库存管理第三章
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markzhuguojun@yahoo.com.cn 19
2. Worked example
If supplier will only deliver batches of 250 units, how does this affect costs?
UC=$40; HC=(0.18+0.01+0.02)*40+2+1.5+4=15.9 D=1000 units/year; RC=$100/order
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markzhuguojun@yahoo.com.cn 6
2.Three other variables (1) Order quantity (Q)
Fixed order size
(2) Cycle time (T)
Time btw two consecutive replenishment
TCo= UC*D+HC*Qo=30*6000+6*500
=$183,000
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markzhuguojun@yahoo.com.cn
15
4. Worked example
What is optimal batch size for item & associated costs? D=1250 units/year; UC=60%*300=$180 HC=0.2*180=$36/unit/year RC=1640+280=$1920 Qo= sqrt(2*RC*D/HC)=
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markzhuguojun@yahoo.com.cn 2
31 Defining economic order quantity
311 Background to the model
1. Wilson EOQ Model(Wilson Formula) The first reference to the work is by Harris(1915) Wilson(1934)independently duplicated the work and marketed the results
Chapter 3
Economic Order Quantity
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markzhuguojun@yahoo.com.cn 1
3 Economic Order Quantity
31 Defining economic order quantity 32 Adjusting EOQ 33 Uncertainty in demand & csots 34 Adding a finite lead time
Sqrt(2*1920*1250/36)=365 units
To=Qo/D=365/1250=0.29=15 wks
TCo= UC*D+HC*Qo=180*1250+36*365 =$238,140
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314 Doing calculations
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3. Model analysis
(1) This model is unrealistic based on these assumptions (2) All models are simplifications of reality and their aims to give useful results rather than be exact representations of actual circumstances (3) This is a basic model that we can extend in many ways
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markzhuguojun@yahoo.com.cn 20
3. Worked example
(a)What size of delivery should Jessica use and what are resulting costs? (b)How much shoud she order if flour has a shelf-life of 2 weeks? (c)How much should she order if bank imposes a maximum order value of $1500? (d)If mill only delivers on Mondays, how much Jessica order and how often?
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(b) Q=2*6*10=120 VC/VCo=1/2[Qo/Q+Q/Qo] VC=315/2[140/120+120/140]=S318.75/year (c) VC/VCo=1/2[Qo/Q+Q/Qo] Q=1500/12=125 sacks VC=315/2[140/125+125/140]=S317.03/year (d) Order per 2 wks, Q=2*6*10=120, so, VC2wks=$318.75/year(b) Q3wks=3*6*10=180 sacks VC3wks=315/2[140/180+180/140]=$325/year It’s clearly cheaper for Jessica to order every 2 weeks
wenku.baidu.com
TC=UC*D + RC*D/Q + HC*Q/2
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markzhuguojun@yahoo.com.cn 10
(3) Find mini cost per unit time TC=UC*D + RC*D/Q + HC*Q/2 d(TC)/dQ=-RC*D/Q2 + HC/2=0
Qo= 2*RC*D/HC
UC*Q+RC*1+HC*T*Q/2
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markzhuguojun@yahoo.com.cn 9
(2) Divides this cost by cycle length T
Total cost per unit time: TC TC=UC*Q/T + RC/T + HC*Q/2 Due to Q=D*T
D=6000 units/year; UC=$30 /unit RC=$125/order; HC=$6/unit/year Qo= sqrt(2*RC*D/HC)=
Sqrt(2*125*6000/6)=500 units
To=Qo/D=500/6000=1/12=1 month
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2.Identificartion of model
(1)Find total cost for a cycle Q=D*T total cost per cycle= unit cost’+reorder cost’+holding cost’=
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(4) Find optimal length of stock cycle
Optimal cycle length To=Qo/D= (2*RC)/(D*HC)
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(5) Optimal VC per unit time
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32 Adjusting EOQ
321 Moving away from EOQ 1. How much costs would rise if we do not use EOQ ? We can place orders for up to 37% more than Qo, or down to 27% less than Qo,and still keep variable cost within 5% of optimal
TC=UC*D + RC*D/Q + HC*Q/2
Unit cost component is fixed, so we can concentrate on the last two terms which form the variable cost D is a constant, Q is variable VC= RC*D/Q + HC*Q/2 Qo=sqrt(2*RC*D/HC) VCo=RC*D/Qo + HC*Qo/2 =HC*Qo
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(6) Optimal total cost per unit time
TCo=UC*D+VCo =UC*D+HC*Qo
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3. Worked example
What is the best ordering policy for the item?
