Question

Problem 3. The Green Company is a retailer of gourmet bottled pickles that purchases its produce whole, a gourmet food manufacturer. Green buys units (from Whole) at a price of and sells them to customers at $45 per unit. Currently Whole produces to Green's order and delivers all requirements at the start of the period. