Question

Audio-Video City (AVC), an electronic supply store, stocks and sells a particular brand of 8K Curve...

Audio-Video City (AVC), an electronic supply store, stocks and sells a particular brand of 8K Curve TVs. It costs the firm $612 each time it places an order with the manufacturer for the 8K 77” Curve TVs.  The cost of carrying one 8K Curve TV in inventory for a year is $159. The store manager estimates the total annual demand for this type of 8K TVs will be 1744 units, with a constant demand rate throughout the year. Orders are received within minutes from a local warehouse of the manufacturer. The store policy is never to have stock-outs of the 8K TVs. The store is open for business every day of the year except Dr. King’s Birthday, Independence Day, Labor Day, Thanksgiving Day, and Christmas Day. Determine:

  1. Optimal order quantity per order (Make practical assumption for rounding and supply supporting justification)
  2. Based on your answer from part-a, minimum total annual inventory cost.

Continuing from the previous problem, the manufacturer of 8K Curve TVs decided to close the local warehouse and ship their 8K Curve TVs directly from their overseas manufacturing facility. As a result, it takes 7 working days for the manufacturer to fulfill any customer order.

  1. It is observed that during lead time, the daily demand for 8K Curve TVs can be expressed by a normal distribution with variance, g = 14.44. If AVC wants to have a minimum of 96.25% service level, at what inventory level of 8K TVs, AVC should place an order?
  2. Continuing from part-a, what should be the safety stock for 8K-TVs?
  3. With $750.00 procurement cost (r) per 8K TV from supplier and the answers from parts: a and b, what should be the annual Total Inventory Cost for this type of 8K TVs?
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Answer #1

Optimal order quantity = [ 2 x demand per annum x cost per order / cost of holding one unit per year]^0.5

= [ 2 x 1744x612/159]^0.5

=115.86 =116 units

(ii)

SD during lead time = ( 14.44)^0.5 =3.8

Safety stock = z x SD of daily demand x ( lead time)^0.5

= 1.78x 3.8 x ( 7)^0.5 = 17.89 =18 units

Reorder point = demand during lead time + safety stock

= (1744/360) x 7 +18 =52 units

Cost of inventory = cost of holding + cost of ordering + cost of holding safety stock

= 116/2 x 159 + 612 x (1744/116) + 18x159 = 21285

Total cost = 21285 +750x1744 = 1329285

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