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UC=$12; RC=$7.5/order HC=(12+6.75)%*12=$2.25/sack/year D=49*6*10=2940 sacks/year
(a) Qo= sqrt(2*RC*D/HC)= Sqrt(2*7.5*2940/2.25)=140 units VCo=HC*Qo=2.25*140=$315/year
(3) Demand (D)
Number of units to be supplied from stock in a given time period
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313 Derivation of EOQ
1. Procedure of derivation (1) Find total cost of one stock cycle (2) Divide this total cost by cycle length to get a cost per unit time (3) Minimize this cost per unit time
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312 Variables used in the analysis
1. 4 costs concerned (1) Unit cost (2) Reorder cost (3) Holding cost (4) Shortage cost
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markzhuguojun@yahoo.com.cn 3
2. Assumptions of model
(1)Demand is known exactly, is continuous and is constant over time (2)All costs are known exactly and do not vary (3)No shortages are allowed (4)Lead time is zero (a delivery is made as soon as the order is placed) (5)An single item, an single order (6)Purchase price and reorder costs do not vary with quantity ordered (7)A single delivery is made for each order (8)All of an order arrives in stock at the same time and can be used immediately
Qo= sqrt(2*RC*D/HC)= Sqrt(2*100*1000/15.9)=112.15 units VCo=HC*Qo=15.9*112.15=$1783/year
If Q=250 (EPQ) VC/VCo=1/2[Qo/Q+Q/Qo] VC=1783/2[112.15/250+250/112.15]=S2388/year VC/VCo==2388/1783=134%
markzhuguojun@yahoo.com.cn 19
2. Worked example
If supplier will only deliver batches of 250 units, how does this affect costs?
UC=$40; HC=(0.18+0.01+0.02)*40+2+1.5+4=15.9 D=1000 units/year; RC=$100/order
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markzhuguojun@yahoo.com.cn 6
2.Three other variables (1) Order quantity (Q)
Fixed order size
(2) Cycle time (T)
Time btw two consecutive replenishment
TCo= UC*D+HC*Qo=30*6000+6*500
=$183,000
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markzhuguojun@yahoo.com.cn
15
4. Worked example
What is optimal batch size for item & associated costs? D=1250 units/year; UC=60%*300=$180 HC=0.2*180=$36/unit/year RC=1640+280=$1920 Qo= sqrt(2*RC*D/HC)=
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markzhuguojun@yahoo.com.cn 2
31 Defining economic order quantity
311 Background to the model
1. Wilson EOQ Model(Wilson Formula) The first reference to the work is by Harris(1915) Wilson(1934)independently duplicated the work and marketed the results
Chapter 3
Economic Order Quantity
im-3
markzhuguojun@yahoo.com.cn 1
3 Economic Order Quantity
31 Defining economic order quantity 32 Adjusting EOQ 33 Uncertainty in demand & csots 34 Adding a finite lead time
Sqrt(2*1920*1250/36)=365 units
To=Qo/D=365/1250=0.29=15 wks
TCo= UC*D+HC*Qo=180*1250+36*365 =$238,140
im-3
markzhuguojun@yahoo.com.cn 16
314 Doing calculations
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markzhuguojun@yahoo.com.cn 4
3. Model analysis
(1) This model is unrealistic based on these assumptions (2) All models are simplifications of reality and their aims to give useful results rather than be exact representations of actual circumstances (3) This is a basic model that we can extend in many ways
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markzhuguojun@yahoo.com.cn 20
3. Worked example
(a)What size of delivery should Jessica use and what are resulting costs? (b)How much shoud she order if flour has a shelf-life of 2 weeks? (c)How much should she order if bank imposes a maximum order value of $1500? (d)If mill only delivers on Mondays, how much Jessica order and how often?
