Sales Rebate Contracts in Fashion Supply Chains

Table 9

Summary of profits in no-sales-effort model (with different demand). Demand sizes: small (mean 𝜇=100, standard deviation 𝜎=30), medium (𝜇=1000, 𝜎=300), and large (𝜇=10000, 𝜎=3000).

(a)  

	Companies
		MRS			MH			RX
					Demand sizes
	Medium	Large	Small	Medium	Large	Small	Medium	Large	Small
SCC
𝐸[𝑅^′s profit]	232350.15	2323501.45	23235.01	36930.36	369303.61	3693.04	17970881.83	179708818.26	1797088.18
𝐸[𝑀^′s profit]	117118.79	1171187.94	11711.88	24059.38	240593.76	2405.94	8410536.48	84105364.76	841053.65
𝐸[SC’s profit]	349468.94	3494689.40	34946.89	60989.74	609897.38	6098.97	26381418.30	263814183.03	2638141.83
Order quantity	1323.30	13233.02	132.33	1373.56	13735.60	137.36	1324.30	13242.99	132.43
𝑈	697.06	697.06	697.06	187.74	187.74	187.74	50053.76	50053.76	50053.76
𝑢 % (of p)	139.69%	139.69%	139.69%	234.68%	234.68%	234.68%	133.12%	133.12%	133.12%
𝑇	1066.53	10665.32	106.65	1049.81	10498.14	104.98	1068.86	10688.63	106.89
No rebate
𝐸[𝑅^′s profit]	231372.28	2313722.81	23137.23	36680.45	366804.48	3668.04	17903826.88	179038268.82	1790382.69
𝐸[𝑀^′s profit]	108318.02	1083180.19	10831.80	21810.15	218101.54	2181.02	7807041.98	78070419.82	780704.20
𝐸[SC’s profit]	339690.30	3396903.01	33969.03	58490.60	584906.02	5849.06	25710868.86	257108688.64	2571086.89
Order quantity	1105.29	11052.86	110.53	1090.51	10905.08	109.05	1115.29	11152.92	111.53
Current practices
𝐸[𝑅^′s profit]	231645.43	2316454.33	23164.54	36724.47	367244.66	3672.45	23186337.56	231863375.55	2318633.76
𝐸[𝑀^′s profit]	108514.33	1085143.26	10851.43	21954.56	219545.64	2195.46	2785164.79	27851647.86	278516.48
𝐸[SC’s profit]	340159.76	3401597.59	34015.98	58679.03	586790.31	5867.90	25971502.34	259715023.42	2597150.23
Order quantity	1110.14	11101.43	111.01	1100.14	11001.43	110.01	1157.70	11576.97	115.77
𝑈	7.485	7.485	7.485	2.4	2.4	2.4	5640	5640	5640
𝑇	1020	10200	102	1050	10500	105	0	0	0

(b)  

	Companies
	SS			LS
	Demand sizes
	Medium	Large	Small	Medium	Large	Small
SCC
𝐸[𝑅^′s profit]	70889.52	708895.23	7088.95	154416.22	1544162.18	15441.62
𝐸[𝑀^′s profit]	57216.39	572163.87	5721.64	151394.49	1513944.94	15139.45
𝐸[SC’s profit]	128105.91	1281059.09	12810.59	305810.71	3058107.12	30581.07
Order quantity	1303.59	13035.88	130.36	1392.78	13927.75	139.28
𝑈	320.97	320.97	320.97	1354.69	1354.69	1354.69
𝑢 % (of p)	168.93%	168.93%	168.93%	347.36%	347.36%	347.36%
𝑇	1052.17	10521.68	105.22	1036.62	10366.20	103.66
No rebate
𝐸[𝑅^′s profit]	70266.49	702664.89	7026.65	152409.02	1524090.24	15240.90
𝐸[𝑀^′s profit]	51609.09	516090.86	5160.91	133329.75	1333297.47	13332.97
𝐸[SC’s profit]	121875.58	1218755.76	12187.56	285738.77	2857387.71	28573.88
Order quantity	1032.18	10321.82	103.22	1033.56	10335.64	103.36
Current practices
𝐸[𝑅^′s profit]	69889.61	698896.11	6988.96	159413.89	1594138.87	15941.39
𝐸[𝑀^′s profit]	53639.01	536390.09	5363.90	127261.25	1272612.47	12726.12
𝐸[SC’s profit]	123528.62	1235286.20	12352.86	286675.13	2866751.35	28667.51
Order quantity	1068.05	10680.48	106.80	1040.92	10409.22	104.09
𝑈	19	19	19	7.8	7.8	7.8
𝑇	1100	11000	110	0	0	0