Discuss the below:
Q1. Company X can purchase a certain component from either Supplier A or Supplier B. Supplier A offers an incremental quantity discount, while Supplier B offers an all-unit quantity discount.
To be specific, Supplier A charges $100 per unit for the first 1,000 units in an order, $90 per unit for the next 1,000 units, and $85 per unit for the rest units in the order. Supplier B charges $95 per unit for orders of no more than 1,500 units and $90 per unit for any bigger orders.
(a) Suppose Company X decides to purchase 2,500 units from Supplier A. What is the average unit cost of the order? Please provide at least one step of calculation and the correct answer for full credit.
(b) For an order of 2,500 units, which supplier offers a lower total cost? Please provide the reason and the correct answer for full credit.
Q2. Given the following information, compute the optimal order quantities as required.
Annual Demand 100,000 units
Order Cost $50 per order
Inventory Holding 20% of unit cost
(a) Suppose the unit cost of the product is $200. What is the Economic Order Quantity of the inventory control system? (You can either round up or round down.) Please include the formula, at least one step of calculation, and the correct answer for full credit.
(b) What is the annual total cost if the Economic Order Quantity is ordered each time? Please include the formula, at least one step of calculation, and the correct answer for full credit.
(c) Suppose the wholesaler of the product offers an all-unit quantity discount that charges $200 per unit for orders of no more than 400 units and $180 per unit for any bigger orders. What is the optimal order quantity in this case? Please give the EOQs for each discount price, the optimal order quantities for each discount price, and the correct answer for full credit. (12 points)
Q3. An assembly line is to operate 8 hours a day with a desired daily output of 600 units. The following table contains information on this product's task times and sequential relationships:
Task Task Time (seconds) Immediate Predecessor
A 30 -----
B 15 -----
C 20 A
D 25 B
E 10 C, D
F 30 D
G 25 E, F
Answer the following questions based on the information given.
(a) Specify the sequential relationships among the tasks using a diagram. An example can be found on the lecture slides for Week 5. Please include all the tasks, arrows, and task times in the diagram for full credit.
(b) What is the required workstation cycle time in this case? Please include the formula, at least one step of calculation, and the correct answer for full credit.
(c) What is the theoretical minimum number of workstations required in this case? Please include the formula, at least one step of calculation, and the correct answer for full credit.
(d) Suppose the application of some primary and secondary assignment rules suggests the following task assignment sequence: A, B, D, C, E, F, G. That is, Task A will be the first task to assign to a workstation, followed by Task B, Task D, Task C, and all the way to Task G. Then which tasks are assigned to each workstation? Label the workstations as Workstation 1, Workstation 2, and so on. Please list the workstation assignment of each task for full credit.
(e) What is the efficiency of your design? Please include the formula, at least one step of calculation, and the correct answer for full credit.
(f) Is the efficiency satisfactory and why? This is an open question.
Q4. Suppose a shipment of 80,000 lbs is originated from point I. An additional 20,000 lbs is to be combined with it at point J and both shipments are to move on to point K. The transportation rate from point I to point J is $0.7/cwt. The transportation rate from point J to point K is $0.3/cwt. The transportation rate from point I to point K is $0.8/cwt. The stop-off charge is $20. Set 1 cwt = 100 lbs.
a) How much is the total transportation cost when transit privilege is not used? Please provide at least one step of calculation and the correct cost for full credit.
b) How much is the total transportation cost when transit privilege is used? Please provide at least one step of calculation and the correct cost for full credit.