Supply Chain Management    Analytical part B:        Time 2hours

Name _____________________________               ID #_________________________

Please provide your detailed answers below every part of each question.  When you are asked to formulate, you must show the mathematical model starting with the definition of the decision variables.  Please answer only the question asked.  For example, the solution to part a) of question 1 should only contain Optimal Lot Size, Cycle Inventory, annual inventory and item Cost. Do not paste the entire spreadsheet.  Problems 1 to 8 are worth 20 points each and the whole test is worth 160 points.

Question 1:  A furniture manufacturer uses 20,000 square feet of plywood per month.  The holding costs are estimated to be 20% per year and fixed cost of each order is $400 regardless of the quantity ordered.  The supplier charges $2.00 per square foot if you order less than 20,000 square feet, $1.80 per square foot for orders 20,000 square feet but less than 50,000 square feet, and $1.70 per square foot for all orders of 50,000 square feet or more.

1. What will be the optimal order quantity for the manufacturer given this pricing structure?  What will be the cycle inventory and the annual inventory cost and annual item cost?

• How many orders will be placed each year?

Question 2:   Metro Tech buys three components from a local wholesaler.  The annual demand for components A, B, and C is 500, 3000, and 6000 units respectively.   The agreed purchase price is $20, $15, and $10per unit for A, B, and C respectively for each product.  The holding cost is estimated to be 20% per year.  The ordering cost consists of handling and trucking costs.  The handling cost is $100 for each type of component regardless of the number of items ordered.  In addition to the handling cost, Metro Tech must pay a trucking cost of $500 for each delivery regardless of the total number of components in the order.  Currently, all three items are being ordered independently using EOQ models.  A proposal has been made to combine the ordering of the three items to save on trucking costs.  Analyze the current and the prosed scenario and show the results below.

Input Data:   

	A	B	C	Combined Order
Demand items/year				No Change
Item Cost in $/item				No Change
Holding Cost as %/year				No Change
Ordering Cost $/order

Current Scenario Analysis (Independent ordering):

	A	B	C	Total
# of Orders/ year
Economic Order Quantity
Holding Cost in $/year
Ordering Cost in $/Year
Total Cost of ordering Independently

Proposed Scenario Analysis (Joint ordering):

	A	B	C	Total
# of Orders/ year
Economic Order Quantity
Holding Cost in $/year
Ordering Cost in $/Year
Total Cost of ordering Jointly

Total cost savings due to ordering jointly:  __________________________________

Can you estimate the total savings in trucking costs?  Why is this different from total savings?

Question 3: 

The annual demand for a product is 64,000 items and the holding cost is $0.50/ item/ year. The operates 300 days per year and lead time is 9 days.  The ordering cost is $250 per order.

1. Find the following assuming that the company is operating in an optimal fashion:

Economic Order Quantity _________

Cycle Time __________

Cycle Inventory _________

Safety Inventory _______

ROP __________

Annual Holding Cost __________

Grand Total Cost ________

• Now assume that the company keeps safety stock of 200 items to account for the standard deviation in demand of 50 items and the lead time standard deviation of 2 days.  Find the following:

Cycle Inventory _________

Safety Inventory _______

ROP _______

CSL_________

E(#Short) ________

Fill rate _______

Average Inventory _________

Average Flow Time __________

Inventory Holding Cost ________

• Now Suppose that the company decides that they operate at a service level of 0.95 What will Cycle Inventory _________

Safety Inventory _______

ROP _______

E(#Short) ________

Fill rate _______

Average Inventory _________

Average Flow Time __________

Inventory Holding Cost ________

Question 4: 

The selling price of a particular food item is $20 per packet.  The cost to the store is $14 per packet.   The unsold packets must be salvaged at the end of the day for $3 per packet.  The store manager believes that the shortage cost is $2 per packet.   How many packets should the store buy each day to maximize profit if demand is:

1. Normal with mean 400 and standard deviation 60?

• Uniform with lower limit to be 200 and upper limit to be 600?

