EOQ Essay

Custom Student Mr. Teacher ENG 1001-04 8 March 2016

EOQ

Introduction

 

  1. Determine the order size for Company A in the scenario found in the attached “QAT1 Task 3 Spreadsheet” that would minimize total annual cost by using the economic order quantity model, showing all of your work.

Economic order quantity model is an in inventory related equation that helps in determining the optimum order quantity that a company should hold in its inventory given a cost of production, demand rate and other variables. This is always done to help in minimizing the variables inventory costs.  The equation is given by

EOQ =

Where:
A= Setup costs
Cp = Demand rate
P = Production cost
I = Interest rate (considered an opportunity cost, so the risk-free rate can be used)

EOQ =   (2 * 400,000 * 42)/ (3% * 500)

= 33600000/ 15

= Sr. 2240000

=1,497 computers

  1. Identify what Company A should do with the information determined in part A

The economic order quantity (EOQ) is the order quantity that minimizes total holding and ordering costs for the year. Even if all the assumptions don’t hold exactly, the EOQ gives us a good indication of whether or not current order quantities are reasonable(Steven, 2009). Therefore, the company uses EOQ in ensuring that the quantity being produced is optimal and is cost effective hence help the production and marketing departments to be effective in terms of production.

           
Order Quantity Holding Cost Order Cost Material Cost Shortage Cost Total Cost
Q hC(Q/2) (R/Q)S CR (B(Q-n)^2)/2Q TC
99.78 $748.33 $168,374.58 $200,000,000.00 $0.00 $200,169,122.91
199.56 $1,496.66 $84,187.29 $200,000,000.00 $0.00 $200,085,683.95
299.33 $2,244.99 $56,124.86 $200,000,000.00 $0.00 $200,058,369.86
399.11 $2,993.33 $42,093.65 $200,000,000.00 $0.00 $200,045,086.97
498.89 $3,741.66 $33,674.92 $200,000,000.00 $0.00 $200,037,416.57
598.67 $4,489.99 $28,062.43 $200,000,000.00 $0.00 $200,032,552.42
698.44 $5,238.32 $24,053.51 $200,000,000.00 $0.00 $200,029,291.83
798.22 $5,986.65 $21,046.82 $200,000,000.00 $0.00 $200,027,033.47
898.00 $6,734.98 $18,708.29 $200,000,000.00 $0.00 $200,025,443.27
997.78 $7,483.31 $16,837.46 $200,000,000.00 $0.00 $200,024,320.77
1097.55 $8,231.65 $15,306.78 $200,000,000.00 $0.00 $200,023,538.43
1197.33 $8,979.98 $14,031.22 $200,000,000.00 $0.00 $200,023,011.19
1297.11 $9,728.31 $12,951.89 $200,000,000.00 $0.00 $200,022,680.20
1396.89 $10,476.64 $12,026.76 $200,000,000.00 $0.00 $200,022,503.40
1496.66 $11,224.97 $11,224.97 $200,000,000.00 $0.00 $200,022,449.94
1596.44 $11,973.30 $10,523.41 $200,000,000.00 $0.00 $200,022,496.72
1696.22 $12,721.64 $9,904.39 $200,000,000.00 $0.00 $200,022,626.02
1796.00 $13,469.97 $9,354.14 $200,000,000.00 $0.00 $200,022,824.11
1895.77 $14,218.30 $8,861.82 $200,000,000.00 $0.00 $200,023,080.12
1995.55 $14,966.63 $8,418.73 $200,000,000.00 $0.00 $200,023,385.36
2095.33 $15,714.96 $8,017.84 $200,000,000.00 $0.00 $200,023,732.80
2195.11 $16,463.29 $7,653.39 $200,000,000.00 $0.00 $200,024,116.68
2294.88 $17,211.62 $7,320.63 $200,000,000.00 $0.00 $200,024,532.26
2394.66 $17,959.96 $7,015.61 $200,000,000.00 $0.00 $200,024,975.56
2494.44 $18,708.29 $6,734.98 $200,000,000.00 $0.00 $200,025,443.27
2594.22 $19,456.62 $6,475.95 $200,000,000.00 $0.00 $200,025,932.56
2693.99 $20,204.95 $6,236.10 $200,000,000.00 $0.00 $200,026,441.05
2793.77 $20,953.28 $6,013.38 $200,000,000.00 $0.00 $200,026,966.66
2893.55 $21,701.61 $5,806.02 $200,000,000.00 $0.00 $200,027,507.63
2993.33 $22,449.94 $5,612.49 $200,000,000.00 $0.00 $200,028,062.43
           
           
           
           
Q Line        
1497 0        
1497 200022449.9        

 

  1. Determine the lot size for Company B in the scenario found in the attached “QAT1 Task 3 Spreadsheet” that would minimize total annual cost by using the economic production lot size model, showing all of your work.

