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Unformatted text preview: n(q, D)) + sE((q Just a name, the
value can be negative D)+ ) cq Alternative ways to view the objective function
• Equivalent forms of the proﬁt function
! ⇡ (q ) = pE(min(q, D)) + sE((q D) ) ⇡ (q ) = (p c)E((q used !
! + c)E(min(q, D)) + (s cq leftover D)+ ) !
• Equivalent form from cost perspective
⇡ (q ) = (p
where c)E(D) (q ) = (p (q )
c)E((D q )+ ) + (c
under s)E((q D)+ )
over Solution
• Analysis (differentiation) • Result
p
F (q ) =
p
⇤ critical ratio c
s optimal quantity q = inf {q
⇤ p
p c
=
s
p 0 : F (q )
pc
c+c p
p c
}
s Cu
=
s
Cu + Co Part 5: Location Model Service Facility Location Planning
• Competitive positioning: prime location can
be barrier to entry. • Demand management: diverse set of market
generators. • Flexibility: plan for future economic changes
and portfolio effect. • Expansion strategy: contiguous, regional
followed by “ﬁllin,” or concentrated. A Location Covering Model
• Assumptions:
•
• • Demands spread uniformly over space
Can locate anywhere in the space GOAL: Determine the number, N, of facilities
to minimize the sum of the
• Fixed facility location costs • Transport costs Analytic Model Inputs & Costs • Fixed cost per facility = f • Density of demands = ρ per unit area • Cost per unit per unit distance = c • Area to be served = A Analytic Model Inputs & Costs Example service area A
divided into N=9 regions
each of area a=A/9
!
Travel at 45 degrees to
sides of diamond service
areas Expected Distance Computation
distance = Expected Distance
E(dist) =
=
=
= p1p A
Z 2N 22
(1
)d
A/N
0
p
3
2
A/2N
(
)0
3A/N
r
r
A
1
A
2N
3 2N
r
1 2A
3N Expected distance...
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This document was uploaded on 01/28/2014.
 Fall '14

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