Collaborative Product Portfolio Design Based on the Approach of Multichoice Goal Programming

Table 5

Sensitivity analysis of the proposed model by varying β₁₂ and β₂₁.

Variety of β12, β21	LMP1	LMP2	LMP1	LMP2	LMP1	LMP2	LMP1	LMP2	LMP1	LMP2
Simultaneous change	β12 = 0.1, β21 = 0.1		β12 = 0.3, β21 = 0.3		β12 = 0.5, β21 = 0.5		β12 = 0.7, β21 = 0.7		β12 = 0.9, β21 = 0.9
	13,592	4530	13,592	4530	13,592	4530	13,592	4530	13,592	4530
Sensitivity	Average changing rate: ΔLMP1 = 0%, ΔLMP2 = 0%.
Single increase (β21)	β12 = 0.1, β21 = 0.1		β12 = 0.1, β21 = 0.3		β12 = 0.1, β21 = 0.5		β12 = 0.1, β21 = 0.7		β12 = 0.1, β21 = 0.9
	13,592	4530	12,940	5097	12,348	5612	11,808	6082	11,312	6513
Sensitivity	Average changing rate: ΔLMP1 = −4.5%, ΔLMP2 = 9.5%.
Single increase (β12)	β12 = 0.1, β21 = 0.1		β12 = 0.3, β21 = 0.1		β12 = 0.5, β21 = 0.1		β12 = 0.7, β21 = 0.1		β12 = 0.9, β21 = 0.1
	13,592	4530	14,198	4004	14,677	3587	15,066	3249	15,388	2969
Sensitivity	Average changing rate: ΔLMP1 = 3.2%, ΔLMP2 = −10.0%.
β12 + β21 = 1, β12 increase	β12 = 0.1, β21 = 0.9		β12 = 0.3, β21 = 0.7		β12 = 0.5, β21 = 0.5		β12 = 0.7, β21 = 0.3		β12 = 0.9, β21 = 0.1
	11,312	6513	12,524	5459	13,592	4530	14,540	3706	15,388	2969
Sensitivity	Average changing rate: ΔLMP1 = 8.0%, ΔLMP2 = −17.8%.
β12 + β21 = 1, β21 increase	β12 = 0.9, β21 = 0.1		β12 = 0.7, β21 = 0.3		β12 = 0.5, β21 = 0.5		β12 = 0.3, β21 = 0.7		β12 = 0.1, β21 = 0.9
	15,388	2969	14,540	3706	13,592	4530	12,524	5459	11,312	6513
Sensitivity	Average changing rate: ΔLMP1 = −7.4%, ΔLMP2 = 21.7%.