Problem 13-6
A produce distributor uses 710 packing crates a month, which it purchases at a cost of $10 each. The manager has assigned an annual carrying cost of 35 % of the purchase price per create. Ordering costs are $28. Currently the manager orders once a month.
How much could the firm save annually in ordering and carrying costs by using the EOQ? (Round intermediate calculations and final answer to 2 decimal places. Omit the “$” sign in your response.)
| Savings | $ 286.25 per year |
Explanation:
| u = 710/month, so D = 12[710] = 8,520 crates/yr. |
| H = .35P = .35($10) = $3.50/crate per yr. |
| S = $28 |
| TC = | Q | H + | D | S |
| 2 | Q |
| Present TC: | 710 | (3.50) + | 8,520 | (28) = $1,578.50 |
| 2 | 710 |
| TC at EOQ: | 369.22 | (3.50) + | 8,520 | (28) = $1,292.25. |
| 2 | 369.22 |
| Savings approx. $286.25 per year. |
Problem 13-20
Given this information:
Lead-time demand = 640 pounds
Standard deviation of lead time demand = 40 points
Acceptable stockout risk during lead time = 4 percent
- What amount of safety stock is appropriate? (Round your answer to the nearest whole number.)
| Safety stock | 70 units |
Explanation:
ss = zσdLT = 1.75 (40 lbs.) = 70 lbs.
- When should this item be recorded? (Round your answer to the nearest whole number.)
| ROP | 710 units |
Explanation:
| ROP = Average demand during lead time + safety stock |
| ROP = 640 + 70 = 710 lbs. |
- What risk of stockout would result from a decision not to have any safety stock? (Omit the “%” sign in your response.)
| Stockout risk | 50 % |
Explanation:
With no safety stock risk is 50%.
Problem 13-22
The injection-molding department of a company uses an average of 30 gallons of special lubricant a day. The supply of the lubricant is replenished when the amount on hand is 170 gallons. It takes four days for an order to be delivered. Safety stock is 45 gallons, which provides a stockout risk of 9 percent. What amount of safety stock would provide a stockout risk of 3 percent? Assume normality. (Round intermediate calculations and final answer to 2 decimal places.)
| Safety stock | 63.00 gallons |
Explanation:
| d = 30 gal./day |
| ROP = 170 gal. |
| LT = 4 days |
| ss = zσdLT = 45 |
| ss = 45 gal. |
| Risk = 9% z = 1.34 Solving, σdLT = ss / z = 45 / 1.34 = 33.58 |
| 3 % → z = 1.88 × 33.58 = 63.13 gal. |
Problem 13-26
A small copy center uses five 500-sheet boxes of copy paper a week. Experience suggests that usage can be well approximated by a normal distribution with a mean of five boxes per week and a standard deviation of one-half box per week. One weeks are required to fill an order for letterhead stationery. Ordering cost is $3, and annual holding cost is 25 cents per box.
- Determine the economic order quantity, assuming a 52-week year. (Round your answer to the nearest whole number.)
| EOQ | 79 boxes |
- If the copy center reorders when the supply on hand is 6 boxes, compute the risk of a stockout (Round “z” value to 2 decimal places and final answer to 4 decimal places.)
| Risk | .0228 |
- If a fixed interval of seven weeks is used for ordering instead of an ROP, how many boxes should be ordered if there are currently 35 boxes on hand, and an acceptable stockout risk for the order cycle is .0023? (Round “z” value to 2 decimal places and final answer to the nearest whole number.)
| Q0 | 35 |