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| Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year. |
| Item cost | $ | 8.00 | Standard deviation of weekly demand | 25 | per week | |
| Order cost | $ | 178.00 | Lead time | 4 | weeks | |
| Annual holding cost (%) | 29 | % of item cost | Service probability | 98 | % | |
| Annual demand | 28,100 | |||||
| Average demand | 562 | per week | ||||
| a. | Determine the order quantity and reorder point. (Use Excel’s NORMSINV( ) function to find your z-value and then round that z-value to 2 decimal places. Do not round any other intermediate calculations. Round your final answers to the nearest whole number.) |
| Optimal order quantity | units |
| Reorder point | units |
| b. | Determine the annual holding and order costs. (Do not round any intermediate calculations. Round your final answers to 2 decimal places.) |
| Holding cost | $ |
| Ordering cost | $ |
| c. | Assume a price break of $50 per order was offered for purchase quantities of 2,100 units per order. If you took advantage of this price break, how much would you save annually? (Do not round any intermediate calculations (including number of setups per year). Round your final answer to 2 decimal places.) |
Expert Answer
Order cost = Co = $178
Annual holding cost per item = Ch = 29% of $8 = $2.32
Basis above, optimum order quantity
EOQ = Square root ( 2 x Co x D / Ch)
= Square root ( 2 x 178 x 28100/ 2.32)
= 2076.51 ( 2076 rounded to nearest whole number)
Standard deviation of weekly demand = d = 25 / week
Lead time = L = 4 weeks
Therefore, standard deviation of demand during lead time
= Standard deviation of weekly demand x Square root ( Lead time )
= 25 x square root ( 4)
= 25 x 2
= 50
Corresponding value of Z for 98% service probability ( i.e. 0.98 probability of no stock out)
= NORMSINV ( 0.98) = 2.053
Therefore safety stock
= Z value x Standard deviation of demand during lead time
= 2.053 x 50
= 102.65 ( 103 rounding to nearest whole number)
Thus safety stock = 103
Hence,
Reorder point
= Average weekly demand x Lead time ( weeks ) + safety stock
= 562 x 4 + 103
= 2248 + 103
= 2351
| OPTIMAL ORDER QUANTITY = 2076 UNITS |
| REORDER POINT = 2351 UNITS |
Annual holding cost , $
= Annual holding cost per item x Average inventory
= Annual holding cost x Optimal Order Quantity / 2
= 2.32 x 2076/2
= 2408.16
Annual ordering cost , $
= Ordering cost x Number of orders per year
= Ordering cost x Annual demand / Optimal order quantity
= 178 x 28100/2076
= 2409.34
| HOLDING COST = $2408.16 |
| ORDERING COST = $2409.34 |
| Cost item | Purchase quantity = EOQ = 2076 PER ORDER | Purchase quantity = 2100 per order |
| Annual Ordering cost, $ | 2409.34 | $128/order x number of orders = $128 x Annual demand/210 = $128 x 28100/2100 =1712.16 |
| Annual inventory holding cost , $ | 2408.16 | Annual holding cost x order quantity/2 = 2.32 x 2100/2 = 2436 |
| Total: | 2409.34 + 2408.36 = 4817.70 | 1712.16 + 2436 = $4148.16 |
Therefore, annual saving by taking advantage of this price break
= $ 4817.70 – $4148.16
= $669.54
| ANNUAL SAVINGS = $669.54 |
