Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems

Table 3

The detailed information of quasi-dead markings.

Marking number	Information of marking; [𝑝1, 𝑝2, 𝑝3, 𝑝4, 𝑝5, 𝑝6, 𝑝8, 𝑝9, 𝑝10, 𝑝11, 𝑝12, 𝑝14, 𝑝15, 𝑝16, 𝑝17, 𝑝18, 𝑝19]	Marking number	Information of marking; [𝑝1, 𝑝2, 𝑝3, 𝑝4, 𝑝5, 𝑝6, 𝑝8, 𝑝9, 𝑝10, 𝑝11, 𝑝12, 𝑝14, 𝑝15, 𝑝16, 𝑝17, 𝑝18, 𝑝19]
𝑀26	[3, 1, 1, 1, 0, 0, 6, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]	𝑀35	[5, 0, 1, 0, 0, 0, 5, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1]
𝑀42	[3, 1, 1, 1, 0, 0, 5, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0]	𝑀52	[5, 0, 1, 0, 0, 0, 4, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]
𝑀59	[3, 1, 1, 1, 0, 0, 5, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]	𝑀68	[4, 0, 1, 1, 0, 0, 5, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1]
𝑀72	[5, 0, 1, 0, 0, 0, 4, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]	𝑀75	[4, 1, 0, 1, 0, 0, 5, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1]
𝑀79	[6, 0, 0, 0, 0, 0, 4, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]	𝑀85	[4, 0, 1, 0, 1, 0, 4, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]
𝑀89	[4, 0, 1, 1, 0, 0, 4, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]	𝑀96	[4, 1, 0, 1, 0, 0, 4, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]
𝑀99	[6, 0, 0, 0, 0, 0, 3, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0]	𝑀100	[2, 1, 1, 1, 0, 1, 6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1]
𝑀106	[4, 0, 1, 0, 0, 1, 4, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]	𝑀107	[4, 0, 1, 0, 0, 1, 5, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1]
𝑀111	[4, 0, 1, 1, 0, 0, 4, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]	𝑀116	[4, 1, 0, 1, 0, 0, 4, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]
𝑀118	[5, 0, 0, 1, 0, 0, 4, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]	𝑀119	[6, 0, 0, 0, 0, 0, 3, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]
𝑀120	[2, 1, 1, 1, 0, 1, 5, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]	𝑀124	[3, 1, 1, 0, 0, 1, 4, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0]
𝑀126	[4, 0, 1, 0, 0, 1, 4, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]	𝑀127	[3, 1, 0, 1, 0, 1, 4, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]
𝑀136	[5, 0, 0, 1, 0, 0, 3, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]	𝑀138	[2, 1, 1, 1, 0, 1, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1]
𝑀141	[3, 0, 1, 1, 0, 1, 4, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]	𝑀142	[3, 0, 1, 1, 0, 1, 5, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1]
𝑀143	[4, 0, 1, 0, 0, 1, 4, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1]	𝑀146	[3, 1, 0, 1, 0, 1, 5, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1]
𝑀150	[5, 0, 0, 0, 0, 1, 4, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]	𝑀151	[5, 0, 0, 1, 0, 0, 3, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]
𝑀155	[3, 0, 1, 1, 0, 1, 4, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]	𝑀159	[3, 1, 0, 1, 0, 1, 4, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0]
𝑀162	[5, 0, 0, 0, 0, 1, 3, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0]	𝑀164	[3, 0, 1, 1, 0, 1, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1]
𝑀166	[3, 1, 0, 1, 0, 1, 4, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1]	𝑀168	[4, 0, 0, 1, 0, 1, 4, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]
𝑀169	[5, 0, 0, 0, 0, 1, 3, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1]	𝑀173	[4, 0, 0, 1, 0, 1, 3, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0]
𝑀175	[4, 0, 0, 1, 0, 1, 3, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1]