Exercise 13-7
Analysis when embroidery is in Sri Lanka
Inputs IBM AT&T HP Cisco Aggregation
Anticipated demand 5,000 7,000 4,000 4,000 20,000
Standard deviation 2,000 2,500 2,000 2,200 4,369
Unit costs $15 $15 $15 $15 $18
Sales price $50 $50 $50 $50 $50
Disposal value $6 $6 $6 $6 $18
Inventory holding costs $3 $3 $3 $3 $4
Salvage value $3 $3 $3 $3 $14
Cost of understocking $35 $35 $35 $35 $32
Cost of overstocking $12 $12 $12 $12 $4
Outputs
Optimal cycle service level 0.7447 0.7447 0.7447 0.7447 Total 0.8889
Optimal production lot size 6,316 8,645 5,316 5,447 25,723 25,333
Expected profits $144,796 $207,245 $109,796 $106,776 $568,612 $610,210
Expected overstock 1,622 2,028 1,622 1,785 7,057 5,568
Analysis with
Postponement
The manager at AnyLogo is considering the purchase of high-speed embroidery machines that will allow it to
embroider on demand. In this case, the apparel will be made in Sri Lanka without any logo; the logo embroidery will
be postponed and will be done in the United States on demand. This will raise the cost per unit to $18. However,
AnyLogo will not have any holiday or company-specific apparel to be disposed of at the end of the season. The
apparel without logos can be sold for $18 a unit to retailers. The cost of holding inventory and shipping adds $4 to
the cost of any apparel left over after the holiday season. With all other information as in Exercise 6, do you
recommend that the manager at AnyLogo implement postponement? What will be the impact of postponement on
profits and inventories?
Exercise 13-7
Solution to problem 6
Inputs IBM AT&T HP Cisco Aggreagation
Anticipated demand 5000 7000 4000 4000 20000
Standard deviation 2000 2500 2000 2200 4369.2104549907
Unit costs 15 15 15 15 18
Sales price 50 50 50 50 50
Disposal value 6 6 6 6 18
Inventory holding costs 3 3 3 3 4
Salvage value =C21-C22 =E21-E22 =G21-G22 =I21-I22 =O21-O22
Cost of understocking =C20-C19 =E20-E19 =G20-G19 =I20-I19 =O20-O19
Cost of overstocking =C19-C25 =E19-E25 =G19-G25 =I19-I25 =O19-O25
Outputs
Optimal cycle service level =C26/(C26+C27) =E26/(E26+E27) =G26/(G26+G27) =I26/(I26+I27) Total =O26/(O26+O27)
Optimal production size =NORMINV(C30,C17,C18) =NORMINV(E30,E17,E18)
=NORMINV(G30,G17,G18)
=NORMINV(I30,I17,I18) =I31+G31+E31+C31 =NORMINV(O30,O17,O18)
Expected profits
=(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))
=(G20-G25)*G17*NORMDIST((G31-G17)/G18,0,1,1)-(G20-G25)*G18*NORMDIST((G31-G17)/G18,0,1,0)-G31*G27*NORMDIST(G31,G17,G18,1)+G31*G26*(1-NORMDIST(G31,G17,G18,1))
=I33+G33+E33+C33
=(O20-O25)*O17*NORMDIST((O31-O17)/O18,0,1,1)-(O20-O25)*O18*NORMDIST((O31-O17)/O18,0,1,0)-O31*O27*NORMDIST(O31,O17,O18,1)+O31*O26*(1-NORMDIST(O31,O17,O18,1))
Expected overstock
=(E31-E17)*NORMDIST((E31-E17)/E18,0,1,1)+E18*NORMDIST((E31-E17)/E18,0,1,0)
=(G31-G17)*NORMDIST((G31-G17)/G18,0,1,1)+G18*NORMDIST((G31-G17)/G18,0,1,0)
=I35+G35+E35+C35
=(O31-O17)*NORMDIST((O31-O17)/O18,0,1,1)+O18*NORMDIST((O31-O17)/O18,0,1,0)
Solution to this problem
The manager at AnyLogo is considering the purchase of high-speed embroidery machines that will allow them to embroider on demand. In this case the apparel will be made in Sri Lanka without any logo and the logo embroidery is postponed and
will be done in the United States on demand. This will raise the cost per unit to $18. However, AnyLogo will not have any holiday or company specific apparel to be disposed at the end of the season. The apparel without logos can be sold for $18 a
unit to retailers. The cost of holding inventory and shipping adds $4 to the cost of any apparel left over after the holiday season. With all other information as in problem 6, do you recommend that the manager at AnyLogo implement postponement?
What will the impact of postponement be on profits and inventories?