Optimal Decisions in a Single-Period Supply Chain with Price-Sensitive Random Demand under a Buy-Back Contract

Table 1

The optimal solutions of buy-back contract when the retailer determines the retail price and the order quantity and the supplier decides the wholesale price; 𝑐=4, 𝐷(𝑝,𝜖)=200𝑝^−𝛽⋅𝜖,  𝜖∼𝑈[0,100].

			Integrated system case					Decentralized system case										Pareto-equilibrium case
𝑏	𝛽		𝑝^∗	𝑧^∗	𝑞^∗	Π^∗		𝑝^∗𝑅	𝑧^∗𝑅	𝑞^∗𝑅	𝑤^∗𝑆	𝜋^∗𝑑𝑆	𝜋^∗𝑑𝑅	Π^∗𝑑	𝜋^∗𝑑𝑆Π^∗𝑑	Π^∗𝑑Π^∗		𝑤^∗𝑝𝑆	𝜋^∗𝑝𝑆	𝜋^∗𝑝𝑅
0	1.5		20	80	178.89	1431.1		60	80	34.43	12	275.41	826.24	1101.6	0.2500	0.7698		6.46	440.14	990.96
0	2		12	66.67	92.59	370.37		24	66.67	23.15	8	92.59	185.19	277.78	0.3333	0.7500		5.5	138.89	231.48
0	2.5		9.33	57.14	42.94	114.52		15.56	57.14	11.97	6.67	31.93	53.22	85.22	0.3750	0.7436		5.09	46.61	67.90
0	3		8	50	19.53	39.06		12	50	5.79	6	11.57	17.36	28.94	0.4000	0.7407		4.85	16.64	22.42
1	1.5		20	80	178.89	1431.1		60.42	80.80	34.41	12.41	275.39	826.06	1101.5	0.2500	0.7697		6.86	440.21	990.89
1	2		12	66.67	92.59	370.37		24.36	68.54	23.11	8.35	92.54	184.98	277.52	0.3335	0.7493		5.83	138.97	231.40
1	2.5		9.33	57.14	42.94	114.52		15.87	59.84	11.93	6.97	31.88	53.08	84.96	0.3753	0.7419		5.37	46.66	67.86
1	3		8	50	19.53	39.06		12.28	53.25	5.75	6.27	11.54	17.28	28.82	0.4005	0.7379		5.10	16.66	22.40
2	1.5		20	80	178.89	1431.1		60.87	81.61	34.37	12.83	275.32	825.58	1100.9	0.2501	0.7693		7.26	440.42	990.68
2	2		12	66.67	92.59	370.37		24.76	70.46	22.98	8.72	92.37	184.30	276.67	0.3339	0.7470		6.17	139.22	231.15
2	2.5		9.33	57.14	42.94	114.52		16.24	62.66	11.79	7.32	31.73	52.61	84.34	0.3762	0.7365		5.66	46.82	67.70
2	3		8	50	19.53	39.06		12.62	56.75	5.65	6.59	11.44	17.02	28.46	0.4019	0.7287		5.36	16.74	22.32
3	1.5		20	80	178.89	1431.1		61.36	82.42	34.29	13.26	275.20	824.76	1100.0	0.2502	0.7686		7.66	440.77	990.33
3	2		12	66.67	92.59	370.37		25.22	72.41	22.77	9.13	92.09	183.16	275.25	0.3346	0.7432		6.51	139.65	230.72
3	2.5		9.33	57.14	42.94	114.52		16.67	65.57	11.56	7.71	31.47	51.82	83.29	0.3778	0.7273		5.95	47.08	67.43
3	3		8	50	19.53	39.06		13.03	60.44	5.47	6.97	11.26	16.57	27.84	0.4047	0.7126		5.61	16.88	22.19