Designing the logistics network

Facility location decisions

• Criteria – Demand and locations of the demand – Distribution systems (Rail, ground, air, sea) – Material sources – Energy sources and cost – Labor: qualifications and cost

Location Problems

• • • • • • • Time Horizon: – Single Period single facility – Multi-period, periodic modifications on the location Facility Typology: – Single kind (RDC or CDC) – Multi kind (RDC and CDC) Material Flow: – Single commodity – Multi commodity Interactions among facilities Dominant material flow: – Inbound material movement is more important – Outbound material movement is more important – Both inbound and outbound material movements are important Demand divisibility – Demand can be acquired from multiple source or single source Influence of transportation on location determination

Modeling and solving location problems

• Single-echelon single-commodity location models – Facilities to be located are homogeneous – Material flow in and out are negligible – All material flows are homogenous. They are treated a single commodity – Transportation cost is linearly correlated with the amount and concave – Facility operating cost is linear and concave

Mathematical model definition

• • • • • • Dj: Demand by customer j Qi: Capacity of a potential facility i Ui: Operations in a facility Sij: amount of product sent from i to j.

Cij(Sij): Cost of shipping Sij unit product Fi(Ui): Operation cost at facility i

𝑛 𝑚 𝑛 𝑚𝑖𝑛 = 𝐶 𝑖𝑗 + 𝐹 𝑖 𝑖=1 S.t.

𝑚 𝑗=1 𝑆 𝑖𝑗=𝑈 𝑖 𝑗=1 ∀𝑖 𝑖=1 𝑛 𝑖=1 𝑆 𝑖𝑗=𝐷 𝑗 Ui<=Qi Sij>=0 Ui>=0 ∀𝑗

What is cost?

• Fi(Ui) is the operating cost. – Includes both fixed and variable cost