀𝑜^(1)33,𝑀𝑝^(2)22+𝑋^(2)(𝑝2)3	max𝑀𝑝^(2)33,𝑀𝑞^(3)22+𝑋^(3)(𝑞3)3	⋯	max𝑀𝑦^(𝑖−1)33,𝑀𝑧^(𝑖)22+𝑋^(𝑖)(𝑧3)3
⋮	⋮	⋮	⋮	⋮	⋮
𝑘	𝑀^(1)(𝑜𝑘−1)𝑘−1+𝑋^(1)(𝑜𝑘)𝑘	max𝑀𝑜^(1)𝑘𝑘,𝑀𝑝^(2)𝑘−1𝑘−1+𝑋^(2)(𝑝𝑘)𝑘	max𝑀𝑝^(2)𝑘𝑘,𝑀𝑞^(3)𝑘−1𝑘−1+𝑋^(3)(𝑞𝑘)𝑘	⋯	max𝑀𝑦^(𝑖−1)𝑘𝑘,𝑀𝑧^(𝑖)𝑘−1𝑘−1+𝑋^(𝑖)(𝑧2)𝑘

The mathematical model is min=max(𝑀⁽²⁾_{(𝑝𝑘)𝑘},𝑀⁽³⁾_{(𝑞𝑘−1)𝑘−1})+𝑋⁽³⁾_{(𝑞𝑘)𝑘}, where 𝑘 is the number of engineering works.