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

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