Discrete Optimization Model and Algorithm for Driver Planning in Periodic Driver Routing Problem

Table 2

sensitivity analysis on workload differential.

ID	K	No consideration of			Consideration of			gap
		ZL	TL			ZL’	TL’
10-1	2	138.0	439	4.60	3	138.0	1930	0.00%
10-2	2	118.6	1960	3.95	3	118.8	1949	0.17%
10-3	2	148.2	1938	4.94	3	148.3	1938	0.07%
10-4	2	148.6	1929	4.95	3	151.3	1946	1.78%
Average			1567				1941	0.51%
15-1	2	809.4	2409	26.98	10	811.1	2714	0.21%
15-2	2	963.8	2470	32.13	12	966.4	2430	0.27%
15-3	3	1188.3	2471	26.41	10	1296.7	3405	8.36%
15-4	2	751.5	1809	25.05	10	751.6	2411	0.01%
Average			2290				2740	2.21%
20-1	2	861.9	1907	28.73	20	862.4	2510	0.06%
20-2	3	1121.4	2517	24.92	20	1238.6	2210	9.46%
20-3	3	1322.1	2235	29.38	20	1328.0	4645	0.44%
20-4	2	876.9	2444	30.20	20	879.6	3362	0.31%
Average			2276				3182	2.57%

Notes:   ‘K’ is the number of drivers; ‘’ denotes the average workload of each driver on a day, which is obtained by the function .     denotes the value of maximal workload differential among drivers which is the input parameter to solve the problem. Here, .   ‘gap’ is calculated by the function gap= (Z_L’- Z_L)/Z_L’; Z_L and T_L are the objective value and CPU time of local branching which do not consider small workload differential, respectively; and Z_L’ and T_L’ are the objective value and CPU time of local branching which consider small workload differential, respectively.