Question

A manufacturer of fortune cups wants to find a new supplier for the plastic cups that are used in making the fortune cups. They have an average annual demand of 1,500 for the plastic cups. For this manufacturer, 1 year is 50 weeks. The manufacturer has two suppliers that have made offers to supply the needed plastic cups. The first supplier has a lower price but a variable lead time. The second supplier has a higher price, but a constant lead time. The retailer experiences an average weekly demand of 30 plastic cups. In both cases the annual holding cost is 7% of the value of the cups and the manufacturer wishes to have a 97.5% service level.

Complete the following table; round part (e) to two decimals; round all other values to the nearest integer.

Supplier 1   Supplier 2
Price    $0.25   $0.55
Order Cost $1.00   $1.00
Holding Cost $0.02   (e)
Lead Time        1 week   1 week
Std. Dev. Of Lead Time     0.75   0
Optimal Order Quantity     (a)    (f)
ROP       (b)    (g)
Safety Stock         (c)   0
Total Cost, including Price and Safety Stock   (d)   (h)

1) What is the value of (a)?
2) What is the value of (b)?
3) What is the value of (c)?
4) What is the value of (d)?
5) What is the value of (e)?
6) What is the value of (f)?
7) What is the value of (g)?
8) What is the value of (h)?
9) Given your analysis, which supplier should the manufacturer use?
10) Give one additional consideration that the manufacturer should think about before choosing a supplier

Answer 1

We tabulate the data and find the values as shown below:

The required values are highlighted in green. The above solution in the form of formulas is shown below for better understanding and reference:

We get answers as shown below:

1) What is the value of (a)? Answer: 414 units
2) What is the value of (b)? Answer: 31 units
3) What is the value of (c)? Answer: 1 unit
4) What is the value of (d)? Answer: $382
5) What is the value of (e)? Answer: $0.04
6) What is the value of (f)? Answer: 279 units
7) What is the value of (g)? Answer: 30 units
8) What is the value of (h)? Answer: $836
9) Given your analysis, which supplier should the manufacturer use?

As seen from above, the total cost is lesser at $382 for Supplier 1 compared to $836 for supplier 2. hence, Supplier 1 should be selected.

10) Give one additional consideration that the manufacturer should think about before choosing a supplier.

Since the lead time is variable, it is based upon probability. While committing to a customer to deliver an order considering the lead time for receipt of cups within a specified lead time, it may lead to risk since the lead time is not 100% certain. Hence, care should be taken for this uncertainty of lead time.

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