Multiobjective Interaction Programming Problem with Interaction Constraint for Two Players

Table 1

Solutions of the three models.

		Profit of 𝐬-joint solution	Profit of Stackelberg solution	Profit of pricing solution
Manufacturer	𝜋𝑚1	563.22	612.5	350
	𝜋𝑚2	657.3	680.625	247.5
	𝜋𝑚3	755.44	765	192
	𝜋𝑚	1976.36	2058.125	789.5
Retailer	𝜋𝑟1	273.22	288.75	875
	𝜋𝑟2	569.1	344.4375	1113.75
	𝜋𝑟3	571.9	433.5	1344
	𝜋𝑟	1414.22	1066.6875	3332.75
System	𝜋	3390.58	3124.8125	4122.25

𝜋_𝑚𝑖(𝑖=1,2,3) denotes the profit of 𝑃_𝑖 for the manufacturer.
𝜋_𝑚=∑³_𝑖=1𝜋_𝑚𝑖 denotes the total profit of 𝑃_𝑖 for the manufacturer.
𝜋_𝑟𝑖(𝑖=1,2,3) denotes the profit of 𝑃_𝑖 for the retailer.
𝜋_𝑟=∑³_𝑖=1𝜋_𝑟𝑖 denotes the total profit of 𝑃_𝑖 for the retailer.
𝜋=𝜋_𝑚+𝜋_𝑟 denotes the total profit of 𝑃_𝑖 for the system, the manufacturer, and the retailer as a whole.