Question

sam's cat hotel operates 52 weeks per year, 6 days, and uses a continuous review inventory system. It purchases kitty litter for $11 per bag   The following information is available about these​ bags:

-Demand: 95 bags (a week)

-Order cost: $52.00 per order

- Annual Holding Cost: 40 percent

- Desired ​cycle-service level: 80 percent

-lead time= 5 days (30 working days)

- Standard Deviation of weekly demand= 15 bags

- Current On-hand Inventory is 320 days with no open orders or back orders

A. Suppose that the weekly demand forecast of 95 bags a week is incorrect and actual demand averages only 75 bags bags per week. How much higher will total costs​ be, owing to the distorted EOQ caused by this forecast​ error?

The costs will be $ ____ higher owing to the error in EOQ. ​(Enter your response rounded to two decimal​ places.)

​

Answer 1

EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST)

ANNUAL HOLDING COST = (EOQ / 2) * HOLDING COST

ANNUAL ORDERING COST = (DEMAND / EOQ) * ORDERING COST

FOR DEMAND = 95,

EOQ = SQRT(2 * 4940 * 52 / 4.4) = 341.71

ANNUAL HOLDING COST = (341.71 / 2) * 4.4 = 751.76

ANNUAL ORDERING COST = (4940 / 341.71) * 52 = 751.75

TOTAL COST = AHC + AOC = 751.76 + 751.75 = 1503.51

FOR DEMAND = 75

EOQ = SQRT(2 * 3900 * 52 / 4.4) = 303.61

ANNUAL HOLDING COST = (303.61 / 2) * 4.4 = 667.94

ANNUAL ORDERING COST = (3900 / 303.61) * 52 = 667.96

TOTAL COST = AHC + AOC = 667.94 + 667.96 = 1335.9

Difference = 1503.51 - 1335.9 = $167.61