Sourcing Decisions in a Supply Chain

Chapter 14: Sourcing Decisions in a Supply Chain

1.

With no buyback:

[pic 1]0.571

Optimal lot-size =[pic 2]= NORMINV(0.571,20000,5000)

= 20,900

Given that:

Border’s sale price (p) = $24

Border’s salvage value (s = b) = $3

Border’s cost (c) = $12:

Expected profits for Border’s = (p – s)μ NORMDIST((O – μ)/σ, 0, 1, 1)

– (p – s)σ NORMDIST((O – μ)/σ, 0, 1, 0) – O (c – s) NORMDIST(O, μ, σ, 1)

+ O (p – c) [1 – NORMDIST(O, μ, σ, 1)] = $198,784

Expected overstock = (O – μ)NORMDIST((O – μ)/σ, 0, 1, 1) + σ NORMDIST((O – μ)/σ, 0, 1, 0)

                        = 2,477

Expected understock =

(μ – O)[1 – NORMDIST((O – μ)/σ, 0, 1, 1)] + σ NORMDIST((O – μ)/σ, 0, 1, 0) = 1,577

Given that:

Publisher’s sale price (c) = $12

Publisher’s buyback price (b) = $0

Publisher’s cost (v) = $1

Publisher’s expected profit = O(c-v) – (overstock)(b) = $229,901

Total supply chain profit = $198,784 + $229,901 = $428,685

With buyback:

We reevaluate the profits for Border’s (with c = b = 8) and the publisher (with b = 5)

Expected profit for Border’s = $214,578

Expected profit for publisher = $236,506

Total supply chain profit = $451,084

EXCEL worksheet 14-1 illustrates these computations

2.

With no buyback:

[pic 3]0.666

Optimal lot-size =[pic 4]= NORMINV(0.666,10000,5000)

= 12,144

Given that:

Blockbuster’s sale price (p) = $19.99

Blockbuster’s salvage value (s = b) = $4.99

Blockbuster’s cost (c) = $10:

Expected profits for Blockbuster = (p – s)μ NORMDIST((O – μ)/σ, 0, 1, 1)

– (p – s)σ NORMDIST((O – μ)/σ, 0, 1, 0) – O (c – s) NORMDIST(O, μ, σ, 1)

+ O (p – c) [1 – NORMDIST(O, μ, σ, 1)] = $72,609

Expected overstock = (O – μ)NORMDIST((O – μ)/σ, 0, 1, 1) + σ NORMDIST((O – μ)/σ, 0, 1, 0)

                        = 3,248

Expected understock =

(μ – O)[1 – NORMDIST((O – μ)/σ, 0, 1, 1)] + σ NORMDIST((O – μ)/σ, 0, 1, 0) = 1,103

Given that:

Studio’s sale price (c) = $10

Studio’s buyback price (b) = $0

Studio’s cost (v) = $1

Publisher’s expected profit = O(c-v) – (overstock)(b) = $109,300

Total supply chain profit = $72,609 + $109,300 = $181,909

With buyback:

We reevaluate the profits for Blockbuster (with c = b = 8.99) and the Studio (with b = 4)

Expected profit for Blockbuster = $90,835

Expected profit for Studio = $122,386

Total supply chain profit = $213,221

EXCEL worksheet 14-2 illustrates these computations

3.

Topgun’s response:

CSL = [pic 5] = 0.771

Optimal lot-size =[pic 6]= NORMINV(0.771,5000,2000)

= 6,487

Expected overstock = (O – μ)NORMDIST((O – μ)/σ, 0, 1, 1) + σ NORMDIST((O – μ)/σ, 0, 1, 0)

                        = 1,752

Expected sales at Topgun = 6,487 – 1,752 = 4,735