Design of Transportation Networks Plant Management

BUSI 410 Business Analytics

Module 6: Design of Transportation Networks Plant Management

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Last lecture

• Nikon (multiple-period production and inventory management, dummy variables) • Merton Truck Company

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Lease-a-Lemon Car Rental

Lease-a-Lemon Car Rental discovered an imbalance in the distribution of its rental cars in the Northeast region at the end of summer. The following surpluses exist: 26 cars in New York, 43 in Washington DC, and 31 in Cleveland. Shortages are 32 cars in Pittsburgh, 28 in Buffalo, and 26 in Philadelphia. The company can move cars at a cost of $1 per mile per car. The inter-city distances in miles are:

City New York Washington DC Cleveland Pittsburgh 439 296 131 Buffalo 396 434 184 Philadelphia 91 133 479

How could Lease-a-Lemon redistribute cars at minimum cost?

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Lease-a-Lemon Car Rental: Notations

Denote surpluses by ������������ : ������1 = 26 (NY), ������2 = 43 (DC), ������3 = 26 (Clev)

Denote shortages by ������������ (demand):

������1 = 32 (Pitt), ������2 = 28 (Buff), ������3 = 26 (Pilly) Denote costs by ������������������ (= distance, because $1/car-mile)

������������������ NY (1) DC (2) Clev (3) Pitts (1) 439 296 131 Buff (2) 396 434 184 Phil (3) 91 133 479

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Lease-a-Lemon Car Rental: Formulation

• Decisions: ������������������ = cars to move from surplus city ������ to shortage city ������ • Objective: minimize total cost

3 ������,������=1 ������������������ ������������������

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Lease-a-Lemon Car Rental: Formulation

Constraints • Availability at surplus cities:

– From NY ������ = 1 : ������11 + ������12 + ������13 ≤ 26 – From DC ������ = 2 : ������21 + ������22 + ������23 ≤ 43 – From Clev ������ = 3 : ������31 + ������32 + ������33 ≤ 31

• Demand at shortage cities:

– To Pitts ������ = 1 : ������11 + ������21 + ������31 ≥ 32 – To Buff ������ = 2 : ������12 + ������22 + ������32 ≥ 28 – To Phil ������ = 3 : ������13 + ������23 + ������33 ≥ 26

• Non-negativity constraints? •...