Race One Motors is an Indonesian car manufacturer. At its largest manufacturing facility, in Jakarta, the company produces subcomponents at a rate of 300 per day, and it uses these subcomponents at a rate of 12,400 per year(of 250 working days). Holding costs are $2 per item per year, and ordering costs are $32 per order. a) What is the economic production quantity?b) How many production runs per year will be made?c) What will be the maximum inventory level?d) What percentage of time will the facility be producing components?e) What is the annual cost of ordering and holding inventory?

a. EPQ = 689.4

b. Np = 17.99

c. Qmax = $575.65

d. %t = 16.54%

e. TC = $1,151.28

Explanation:

Let's begin by listing out the variables:

Production per day (P) = 300, Component rate usage (D) for 250 days = 12,400, Holding cost (H) = $2 per item per year, Ordering cost (S) = $32 per order

To calculate the component rate usage per day, we have:

d = D ÷ 250 = 12400 ÷ 250 = 49.6

d/P = 49.6/300 = 0.165

a) EOQ = square root of [(2 times the annual demand in units times the incremental cost to process an order) divided by (the incremental annual cost to carry one unit in inventory)]

EPQ =

EPQ = [2 * 12400 * 32 ÷ 2 (1 - 0.165)]

EPQ =  [793600 ÷ 1.67]

EPQ = sqrt[475209.58] = 689.35

EPQ = 689.4

b) To calculate the production runs per year, we have:

Np = D ÷ EPQ = 12400 ÷ 689.4 = 17.9867

Np = 17.99

c) To calculate maximum inventory level, we have:

Qmax = EPQ * (1 - d/P) = 689.4 * (1 - 0.165)

Qmax = 689.4 * 0.835 = 575.649

Qmax = $575.65

d) Percentage of time the company produces is calculated thus:

%t = (EPQ *Np * 100%) ÷ (P * t)

%t = (689.4 * 17.99 * 100%) ÷ (300 * 250)

%t = 16.54%

e) The annual cost of ordering and holding inventory is calculated thus:

TC = (Np * S) + [(Qmax ÷ 2) * H]

TC = (17.99 * 32) + [(575.6 ÷ 2) * 2]

TC = 575.68 + 575.6

TC = $1,151.28

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