1. Presented By: Brian Murphy and Scott Lichtor
Solving Model 7
Presented By: Brian Murphy and Scott Lichtor

2. Background
Dairy plant produces various flavors of ice creams in 3 gallon containers and distributes them to a chain of ice cream parlors.
Dairy plant knows exact demand from parlors for the next twelve months (January-December).
Plant has huge freezer-warehouse that can store surplus in any one month for sale in future months.
Plant can produce ice cream in regular time or overtime.
Production capabilities vary from month to month due to variations in demand.
Question:
How many gallons should the dairy plant produce in each month in order to reduce total costs?

3. Key Figures *Cost of storage is 10 cents per month for each month
Demand:
Regular time production:
Overtime production:
Month
Jan.
Feb.
Mar.
Apr.
May
June
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
No. of containers ordered 75 80 85 95
120
140
175
190
130
110 90
Month
Jan.
Feb.
Mar.
Apr.
May
June
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Production Capacities
100 90 80
Cost per 3 gallons (cents) 65 70 75
Month
Jan.
Feb.
Mar.
Apr.
May
June
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Production Capacities 40 50 60
Cost per 3 gallons (cents) 85 90 95

4. Assumptions and Variables
Dairy plant has no finite storage capacity.
Ice cream kept in storage does not go bad or lose value (ice cream produced in January can be sold in December).
All ice cream produced is eventually sold (no leftovers)
Variables:
xij = containers produced during regular time in month j for use in month i.
yij = containers produced during overtime in month j for use in month i.

5. Objective Function … Minimize z = total costs
Broken down into production and storage costs for each month.
January: 0.65∑xi, ∑yi, ∑(i-1)(xi,1+yi,1)
+February: 0.65∑xi, ∑yi, ∑(i-2)(xi,2+yi,2)
+December: .65xi, yi,12
Regular Production Cost
Overtime Production Cost
Storage Cost 12 12 12
i=1
i=1
i=1
i=2
i=2
i=2 …

6. Constraints … Demand Constraints: January: x1,1 + y1,1 = 75
February: ∑(x2,j + y2,j) = 80
December: ∑(x12,j + y12,j) = 90 12
j=1 12 …
j=1

7. Constraints (Cont.) … Production Constraints:
January: ∑xi,1 ≤ 100, ∑yi,1 ≤ 40
February: ∑xi,2 ≤ 100, ∑yi,2 ≤ 40
December: x12,12 ≤ 90, y12,12 ≤ 50 12 12
i=1
i=1
i=2
i=2 …

8. Solution
See Excel Sheet