Mathematical Formulation of the Order Allocation Problem

The conflicting objectives used in the model are simultaneous minimization of price, lead-time, and rejects. It is relatively easy to include other objectives also. The mathematical form for these objectives is as follows  

Price (Zi) Total cost of purchasing has two components fixed and the variable cost. 

Total variable cost The total variable cost is the cost of buying every additional unit from the suppliers and is given by  

Fixed cost If a supplier k is used then there is a fixed cost associated with it, which is given by  

The product of lead-time of each product and quantity supplied is summed over all the products, buyers, and suppliers and should be minimized. This represents weighted average lead-time. 

---