Question

A manufacturer of baby cereals is test marketing a new product next month and requires 20,000 boxes made to specification. The firm plans to purchase these from a number of small paper processors with whom it has dealt in the past and has requested each of these suppliers to submit a bid. N suppliers have responded; each has specified the maximum order deliverable by the beginning of next month and, to guarantee themselves some profit in the event that less than a break-even quantity is ordered, each has specified a setup charge. The bids are shown in Table 2. Table 2: Supplier Costs and Capacities Supplier 1 Supplier2 Supplier 3 Set-up $200 S250 $300 Variable Cost/100 boxes $2.83 $2.66 S1.87 Max. Quantity 5000 7000 4000 p Generalize the formulation for this problem as a mathematical programming problem. Identify and label all decision variables, parameters, and sets. Write the objective function. Write and label all constraints n variables, parameters, and sets Mca

Answer 1

The generalised mathematical model is following

Decision variables: Xi be binary variable such that Xi = 1 indicates the some order be placed on supplier i

Yi be the Number of boxes ordered from supplier i

Objective: Min $\sum_{i} S_{i}*X_{i} + \sum_{i} V_{i}*Y_{i}/100$ , where Si the setup cost and Vi is the variable cost (per 100 boxes) of supplier i

Constraints:

Qi * Xi - Yi >= 0 , where Qi is the max quantity that supplier i can supply (this constraint is to ensure that Yi < Qi and when Yi >0 , then Xi = 1 )

SUM(Yi) = 20000   (this constraint represents that total quantity ordered from all the suppliers should equal 20000 boxes)

Xi $\in$ {0,1}

Yi >= 0