MÜHENDİSLİKTE MATEMATİKSEL PROGRAMLAMA MODELLERİ

uygulama

Identifying Relevant Symptoms

Data

Variables

Objective Function

Constraint

Supply Chain Network Design

A company sells household goods to its customers in different cities.Products are manufactured in the manufacturing plant of companyfirst. Then they are sent to warehouses in different cities and finallythey are sent to customers from warehouses. Direct shipment frommanufacturing plant to customers is prohibited.

Create a network design model that determines the locations ofwarehouses, flows between facilities.

Model• 𝑖: 𝑆𝑒𝑡 𝑜𝑓 𝑤𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒𝑠

• j: 𝑆𝑒𝑡 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠

• 𝑑𝑚𝑖: distance between manufacturing plant and warehouse i

• 𝑑𝑤𝑖𝑗: distance between ith warehouse and jth customer

• 𝑟𝑑𝑗: average demand of jth city

• 𝑐𝑖: 𝑎𝑛𝑛𝑢𝑎𝑙 𝑤𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 𝑓𝑜𝑟 𝑖𝑡ℎ 𝑤𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒

• 𝐶𝑎𝑝: Capacities of warehouses

• 𝑎𝑖: 𝑓𝑙𝑜𝑤 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑝𝑙𝑎𝑛𝑡 𝑎𝑛𝑑 𝑖𝑡ℎ 𝑤𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒

• 𝑏𝑖𝑗: flow between plant and ith warehouse

• 𝑤𝑖: flow between ith warehouse and jth customer

Model

min 𝑧 =

𝑖

𝑑𝑚𝑖𝑎𝑖 +

𝑖

𝑗

𝑑𝑤𝑖𝑗𝑏𝑖𝑗 +

𝑖

𝑤𝑖𝑐𝑖

𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜𝑎𝑖 ≤ 𝑤𝑖𝐶𝑎𝑝 ∀𝑖

𝑎𝑖 =

𝑗

𝑏𝑖𝑗 ∀𝑖

𝑖

𝑏𝑖𝑗 = 𝑟𝑑𝑗 ∀𝑗