In: Operations Management
Assume that a production line operates such that the production lot size model of is applicable. Assume that D = 6,500 units per year, Co = $120, and Ch = $3 per unit per year.
a. | i. | 8,300 units per year |
ii. | 11,000 units per year | |
iii. | 34,500 units per year | |
iv. | 90,000 units per year |
If required, round your answers to the nearest whole number. |
i. | P = 8,300 | Q* = |
ii. | P = 11,000 | Q* = |
iii. | P = 34,500 | Q* = |
iv. | P = 90,000 | Q* = |
b. Compute the EOQ recommended lot size using equation | |
If required, round your answer to the nearest whole number. | |
Q* = |
Comparing the EOQ lot size to the production lot sizes in parts
i, ii, iii, and iv, what two
observations can you make about the relationship between the EOQ
model and the production lot size model?
Production Lot Size Q* is always (Greater or less) than the EOQ Q* with the same D, Co, and Ch
As the production rate P (Increases or decreases) , the recommended Q* decreases, but always remains (Greater or Less)
than the EOQ Q*.
Annual Demand | Days per year |
Daily Demand |
6500 | 365 | 17.808 |
Annual Production capacity | 8300 | 11000 | 34500 | 90000 | ||
Days per year | 365 | 365 | 365 | 365 | ||
Daily production rate, p | Given | 22.74 | 30.14 | 94.52 | 246.58 | |
Daily demand/usage rate, d | D/o | 17.808 | 17.808 | 17.808 | 17.808 | |
Annual demand, D= | demand per day*operation days per year | 6500 | 6500 | 6500 | 6500 | |
Setup or cost per order, S | Given | $120.00 | $120.00 | $120.00 | $120.00 | |
holding cost per year, H= | holding cost percent*item cost | $3.00 | $3.00 | $3.00 | $3.00 | |
Production order quantity, Q= | SQRT(2*S*D/(H*(1-d/p))) | 1548.48 | 1127.44 | 800.45 | 748.65 | |
Production order quantity, Q= | rounded-off | 1548 | 1127 | 800 | 749 | |
Answer a (i) | Answer a (ii) | Answer a (iii) | Answer a (iv) |
Answer b: (i)
Annual demand, D= | (demand per period)*(periods per year) | 6,500 | |
Order cost or setup cost, S | 120 | ||
holding cost per year, H= | (holding cost percent)*(item cost) | $3.00 | |
Order quantity, Q= | squareroot(2*S*D/H) | 721.110 | |
Order quantity, Q= | rounded-off | 721 units | Answer |
Comparing the EOQ lot size to the production lot sizes in parts i, ii, iii, and iv, what two observations can you make about the relationship between the EOQ model and the production lot size model?
Production Lot Size Q* is always Greater than the EOQ Q* with the same D, Co, and Ch
As the production rate P Increases , the recommended Q* decreases, but always remains Greater than the EOQ Q*.