Problem 1: Optimizing Service Performance (10 points)
Annual demand for a product is 5,000 units. If the service level were to increase by 1%, the increase in revenue would be .25%. Product costs are $35 per unit, margin is $4 per unit and carrying costs are 20% of product costs. Lead time for replenishment of the product is 1 week and the standard deviation of demand over this lead time is 119 units.
ΔSL (%) | ZU – ZL | Δz |
87-86 | 1.125-1.08 | .045 |
88-87 | 1.17-1.125 | .045 |
89-88 | 1.23-1.17 | .05 |
90-89 | 1.28-1.23 | .05 |
91-90 | 1.34-1.28 | .06 |
92-91 | 1.41-1.34 | .07 |
93-92 | 1.48-1.41 | .07 |
94-93 | 1.55-1.48 | .07 |
95-94 | 1.65-1.55 | .10 |
96-95 | 1.75-1.65 | .10 |
97-96 | 1.88-1.75 | .13 |
98-97 | 2.05-1.88 | .17 |
99-98 | 2.33-2.05 | .28 |
Problem 2: Warehouse Sizing (10 points)
A private warehouse has an annual throughput of 20,000 items and an average material handling cost per item of $0.20/ft. The warehouse size is to be 500,000 sq. ft. Annual construction and maintenance costs are $300/ft. of perimeter.
Problem 3: Facility Location – Center of Gravity Method (10 points)
A warehouse is to be built that will support three factories. The (x,y) location of each factory, annual volume and transportation rate from each factory is given below. Use a map scaling factor of k=500 miles.
Factory | Xi | Yi | Vi: Annual Volume (cwt) | Ri: Rate ($/cwt per mile) |
1 | 0.6 | 7.3 | 22,000 | 0.09 |
2 | 8.6 | 3.0 | 100,000 | 0.10 |
3 | 2.0 | 3.0 | 7,000 | 0.15 |