Question Details

(25 points)

1. Powered By Koffee (PBK) is a new coffee store. PBK uses 50 bags of whole bean coffee every month, and assume that demand is perfectly steady throughout the year.

PDK purchases its coffee from a local supplier, Phish Roasters, for the price of $25 per bag and $85 fixed cost for every delivery independent of order size. Phish Roasters delivers the orders in 2 months. The holding cost due to handling and storage is $1 per bag per month. PBK uses a cost of capital of 2% per month.

(10 points)

a) Find the optimal order quantity, the reorder point and the annual total cost associate with it for PBK. On average, how many months of demand of coffee does PBK hold in inventory under this policy?

(7 points)

b) Suppose a South American import/export company has offered PBK a deal. That is, PBK can buy a years’ demand worth of coffee directly from the South American supplier for $20 per bag and a fixed delivery cost of $2,000. The lead-time for delivery of orders is 6 months in this case. Assume the estimated cost of handling and storage is $1 per bag per month and a cost of capital of 2% per month as before. What will be the order quantity, reorder point and then average monthly total cost in this case? Should PBK switch his supplier and buy from the South American company?

(8 points)

c) Recently, Discount Wholesale (DW), a local supplier of coffee beans has offered PBK the following terms: A price per bag of $23 plus a flat cost of $200 per delivery. However, orders should be in batches of 50 bags only. Order lead-time will be two months. As before, the holding cost due to handling and storage is $1 per bag per month and the cost of capital is 2% per month. Find the optimal order quantity, the reorder point, the average months of demand of coffee in inventory and the average total monthly cost if DS is employed? Based on your result, should PBK select DW as his supplier?

2

(25 Points)

2. Annual demand for products X and Y are uniform and equal to 500 and 1000, respectively. Two suppliers are considered: Supplier one, ALL-UNITS Quantity Inc., provides his services and deliveries on an All Unit Quantity Discount Schedule. The second supplier, INCREMENTAL Quantity Inc., employs Incremental Quantity discounts only. Below are all relevant information on the products and suppliers:

ALL-UNITS Quantity Inc. Supplier

Product X: Order Cost=$500, Lead-time=1 month, discount schedule based on All-Units quantity discount:

Quantity Ordered Unit Cost (c)

0<Q< 200

100

200≤Q

98

Product Y: Order Cost=$2,000, discount schedule based on All-Units quantity discount:

Quantity Ordered Unit Cost (c)

0<Q< 1,000

150

1,000≤Q

148

INCREMENTAL Quantity Inc. Supplier

Product X: Order Cost=$500, discount schedule based on Incremental quantity discount:

Quantity Ordered Unit Cost (c)

0<Q≤ 200

99

200<Q

98

Product Y: Order Cost=$2,000, discount schedule based on Incremental quantity discount:

Quantity Ordered Unit Cost (c)

0<Q≤ 200

148

200<Q

140

3

(13 Points)

a) Assuming an annual holding cost rate of 20%, from which supplier should each product be ordered? What are the optimal order quantities reorder points and the aggregated total annual cost associated with Replenishment/Stocking of the two products.

(10 Points)

b) Recently, the firm is considering a new supplier, Joint-Source Inc., who delivers the products only if they are jointly replenished. That is, both products have to be ordered together (at the same time). The idea is appealing as there will be savings in order cost. Joint-Source offers a constant unit price for the two products. Specifically, the price per unit for Products X and Y are $100 and $149, respectively. Each time an order is placed, an order cost of $1500 is charged.

Assuming an annual holding cost rate of 20%, find the optimal order quantities and the total annual cost associated with Replenishment/Stocking if this supplier is chosen.

(2 Points)

c) Based on your analysis from (a) and (b), recommend the optimal sourcing strategy for the company. That is, for each product, specify the supplier, the order quantity, the reorder point and then the aggregated annual total cost.

(25 points)

3. The following data is available on four products that are produced on a single machine.

Product Annual Demand Annual Production Rate Unit Cost ($) Set-up Cost ($) Set-up Time (Days)

1

6500

26000

200

400

1

2

150

1200

7

1000

2

3

8600

40000

10

400

1

4

120

400

25

1000

5

Suppose the annual holding cost rate is 24%. Assume a 30 days per month or 360 days per year in your calculations.

(15 points)

a) Find the optimal time between production of each product, their optimal production quantities and the average annual total cost.

(10 points)

b) Suppose that through upgrading the existing machine, Set-up times can be eliminated; however, Set-up costs which are mainly due to instrument changes hold as before. What is the maximum investment the company is willing to make (if any) on this upgrade? (In all your financial analysis, assume that relevant cash flows continue in perpetuity, the nominal cost of capital is 24% per year compounding monthly)

4

Hint: When Cash Flows continue in perpetuity with a nominal interest rate of x and cash flows

are compounded monthly, an investment made can be spread into per month annuity by dividing

it by the monthly interest rate. That is, if a $A investment is made, then it can be spread into

monthly annuities of A*y where y=x/12 is the monthly interest rate.

(25 points)

4. The following are the sales figures for 2014 through 2016 for a product. Data for a year is

available in two halves of the year, months January though June, and then July though December

(Half-year 2).

Half-year 2014 2015 2016

1 1250 1200 1180

2 840 800 780

Suppose we are interested in setting up a forecasting model using the Winter’s Method.

(15 points)

a) Initialize the system based on the data provided for 2014 and 2015 using the procedure

discussed in class.

(5 points)

b) Suppose the smoothing factors are a =b =g =0.2. Employing the method discussed in

class, forecast for the first half of 2016 and then the second half of 2016 by incorporating

the sales for the first half of 2016. Calculate the MAD based on 2016 actuals and

forecasts.

(5 points)

c) Forecast sales for the two halves of 2017 and 2018.