Exercise 13-6: AnyLogo
Inputs IBM AT&T HP Cisco
Anticipated demand 5,000 7,000 4,000 4,000
Standard deviation 2,000 2,500 2,000 2,200
Unit costs $15 $15 $15 $15
Sales price $50 $50 $50 $50
Disposal value $6 $6 $6 $6
Inventory holding costs $3 $3 $3 $3
Salvage value $3 $3 $3 $3
Cost of understocking $35 $35 $35 $35
Cost of overstocking $12 $12 $12 $12
Outputs IBM AT&T HP Cisco
Optimal cycle service level 0.7447 0.7447 0.7447 0.7447 Total
Optimal production lot size 6,316 8,645 5,316 5,447 25,723
Expected profits $144,796 $207,245 $109,796 $106,776 $568,612
Expected overstock 1,622 2,028 1,622 1,785 7,057
AnyLogo supplies firms with apparel containing their logo to be used for promotional purposes. AnyLogo has four major customers—
IBM, AT&T, HP, and Cisco. During the holiday season, the logos are adorned with a Christmas motif. Demand from each firm for apparel
with the Christmas motif is normally distributed, as shown in Table 13-7. AnyLogo currently produces all the apparel including the logo
embroidery in Sri Lanka in advance of the holiday season. Each unit costs $15 and is sold by AnyLogo for $50. Any leftover inventory at
the end of the holiday season is essentially worthless and cannot be repurposed for a different company. It is thus donated by AnyLogo
to charity. Holding the apparel in inventory adds another $3 to the cost per unit donated to inventory. However, the donation allows
AnyLogo to recover $6 per unit in tax savings. What production quantities do you recommend for AnyLogo? What is the expected profit
from the policy? On average, how much does AnyLogo expect to donate to charity each year?
Exercise 13-6: AnyLogo
Inputs IBM AT&T HP Cisco
Anticipated demand 5000 7000 4000 4000
Standard deviation 2000 2500 2000 2200
Unit costs 15 15 15 15
Sales price 50 50 50 50
Disposal value 6 6 6 6
Inventory holding costs 3 3 3 3
Salvage value =C21-C22 =D21-D22 =E21-E22 =F21-F22
Cost of understocking =C20-C19 =D20-D19 =E20-E19 =F20-F19
Cost of overstocking =C19-C25 =D19-D25 =E19-E25 =F19-F25
Outputs
Optimal cycle service level =C26/(C26+C27) =D26/(D26+D27) =E26/(E26+E27) =F26/(F26+F27)
Total
Optimal lot size =NORMINV(C30,C17,C18) =NORMINV(D30,D17,D18) =NORMINV(E30,E17,E18) =NORMINV(F30,F17,F18) =F31+E31+D31+C31
Expected profits
=(C20-C25)*C17*NORMDIST((C31-C17)/C18,0,1,1)-(C20-C25)*C18*NORMDIST((C31-C17)/C18,0,1,0)-C31*C27*NORMDIST(C31,C17,C18,1)+C31*C26*(1-NORMDIST(C31,C17,C18,1))
=(D20-D25)*D17*NORMDIST((D31-D17)/D18,0,1,1)-(D20-D25)*D18*NORMDIST((D31-D17)/D18,0,1,0)-D31*D27*NORMDIST(D31,D17,D18,1)+D31*D26*(1-NORMDIST(D31,D17,D18,1))
=(E20-E25)*E17*NORMDIST((E31-E17)/E18,0,1,1)-(E20-E25)*E18*NORMDIST((E31-E17)/E18,0,1,0)-E31*E27*NORMDIST(E31,E17,E18,1)+E31*E26*(1-NORMDIST(E31,E17,E18,1))
=(F20-F25)*F17*NORMDIST((F31-F17)/F18,0,1,1)-(F20-F25)*F18*NORMDIST((F31-F17)/F18,0,1,0)-F31*F27*NORMDIST(F31,F17,F18,1)+F31*F26*(1-NORMDIST(F31,F17,F18,1))
=F33+E33+D33+C33
Expected overstock
=(C31-C17)*NORMDIST((C31-C17)/C18,0,1,1)+C18*NORMDIST((C31-C17)/C18,0,1,0)
=(D31-D17)*NORMDIST((D31-D17)/D18,0,1,1)+D18*NORMDIST((D31-D17)/D18,0,1,0)
=(E31-E17)*NORMDIST((E31-E17)/E18,0,1,1)+E18*NORMDIST((E31-E17)/E18,0,1,0)
=(F31-F17)*NORMDIST((F31-F17)/F18,0,1,1)+F18*NORMDIST((F31-F17)/F18,0,1,0)
=F35+E35+D35+C35