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.

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.)

Determine the annual holding and order costs. (Do not round any intermediate calculations. Round your final answers to 2 decimal places.)

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.)

  Item cost $ 9.00   Standard deviation of weekly demand 30 per week   Order cost $ 230.00   Lead time 3 weeks   Annual holding cost (%) 34 % of item cost   Service probability 98 %   Annual demand 27,500   Average demand 550 per week

Explanation / Answer

  Item cost $ 9   Standard deviation of weekly demand 30 per week   Order cost, O $ 230   Lead time 3 weeks   Annual holding cost ,H % of item cost 34 $       3.06   Service probability 98 %   Annual demand, D 27,500 ( H = 0.34*9) z 2.05   Average demand,d per week 550 no of weeks/year 50 a. Determine the order quantity and reorder point.   Optimal order quantity = EOQ, Q= sqrt ( (2* D* O)/ H) Q 2033 units Reorder Point, R = (avg weekly demand*lead time in weeks)+z* std dev demand * sqrt( lead time) R 1757 units Optimal order quantity 2033 units   Reorder point 1757 units b. Determine the annual holding and order costs. Annual Ordering Cost =( D/Q)*O $                       3,110.83 Annual Holding Cost = (Q/2)*H $                       3,110.83   Holding cost $3,110.83   Ordering cost $3,110.83 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? Total Cost = Item cost + Holding cost + Ordering Cost in Case of Q = 2033 units (EOQ) the TC = $                   2,53,721.66 in case Q = 2100 units 2100 Number of orders = D/Q = 13.0952381 Savings = $                    654.761905 (=$50 * no of orders) Item Cost = $                   2,47,500.00 (= $9*D) Annual Holding Cost = $ 3,213.00 Annual ordering Cost = $ 3,011.9048 Total cost w/o savings = $ 2,53,724.90 Total Cost (Annual cost-Savings) = $ 2,53,070.14 Annual Savings = TC(Q=2033) - TC (Q=2100) Annual Savings $ 651.51

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