Problem
Coop Mart has received the following demands for a product this year:
|
Month
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|
Demand
|
300
|
700
|
800
|
900
|
3300
|
200
|
600
|
900
|
200
|
300
|
1000
|
800
|
Suppose ordering cost (OC) is $504 and holding cost (HC) of one unit of product in a year is $3. There is no shortage cost. Backordering is not allowed in this model.
A. Given that the total demand of the whole year is 10,000 products, suppose the company is going to use the EOQ model for the accumulated demand of one year (10,000). In other words, ignore the monthly demand. Compute:
a) Optimal order quantity (Q*)
b) Total cost
c) Frequency of orders
d) Time between orders
B. Use mixed integer linear programming to solve the problem regarding the monthly demand. Suppose that holding cost is applied to the ending inventory.
a) Develop the mathematical model in the Word document.
b) Solve the problem in MS Excel
c) Develop a plan in the Word document and explain when and how many products should be ordered in order to minimise the total cost.
d) Recalculate the optimal value of objective function (total cost with the new assumption that the holding cost is applied to the average inventory (not ending inventory).