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
𝑚𝑖𝑛 =
𝐶𝑖𝑗 +
𝑖=1 𝑗=1
S.t.
𝑚
𝑗=1 𝑆𝑖𝑗=𝑈𝑖
∀𝑖
𝑛
𝑖=1 𝑆𝑖𝑗=𝐷𝑗
∀𝑗
Ui<=Qi
Sij>=0
Ui>=0
𝑛
𝐹𝑖
𝑖=1
What is cost?
• Fi(Ui) is the operating cost.
– Includes both fixed and variable cost