HW-cycle&safety-stock NM

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Capella University *

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640

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Finance

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Apr 3, 2024

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SEL ECT THE APP ROP RIA TE LAB EL FRO M THE "SE NSI TIVI TY" TAB ON THE HO ME TO OL BAR Homework Assignment Solution – Cycle & Safety Stock 1. Revisit the ImportHome.com case study. Assume that the costs of the GM soymilk maker and GM cooker are $35 per unit, and the annual inventory holding cost is 18% of the product cost. All shipping data (shipping quantity, cost per shipment, and lead time) and service level remain the same as the in-class example. Answer the following questions based on the demand data of these two products provided in the Excel file (round the mean and standard deviation of the demand to the nearest integers; assume that one year has 53 weeks in all calculations). (a) (10 points) For GM soymilk maker, calculate the annual shipping and inventory carrying costs under both full container and half container. Which is better: full container vs. half container? Solution: When we look at the data, the mean is 25 units while the standard deviation is 8 units. Below you will see a chart for full and half containers. Full Container Half Container Shipping quantity (units) 1400 700 Cost per shipment ($) 3300 2600 Lead time (weeks) 13 15 For full container: Annual shipping cost: 25 × 53 ÷ 1400 ×$ 3300 = $ 3123.21 Safety stock: s ¿ = z α σ τ = normsinv ( 0.95 ) × 8 × 13 = 47 Average on-hand inventory: s ¿ + Q 2 = 47 + 1400 2 = 747 Annual inventory cost: 747 × ( $ 35 × 0.18 ) = $ 4708.90 Total annual ops cost: $ 3123.21 + $ 4708.90 = $ 7832.11 For half container: Annual shipping cost: 25 × 53 ÷ 700 ×$ 2600 = $ 4921.43 Safety stock: s ¿ = z α σ τ = normsinv ( 0.95 ) × 8 × 15 = 51
SEL ECT THE APP ROP RIA TE LAB EL FRO M THE "SE NSI TIVI TY" TAB ON THE HO ME TO OL BAR Average on-hand inventory: s ¿ + Q 2 = 51 + 700 2 = 401 Annual inventory cost: 401 × ( $ 35 × 0.18 ) = $ 2526.07 Total annual ops cost: $ 4921.43 + $ 2526.07 = $ 7447.50 After reviewing the numbers we see that half containers are better overall. (b) (10 points) For GM cooker, calculate the annual shipping and inventory carrying costs under both full container and half container. Which is better: full container vs. half container? Solution: When we look at the data, the mean is 35 units and standard deviation is 10 units. For full container: Annual shipping cost: 3 5 × 53 ÷ 1400 ×$ 3300 = $ 4372.50 Safety stock: s ¿ = z α σ τ = normsinv ( 0.95 ) × 10 × 13 = 59 Average on-hand inventory: s ¿ + Q 2 = 59 + 1400 2 = 759 Annual inventory cost: 759 × ( $ 35 × 0.18 ) = $ 4783.63 Total annual ops cost: $ 4372.50 + $ 4783.63 = $ 9156.13 For half container: Annual shipping cost: 35 × 53 ÷ 700 ×$ 2600 = $ 6890.00 Safety stock: s ¿ = z α σ τ = normsinv ( 0.95 ) × 10 × 15 = 64 Average on-hand inventory: s ¿ + Q 2 = 64 + 700 2 = 414 Annual inventory cost: 414 × ( $ 35 × 0.18 ) = $ 2606.34 Total annual ops cost: $ 6890.00 + $ 2606.34 = $ 9496.34 After reviewing the data we see that the full container is a better option.
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