Question

Danis supply provides industrial storage and handling systems. Danis’ total revenue (in millions) is estimated as ?=2∗??1/3 where ?? is the service level (% of orders having a 5-day order-cycle time). For example, if 64% of orders have a 5-day cycle time, then Danis would generate a revenue (R) = 2∗(64)1/3=8 million.

Danis’ annual total cost (in millions) ? = .00001∗??3. For example, if 64% of orders have a 5- day cycle time, then their costs are ?= .00001∗643≈2.62 million

3. Given this information, what is the optimum service level for Danis Supply?

4. What is the optimal profit?

5. What is the profit when Dani operates at a 40% service level?

6. What is the profit when Dani operates at 45% service level?

Answer 1

For a service level SL, the profit function can be written as

P = 2*SL^(1/3) – 0.00001*SL^3

Using it on excel solver, we can determine that the optimal service level for the company is 42.66%

X f r 42.6624023592813 K LA B 42.6624 Solver Results 1 SL 2 Revenue Cost 5 Profit 6.98841 0.77649 6.21192 Solver found a solution. All Constraints and optimality conditions are satisfied. Reports Answer Keep Solver Solution Sensitivity Limits O Restore Original Values Return to Solver Parameters Dialog Outline Reports OK Cancel Cancel Save Scenario... Solver found a solution. All Constraints and optimality conditions are satisfied. When the GRG engine is used, Solver has found at least a local optimal solution. When Simplex LP is used, this means Solver has found a global optimal solution.

The optimal profit is 6.21 million

The profit when Dani operates at 40%

P = 2*40^(1/3) -0.00001*40^3 = 6.19 million

The profit when Dani operates at 45%

P = 2*45^(1/3)-0.00001*45^3 = 6.20 million