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.
- 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.
- Find the following assuming that the company is operating in an optimal fashion:
Economic Order Quantity _________
Cycle Time __________
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:
- 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
- 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 | ||||
- 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:
- 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.
