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A restaurant that is open 7 days per week experiences level demand throughout the year. The...

A restaurant that is open 7 days per week experiences level demand throughout the year. The average annual demand for disposable napkins, which costs $0.20 apiece,is 45000per year. The annual holding cost rate 10% and the ordering cost is estimated to be $25per order. The forecast CV is of 15%and the lead time from order to receipt is 2days. A cycle service level of 98% is targeted.

Calculate the optimal order quantity and the reorder point (ROP).

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Answer #1

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From the given data, we have,

Annual Demand = D = 45000 units / year

Holding Rate = h = 10 % / unit / year

Ordering Cost = K = 25 $ / order

Purchase price = c = 0.2 $ / unit

CV = 15 %

Lead TIme = LT = 2 days

The economic order quantity is calculated using the formula EOQ = SQRT [2*K*D / (h*c)]

EOQ = SQRT [2 * 25 * 45000 / (0.1 * 0.2)]

= 10606.6 units

Standard Deviation of Demand = σD = C.V * Mean Demand

= 0.15 * (45000 / 365)

= 18.5 units

Standard Deviation of Demand during lead time chase = σDL = σ * Sqrt (2)

= 18.5 * Sqrt (2)

= 26.16 units.

For a 98% probability of remaining in stock, corresponding z value for 0.9800 probability = 2.05.

Safety Stock = z * σDL

= 2.05 * 26.16

= 53.73 = 54 units.

Demand During lead time = μDLT = (μD * μLT )

= 123.3 * 2

= 246.57 = 247 units

Reorder point = μDLT + Safety Stock

=247 + 54

= 301 units

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