Given the following information, formulate an inventory management system. The i

Question

Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year Item cost Order cost Annual holding cost (%) Annual demand Average demand $ 7.00 $ 261.00 34 27,800 Standard deviation of weekly demand Lead time Service probability 20 per week 3 weeks 99% % of item cost 556 per week a. Determine the order quantity and reorder point. (Use Excel's NORMSINV) function to find the correct critical value for the given a-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.) 2469.27 units Optimal order quantity Reorder point units b. Determine the annual holding and order costs. (Round your answers to 2 decimal places.) 2938.43 Holding cost Ordering cost 2938.44 c. Assume a price break of $55 per order was offered for purchase quantities of 2,100 or more units per order. If you took advantage of this price break, how much would you save annually? (Round your answer to 2 decimal places.) Annual savings

Explanation / Answer

Given are :

Average weekly demand = m = 556 per week

Standard deviation of weekly demand = Sd = 20 per week

Lead Time = L = 3 weeks

Service probability = 99% ( i.e. 0.99)

Hence, Standard deviation of demand during lead time

= Standard deviation of weekly demand x Square root ( Lead time )

= 20 x Square root ( 3 )

= 20 x 1.732

=34.64

Corresponding Z value for service probability of 0.99 = NORMSINV ( 0.99) = 2.3263

Therefore ,

Safety stock

= Z value x Standard deviation of demand during lead time

= 2.3263 x 34.64

= 80.583 ( 81 rounding to nearest whole number )

Therefore , Safety stock = 81 units

Reorder point will be calculated as :

Reorder point = Average weekly demand x Lead time ( weeks ) + Safety stock

                            = 556 x 3 + 81

                             = 1668 + 81

                               = 1749

REORDER POINT = 1749 UNITS

Optimal order quantity = 2469.27 units

Annual demand = 27800

Therefore , number of orders in a year = 27800 / 2469.27 = 11.258

Since price break per order is applicable for order quantity > 2100, this price break is available for optimal order quantity of 2469.27

Given, Price break per order   = $ 55

Therefore , total annual savings

= Price break per order x Number of orders

= $55 x 11.258

= $619.19

TOTAL ANNUAL SAVINGS = $619.19

REORDER POINT = 1749 UNITS

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