Question

A shop that makes candles offers a scented candle, which has a monthly demand of 360 boxes. Candles can be produced at a rate of 36 boxes per day. The shop operates 20 days a month. Assume that demand is uniform throughout the month. Setup cost is $60 for a run, and holding cost is $2 per box on a monthly basis.
Determine the following:

(A) the economic run size
(B) the maximum inventory
(C) the number of days in a run

The daily usage rate (u) is 18 boxes. The daily production rate (p) is 36 boxes.

Answer 1

Answer:

A) 208

B) 104

C) 5.77 days

Explanation:

EOQ:

$Q_{opt} = \sqrt{\frac{2DS}{H}} \sqrt{\frac{p}{p-u}}$

Where:

D = monthly demand = 360

S= setup cost = ordering cost = 60

H= Holding Cost = $2 per month

p = production rate: 36

u = daily usage

$Q_{opt} = \sqrt{\frac{2(360)(60)}{2}}\sqrt{\frac{36}{36-18}}$

EOQ: 208

Maximum Inventory

$\frac{EOQ}{p} (p-u)$

$\frac{208}{36} (36-18)$

Max Inventory: 104

days per run:

$\frac{EOQ}{p}$

$\frac{208}{36}$

days per run: 5.77 (almost 6 days)