1-LP Formulation (20 pts). Formulate a LP model for the following problem. (Do n
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1-LP Formulation (20 pts). Formulate a LP model for the following problem. (Do not solve) Demand for a product for the following quarters is 500, 70o, 600, 300 units, respectively. The price per units starts at $30 in supplier can provide no more than 500 units in any one quarter. Although we can take advantage of lower prices in early quarters, a storage cost per units starts at $3 in the first quarter the first quarter and increases by $5 each quarter thereafter. The and increase by $1 each quarter thereafter (Storage cost is charged on end-of-month inventory). In addition, the number of units that can be held over form one quarter to the next must be 50 or less. Develop an LP model to determine the optimum schedule for purchasing the item to meet the demand. a. (7 pts) Define the decision variables b. (3 pts) Write down the LP objective function. c. (10 pts) Write down the LP constraints.Explanation / Answer
Demand (In Units)
Q1
500
Q2
700
Q3
600
Q4
300
Inventory Holding Cost (In $/Unit)
Q1
3
Q2
4
Q3
5
Q4
6
Cost of Item (In $/Unit)
Q1
30
Q2
35
Q3
40
Q4
45
Supplier Cannot Provide More than 500 Items in any given Quarter
Decision Variables can be defined as Quantity (Q) and Excess inventory (E) in any Given Quarter hence, the objective variable will be to minimize the cost of Holding the Inventory. We will multiply the whole sum by 3 as there will be 3 months in any given quarter and Inventory cost is charged at the end of the month
Min (30*E1+35*E2+40*E3+45*E4)*3
S.T.
Q1+E1<=500 (Supplier Constraint)
Q2+E2<=500 (Supplier Constraint)
Q3+E3<=500 (Supplier Constraint)
Q4+E4<=500 (Supplier Constraint)
Q1+E1<=500 (Demand Constraint)
Q2+E2<=700 (Demand Constraint)
Q3+E3<=600 (Demand Constraint)
Q4+E4<=300 (Demand Constraint)
Qi,Ei>=0, i=1,2,3,4,
Intuitive way
Q1 Total demand is 500 and supplier can only provide 500 So no excess Inventory
Q2 Total Demand is 700 and Supply only for 500, therefore shortage and Loss
Q3 Total Demand 600 and Supply of 500, Again loss
Q4 Total Demand 300 and Supply of 500 so Just order only for 300
Q1
500
Q2
700
Q3
600
Q4
300
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