Question

You manage the shipping of item #A452 from your supplier. The shipments for this item are delivered to the nearest port, and you have to transport them to the distribution center. You have two options, truck load (TL) and less than truck load (LTL).

Your company needs 5000 units of #A452 per year and it is purchased at a price of $36 per unit. Each order costs $92. Your company uses a holding charge of 0.13, a cycle service level of 90% and 365 days per year for planning purposes.

The truck load (TL) option costs $1300 per load. It takes 4 days to deliver and each truck can carry up to 1200 items.

The less than truck (LTL) load option costs $2.4 per item. It takes 6 days to deliver.

You have three options,

OPTION A: to use the TL option and deliver full truck loads,

OPTION B: to use the TL option and deliver the economic order quantity

OPTION C: to use LTL option and deliver the economic order quantity.

For all following parts, consider transportation costs as an item cost unless otherwise specified. i.e., the total variable cost of #A452 in the Full truckload is $1300/1200items + $36/item = $37.083333333333336/item.

(Option A) Full truckload

What is the sum of average pipeline and cycle inventory, ordering, and purchase costs for option A?

(Option B) Truckload with EOQ

What is the economic order quantity? Use the item cost without the transportation for this calculation.

If you order the EOQ calculated earlier (rounded to a whole number), what is the sum of average pipeline, cycle inventory, ordering, and purchase costs for option B? Consider transportation costs a part of the item cost.

(Option C) Less than truckload

What is the sum of average pipeline and cycle inventory, ordering, and purchase costs for option C? Consider transportation costs as an item cost, and use the EOQ in whole numbers for calculation.

Please answer all 4 questions above.

Answer 1

Given that,

Annual demand, D = 5000 units

Order cost, S = $ 92

Holding charge, h = 0.13

Daily demand rate, d = 5000/365 = 13.7

(Option A) Full Truckload (TL)

Truckload quantity, Q = 1200 units

Lead time, L = 4 days

Holding cost, H = 36*0.13 = $ 4.68

Pipeline inventory = d*L = 13.7*4 = 55

Cycle inventory = Q/2 = 1200/2 = 600

Unit cost, C = 36+1300/1200 = $ 37.083

Sum of average pipeline and cycle inventory, ordering, and purchase costs = (55+600)*4.68 + (5000/1200)*92 + 5000*37.083 = 3,065.4‬ + 383.33 + 185,415 = $ 188,863.73

(Option B) Truckload with EOQ

EOQ = SQRT(2DS/H) = SQRT(2*5000*92/4.68) = 443

Cycle inventory = Q/2 = 443/2 = 222

Unit cost, C = 36 + 1500/443 = $ 39.4

Sum of average pipeline and cycle inventory, ordering, and purchase costs = (55+222)*4.68 + (5000/443)*92 + 5000*39.4 =1,296.36 + 10,697.67 + 197,000 =    $ 208,994.

(Option C) Less Than Truckload (LTL)

Lead time, L = 6 days

Pipeline inventory = d*6 = 13.7*6 = 82

Cycle inventory = Q/2 = 443/2 = 222

Unit cost, C = 36 + 2.4 = $38.4

Sum of average pipeline and cycle inventory, ordering, and purchase costs = (82+222)*4.68 + (5000/443)*92 + 5000*38.4 = 1,422.72 + 1,038.37 + 192,000 = $ 194,461

Option A (Full Truckload) is the most economical one.

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