Linear programming - Supply chain network
I have different suppliers, assembly plants, distribution centers and retailers. Suppliers feed assembly plants with components, assembly plants assembles components and sends 2 types of finished products to distribution center and distribution center sends products to retailers. I will try to describe what is going on at each site:
Suppliers : annual capacity constraint in units, cost of component different at each site and all suppliers do not necessarily carry all the components
Assembly plants: annual capacity constraint in weight, cost per product for assembling a finished good.
Product 1= component 1 + comp. 2+ comp.3 Product 2= 2*component 4 + 2* comp. 5+ comp. 6
Distribution Center: fixed cost associated, handling costs per products, annual capacity constraint in weight
Retailers : annual demand is available
Between supplier and assembly: truck with weight limit, unit cost per km
Between Assembly plants and Distribution center: truck with weight limit, unit cost per km
Between Distribution center and retailers: unit cost per kg.km
I need to write a linear model minimizing the costs. Thanks for your input.