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# Q peminq d seq d q p ceq used ceminq

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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 “ﬁll-in,” 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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