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markzhuguojun@yahoo.com.cn 22
(b) Q=2*6*10=120 VC/VCo=1/2[Qo/Q+Q/Qo] VC=315/2[140/120+120/140]=S318.75/year (c) VC/VCo=1/2[Qo/Q+Q/Qo] Q=1500/12=125 sacks VC=315/2[140/125+125/140]=S317.03/year (d) Order per 2 wks, Q=2*6*10=120, so, VC2wks=$318.75/year(b) Q3wks=3*6*10=180 sacks VC3wks=315/2[140/180+180/140]=$325/year It’s clearly cheaper for Jessica to order every 2 weeks
wenku.baidu.com
TC=UC*D + RC*D/Q + HC*Q/2
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markzhuguojun@yahoo.com.cn 10
(3) Find mini cost per unit time TC=UC*D + RC*D/Q + HC*Q/2 d(TC)/dQ=-RC*D/Q2 + HC/2=0
Qo= 2*RC*D/HC
UC*Q+RC*1+HC*T*Q/2
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markzhuguojun@yahoo.com.cn 9
(2) Divides this cost by cycle length T
Total cost per unit time: TC TC=UC*Q/T + RC/T + HC*Q/2 Due to Q=D*T
D=6000 units/year; UC=$30 /unit RC=$125/order; HC=$6/unit/year Qo= sqrt(2*RC*D/HC)=
Sqrt(2*125*6000/6)=500 units
To=Qo/D=500/6000=1/12=1 month
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markzhuguojun@yahoo.com.cn 8
2.Identificartion of model
(1)Find total cost for a cycle Q=D*T total cost per cycle= unit cost’+reorder cost’+holding cost’=
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markzhuguojun@yahoo.com.cn 11
(4) Find optimal length of stock cycle
Optimal cycle length To=Qo/D= (2*RC)/(D*HC)
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(5) Optimal VC per unit time
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32 Adjusting EOQ
321 Moving away from EOQ 1. How much costs would rise if we do not use EOQ ? We can place orders for up to 37% more than Qo, or down to 27% less than Qo,and still keep variable cost within 5% of optimal
TC=UC*D + RC*D/Q + HC*Q/2
Unit cost component is fixed, so we can concentrate on the last two terms which form the variable cost D is a constant, Q is variable VC= RC*D/Q + HC*Q/2 Qo=sqrt(2*RC*D/HC) VCo=RC*D/Qo + HC*Qo/2 =HC*Qo
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(6) Optimal total cost per unit time
TCo=UC*D+VCo =UC*D+HC*Qo
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markzhuguojun@yahoo.com.cn 14
3. Worked example
What is the best ordering policy for the item?
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markzhuguojun@yahoo.com.cn 21
UC=$12; RC=$7.5/order HC=(12+6.75)%*12=$2.25/sack/year D=49*6*10=2940 sacks/year
(a) Qo= sqrt(2*RC*D/HC)= Sqrt(2*7.5*2940/2.25)=140 units VCo=HC*Qo=2.25*140=$315/year
(3) Demand (D)
Number of units to be supplied from stock in a given time period
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markzhuguojun@yahoo.com.cn 7
313 Derivation of EOQ
1. Procedure of derivation (1) Find total cost of one stock cycle (2) Divide this total cost by cycle length to get a cost per unit time (3) Minimize this cost per unit time
im-3
markzhuguojun@yahoo.com.cn 5
312 Variables used in the analysis
1. 4 costs concerned (1) Unit cost (2) Reorder cost (3) Holding cost (4) Shortage cost
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markzhuguojun@yahoo.com.cn 3
2. Assumptions of model
(1)Demand is known exactly, is continuous and is constant over time (2)All costs are known exactly and do not vary (3)No shortages are allowed (4)Lead time is zero (a delivery is made as soon as the order is placed) (5)An single item, an single order (6)Purchase price and reorder costs do not vary with quantity ordered (7)A single delivery is made for each order (8)All of an order arrives in stock at the same time and can be used immediately
Qo= sqrt(2*RC*D/HC)= Sqrt(2*100*1000/15.9)=112.15 units VCo=HC*Qo=15.9*112.15=$1783/year
If Q=250 (EPQ) VC/VCo=1/2[Qo/Q+Q/Qo] VC=1783/2[112.15/250+250/112.15]=S2388/year VC/VCo==2388/1783=134%