MATH3202/7232 Operations Research & Mathematical Planning 2021
Week 8 – Dynamic Programming
Inventory Problem
A company knows that the demand for its product during each of the next four months will be as follows:
At the beginning of each month, the company must determine how many units should be produced during the current month. During a month in which units are produced, a setup cost of $3 is incurred. In addition, there is a variable cost of $1 for every unit produced. At the end of each month, a holding cost of 50 cents per unit on hand is incurred. Capacity limitations allow a maximum of 5 units to be produced during each month. The size of the company’s warehouse restricts the ending inventory of each month to at most 4 units.
How many units should the company produce each month to satisfy demand and minimise total cost?
Nonlinear Objective
Maximize (x1+5)(x2+1)(x3+2) subject to 3×1 + 2×2 + x3 ≤ 6, with x1, x2, x3 all nonnegative integers.
Minimal Studying
In order to graduate from State University, Angie Warner needs to pass at least one of the three subjects she is taking this semester. She is now enrolled in Algebra, Calculus, and Statistics. Angie’s busy schedule of extra-curricular activities allows her to spend only 4 hours per week on studying. Angie’s probability of passing each course depends on the number of hours she spends studying for the course, as follows:
Month
1
2
3
4
Demand
2
3
2
4
Hours of study per week
Probability of Passing
Algebra
Calculus
Statistics
0
.20
.25
.10
1
.30
.30
.30
2
.35
.33
.40
3
.38
.35
.45
4
.40
.38
.50
How many hours per week Angie should spend studying each subject?