Closed-Loop Supply Chain Network under Oligopolistic Competition with Multiproducts, Uncertain Demands, and Returns

Table 1

Optimal strategies for all firms for Examples 15 and 16.

			Example 15	Example 16
			𝜌=10	𝜌=20	𝜌=30
Optimal strategies involving product 1	Optimal product supplied by firm 1 to demand market 𝑅𝑘	𝑘=1	11.6932	11.4632	11.2332
		𝑘=2	11.9248	11.6972	11.4698
		𝑘=3	11.7521	11.5226	11.2931
	New manufactured product	Firm 𝟏	23.3670	22.6798	21.9928
	Optimal product supplied by firm 2 to demand market 𝑅𝑘	𝑘=1	11.5616	11.3353	11.1090
		𝑘=2	11.6707	11.4453	11.2199
		𝑘=3	11.3932	11.1648	10.9364
	New manufactured product	Firm 𝟐	22.6223	21.9421	21.2620
	Optimal product supplied by firm 3 to demand market 𝑅𝑘	𝑘=1	11.2101	10.9846	10.7592
		𝑘=2	11.3140	11.0894	10.8648
		𝑘=3	11.0443	10.8167	10.5891
	New manufactured product	Firm 𝟑	21.5653	20.8875	20.2099
	Optimal product supplied by firm 4 to demand market 𝑅𝑘	𝑘=1	10.9701	10.7471	10.5241
		𝑘=2	11.0185	10.7959	10.5733
		𝑘=3	10.9216	10.6981	10.4746
	New manufactured product	Firm 𝟒	20.9070	20.2378	19.5688
Optimal strategies involving product 2	Optimal product supplied by firm 1 to demand market 𝑅𝑘	𝑘=1	9.4356	9.2237	9.0118
		𝑘=2	9.5625	9.3526	9.1427
		𝑘=3	9.4690	9.2574	9.0459
	New manufactured product	Firm 𝟏	16.4640	15.8306	15.1973
	Optimal product supplied by firm 2 to demand market 𝑅𝑘	𝑘=1	9.4141	9.2109	9.0077
		𝑘=2	9.4708	9.2684	9.0660
		𝑘=3	9.3299	9.1251	8.9205
	New manufactured product	Firm 𝟐	16.2112	15.6009	14.9907
	Optimal product supplied by firm 3 to demand market 𝑅𝑘	𝑘=1	9.2479	9.0514	8.8549
		𝑘=2	9.2970	9.1012	8.9055
		𝑘=3	9.1719	8.9740	8.7760
	New manufactured product	Firm 𝟑	15.7130	15.1228	14.5327
	Optimal product supplied by firm 4 to demand market 𝑅𝑘	𝑘=1	9.1150	8.9268	8.7385
		𝑘=2	9.1351	8.9472	8.7593
		𝑘=3	9.0942	8.9056	8.7170
	New manufactured product	Firm 𝟒	15.3400	14.7752	14.2106