• Demand for the last 400 days was as shown below

            Demand        200     250     350     500

Frequency    80     200    80     40 

• Calculate the average daily profit for part c)

Question 5:  Avery owns four large dealerships in the metropolitan area.  Each of these locations currently keep inventory of required components used for the repairs of the cars.   It is possible for the company to keep all the high-priced parts at one of these locations and then deliver to any other location within one hour.  The cost of space and the delivery vehicle is negligible but the labor cost of the driver for making all the required deliveries to all three locations will be $180 per day.  You have been hired as a supply chain consultant to help Avery in making this decision.  Use the following data to calculate the total relevant costs of both the current and the proposed scenario:

Average Price of the High-Priced Components = $150

Annual Demand for the High -Priced Components = 20,000 items per location

Number of Work-Days = 250 per year

Annual Holding Costs = 30% per year

Lead Time for replenishment from the manufacturer = 9 days

Fixed Costs of placing an order with the manufacturer = $150 per order

Target cycle service level = 0.95

1. Calculate the EOQ and the savings in total inventory costs for the current and the proposed scenario. 

• Now assume that the demand at each location is not constant but it is Normal with mean 100 and standard deviation of 15 High-Priced items per day.   Calculate the cost of safety inventory for the current and the proposed scenario.

• What is your recommendation and how much will Avery save if the demand was probabilistic?

Problem 6:  The demand for a product is 4000 boxes per month.  The holding cost is 20 %/year and the fixed ordering cost is $600 per order.  The company is currently using EOQ policy.  The supplier regularly charges $4 per box.    The supplier is offering a short-term trade promotion to lower price to $3.60 per box. 

	Current situation using EOQ	Using Trade promotion
EOQ   Optimal Q
Q we end up using
Annual Holding Cost
Annual Ordering Cost
Total Inventory Cost
# of orders/year
Annual Item cost
Grand Total Cost
Cycle Time
Avg. Flow Time
Cycle Inventory

How much is the forward buying?  _______________

Annual Savings by accepting the promotion? ___________

Problem 7:   DryIce, Inc., is a manufacturer of air conditioners anticipates nationwide demand in thousands of units for the next year to be 120 in the South, 110 in the Midwest, 70 in the East, and 90 in the West. The product is delivered to the customers from a regional Distribution Center (DC) whose coordinates are shown in the data below.  DryIce has selected four potential plant sites—A, B, C and D. Plant opened in any city would have a capacity of 300 thousand units per year. For each potential location, the annual fixed costs for the plants, coordinates, the variable costs per unit, and the shipping costs to each of the four DC are shown in the table below. (Hint: Be careful of units of costs)

Plant	Shipping Costs to DC in Regions ($/unit)				VC	Fixed cost	Coordinates
Locations	East	South	Midwest	West	/unit	thousands		X, Y
New York	7	9	10	11	$200	$800/yr		700,700
Chicago	9	8	5	10	$200	$700/yr		500,800
Atlanta	10	7	4	9	$180	$500/yr		600,400
San Diego	9	6	8	5	$220	$700/yr		300,300
Coordinates	800,700	400,500	400,800	200,400

1. Where should the plant be opened and at what capacity each should be operated assuming that we ship directly from each open plant various DCs?

• Specify the shipping schedule for part a) and the summary of costs:

Plant	Regions				Remaining
Locations	East	South	Midwest	West	Capacity
New York
Chicago
Atlanta
San Diego
Demand Met

Total Annual Shipping Cost :   _______________________________________

Total Annual Variable Cost: _________________________________________

Total annual Fixed Cost:     ___________________________________

Total Annual Cost: ________________________________________

• The company is thinking about building a hub where items could be shipped in bulk from the operating plants and the hub and then to the DCs in each region.  The shipping costs from any plant to hub would $ .01/unit/mile and from hub to any DC would be $.015/unit/mile.  What would best hub location and does it make economic sense to build the hub? Why?

Problem 8:

1. A medical facility typically serves an average of 20 patients per hour.   Several random observations show that on an average, there are about 14 patients in the facility at any given time.  On an average, how much time each patient spends within the facility?

• A company wants to decide between two leasing options for warehouse for the next 3 years.  Option A will require a deposit of $70,000 (refundable after the lease period) and a payment of $60,000 to be paid at the beginning of each month for the next 36 months.  Option B has three annual payments of $700,000 each: first today or beginning of year 1, next at the beginning of year 2, and the last payment at the beginning of year 3. Use an interest rate of 10% per year.  Find the present value of the total cost of each option and select the better option.