Economic order quantity model is an in inventory related equation that helps in determining the optimum order quantity that a company should hold in its inventory given a cost of production, demand rate and other variables. This is always done to help in minimizing the variables inventory costs.  The equation is given by

EOQ =

Where:
A= Setup costs
Cp = Demand rate
P = Production cost
I = Interest rate (considered an opportunity cost, so the risk-free rate can be used)

EOQ =   (2 * 5200,000 * 500)/ (4% * 250)

= 5,200,000,000/ 10

= Sr. 520,000,000

= 22804 computers

  1. Identify what Company B should do with the information determined in part B

The economic order quantity (EOQ) is the order quantity that minimizes total holding and ordering costs for the year. Even if all the assumptions don’t hold exactly, the EOQ gives us a good indication of whether or not current order quantities are reasonable (Steven, 2009). Therefore, the company uses EOQ in ensuring that the quantity being produced is optimal and is cost effective hence help the production and marketing departments to be effective in terms of production.

Order Quantity Holding Cost Order Cost Material Cost Shortage Cost Total Cost
Q hC(Q/2) (R/Q)S CR (B(Q-n)^2)/2Q TC
1520.23 $7,601.17 $1,710,263.14 $1,300,000,000.00 $0.00 $1,301,717,864.31
3040.47 $15,202.34 $855,131.57 $1,300,000,000.00 $0.00 $1,300,870,333.91
4560.70 $22,803.51 $570,087.71 $1,300,000,000.00 $0.00 $1,300,592,891.22
6080.94 $30,404.68 $427,565.78 $1,300,000,000.00 $0.00 $1,300,457,970.46
7601.17 $38,005.85 $342,052.63 $1,300,000,000.00 $0.00 $1,300,380,058.48
9121.40 $45,607.02 $285,043.86 $1,300,000,000.00 $0.00 $1,300,330,650.87
10641.64 $53,208.19 $244,323.31 $1,300,000,000.00 $0.00 $1,300,297,531.49
12161.87 $60,809.36 $213,782.89 $1,300,000,000.00 $0.00 $1,300,274,592.25
13682.11 $68,410.53 $190,029.24 $1,300,000,000.00 $0.00 $1,300,258,439.76
15202.34 $76,011.70 $171,026.31 $1,300,000,000.00 $0.00 $1,300,247,038.01
16722.57 $83,612.86 $155,478.47 $1,300,000,000.00 $0.00 $1,300,239,091.33
18242.81 $91,214.03 $142,521.93 $1,300,000,000.00 $0.00 $1,300,233,735.96
19763.04 $98,815.20 $131,558.70 $1,300,000,000.00 $0.00 $1,300,230,373.91
21283.27 $106,416.37 $122,161.65 $1,300,000,000.00 $0.00 $1,300,228,578.03
22803.51 $114,017.54 $114,017.54 $1,300,000,000.00 $0.00 $1,300,228,035.09
24323.74 $121,618.71 $106,891.45 $1,300,000,000.00 $0.00 $1,300,228,510.16
25843.98 $129,219.88 $100,603.71 $1,300,000,000.00 $0.00 $1,300,229,823.60
27364.21 $136,821.05 $95,014.62 $1,300,000,000.00 $0.00 $1,300,231,835.67
28884.44 $144,422.22 $90,013.85 $1,300,000,000.00 $0.00 $1,300,234,436.07
30404.68 $152,023.39 $85,513.16 $1,300,000,000.00 $0.00 $1,300,237,536.55
31924.91 $159,624.56 $81,441.10 $1,300,000,000.00 $0.00 $1,300,241,065.66
33445.15 $167,225.73 $77,739.23 $1,300,000,000.00 $0.00 $1,300,244,964.96
34965.38 $174,826.90 $74,359.27 $1,300,000,000.00 $0.00 $1,300,249,186.17
36485.61 $182,428.07 $71,260.96 $1,300,000,000.00 $0.00 $1,300,253,689.03
38005.85 $190,029.24 $68,410.53 $1,300,000,000.00 $0.00 $1,300,258,439.76
39526.08 $197,630.41 $65,779.35 $1,300,000,000.00 $0.00 $1,300,263,409.76
41046.32 $205,231.58 $63,343.08 $1,300,000,000.00 $0.00 $1,300,268,574.66
42566.55 $212,832.75 $61,080.83 $1,300,000,000.00 $0.00 $1,300,273,913.57
44086.78 $220,433.92 $58,974.59 $1,300,000,000.00 $0.00 $1,300,279,408.51
45607.02 $228,035.09 $57,008.77 $1,300,000,000.00 $0.00 $1,300,285,043.86
           
           
           
           
Q Line        
22804 0        
22804 1300228035        
           

 

Reference

Steven A. (2009) Management Science Applications in Project Management Project       Management LP Models in Scheduling, Integer Programming           www.eng.umd.edu/~sgabriel. uk

 

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