Question

Courtney Lee Manufacturing and Logistics (CLM&L) currently uses eight distribution centers for fulfilling orders received from customers throughout North America. Based on a recent customer service survey, CLM&L is considering whether to divide the customer base into only four distribution regions. Each region would have equal demand and costs (ordering and holding). A CLM&L hydraulic pump currently has a total annual holding and ordering cost of $95,000. How would the consolidation from eight to four distribution centers affect the annual holding and ordering costs for this pump? [Show calculations of the effect.]

Must use this formula:
X₂ = (X₁) √ (n₂/n₁₎

n₁ = Number of Existing Facilities

n₂ = Number of Future Facilities

X₁ = Total Inventory of Existing Facilities

X₂ = Total Inventory of Future Facilities

Answer 1

Solution:--

Hope its helps you..

X2 = (X1) √ (n2/n1)

n1 = Number of Existing Facilities

n2 = Number of Future Facilities

X1 = Total Inventory of Existing Facilities

X2 = Total Inventory of Future Facilities

-• Current scenario: 8 distribution centers

Let D be the annual demand of each distribution center.

S be the ordering cost per order and,

H be the holding cost per unit per year

EOQ, Q = sqrt(2SD/H) for each distribution center

Total annual cost = HQ/2+SD/Q , substituting the value of Q in this, we get,

Total annual cost = H*sqrt(2SD/H)/2+SD/sqrt(2SD/H) = sqrt(2SDH)

Total annual cost of 8 distribution centers = 8*sqrt(2SDH)

• New scenario: 4 distribution centers

Annual demand of each distribution center = 2D

Total annual cost of 4 distribution centers = 4*sqrt(2S(2D)H) = 8*sqrt(SDH)

Ratio of new total cost vs old total cost = 8*sqrt(SDH)/(8*sqrt(2SDH) = 1/Sqrt(2) = 0.7071

Therefore, after consolidation from eight to four DCs, annual holdiing and ordering cost this pump will change to = 95000*0.7071

= $ 67,175 ANSWER