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 20 per week Order cost $ 207.00 Lead time 3 week(s) Annual holding cost (%) 24 % of item cost Service probability 99 % Annual demand 27,400 Average demand 548 per week a. Determine the order quantity and reorder point.

Order quantity = 478units

Reorder point = 420 per week

Explanation:

Given

Item cost =$8

Standard deviation of weekly demand = 20 per week

Order cost(C) = $207

Lead time = 3 weeks

Annual holding cost (H) = 24% of item cost

Service probability = 99%

Annual demand(D) = 27,400

Average demand = 548 per week

Order quantity = sqrt[(2 × D × C) ÷ H]

Order quantity = sqrt[(2 × 27400 × 207) ÷ (0.24 × 207)]

sqrt[ 11343600 ÷ 49.68]

= 477.84

Order quantity = 478 units

Reorder Point = Lead time × daily usage

21 × 20 = 420

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