Isye 3104B Midterm Exam Solution

ISyE 3104B Midterm Exam Solution

Fall 2003

1. (30 points) Answer the 2 of the following 3 questions.

a)Snap-in brackets are used on an assembly floor at the fairly steady rate of 200 per year. The brackets cost the company $5 each. It costs the company $400 to initiate an order, and holding costs are based on an annual interest rate of 15 percent. Determine the optimal number of brackets for the company to purchase in each order. Also determine the optimal average total cost per year for the optimal plan. (15 points)

Solution:

b)Suppose that the estimated use is 200 per year, but that it turns out to actually be 220 per year. What percentage increase in cost was caused by using the order quantity based on the bad estimate (200 per year) rather than the correct demand amount (220 per year)? (15 points)

Solution:

c)Given the data below for two products (with a carrying charge of 0.1 $/$/yr), and assuming that a delivery is possible every day (assume 365 days per year), what would the order quantities for each product by using the powers-of-two policy?

(15 points)

Solution:

2. (30 points) Answer 2 of the following 3 questions.

a)A manufacturer uses large quantities of a purchased part in his assembly operations. He wants to use a constant purchase lot size, and he specifies that no shortages be planned. The following data are relevant to the problem of determining the optimal lot size:

-Annual requirements – 300,000 units, uniformly required over the year.

-Manufacturer’s fixed cost of placing an order – $80.

-Annual cost of interest, insurance, and taxes on average inventory investment

= 20 percent of the value of average inventory.

-Cost of storage – 10 cents per month, based on average quantity stored.

-Vendor’s price schedule – a fixed charge of $20 per order, plus a charge per

unit determined according to the following schedule:

Find the optimal lot size and optimal average total cost to this problem.

(15 points)

Solution:

Compare G(6547), G(10000),

b)Suppose the price schedule of question (a) had been changed to the incremental discount type instead of all units discount. Fine the optimal lot size and optimal average total cost to the problem. (15 points)

Solution:

c)A small manufacturing company needs three main raw materials, A, B and C. They forecast the demand in the next year to be 250, 375 and 500 for each material type respectively. The unit costs of these three materials are $20, $30 and $400 respectively. It costs $10, $10, and $100 respectively to place orders for each raw material. The company does not want to invest more than $11,250 on inventory for these three materials combined at any point in time. Holding cost is based on a 10 percent annual interest rate for each material. What lot sizes do you recommend for each raw material type? (15 points)

Solution:

3. (20 points) A co-op student is trying to use linear programming to solve a three month aggregate planning problem for your company to determine the number of workers to hire each month (Ht), the number of workers to fire each month (Ft), and the amount of inventory to be held each month (It). The cost of hiring a worker is $400, the cost of firing a worker is $750, and the cost of carrying one case of inventory in warehouse A for one month is $15. The capacity of warehouse A is 3,000 cases. The amount produced in month t is (Pt) and the number of workers working in month t is (Wt). The starting inventory is 300 cases, the initial workforce is 200 workers, and the ending inventory must be at least 500 cases. Demand for the first month is predicted to be 8,640 cases, for the second month 4,380 cases, and for the third month 6,750 cases. Each worker can produce approximately 50 cases per month. There is no subcontracting, overtime, or idle time allowed.

a)If the cost of backordering one case of inventory for one month is $20, can you help this co-op develop the LP model for this problem? The objective is to minimize hiring, firing, inventory, and backordering costs. (Please define new decision variables needed and write the LP problem.) (8 points)

Solution:

b)If backorder is not allowed and there is warehouse B with the capacity of 2,000 cases and the carrying cost of $16 per case per month, can you help this co-op develop the LP model for this problem? (we can only use warehouse B when warehouse A is full.) (8 points)

Solution:

c)If backorder is not allowed and there is warehouse B with the capacity of 2,000 cases and the carrying cost of $14 per case per month, can you use the same model structure in b to solve this problem? (we can only use warehouse B when warehouse A is full.) Explain you reasons. (4 points)

Solution:

No, you can’t use the previous LP model because the cost function is not convex any more. In another word, the previous LP will give the solution that fill warehouse B before warehouse A.

4. (20 points) A company buys parts from supplier for $12 a piece. They paint each of the parts (at a cost of $5 per part) before placing it in finished goods inventory. The rate at which they can paint is 100 parts per week. The average demand they face is 75 parts per week for finished goods. Every time they order from their supplier, the ordering cost of $100 is charged. Every time they start painting one batch of parts, the setup cost of $50 is charged. By using a carrying charge of 0.2$/$/yr, answer the following questions (assume 52 weeks per year and that back orders never happen):

(Writing the inventory graph for each type of product will help.)

a)What is the optimal order quantity that this company should order from their supplier per order? (The objective is to minimize the average total cost per year.)

(10 points)

Solution:

b)What is the optimal average total cost per year for this problem? (10 points)

Solution: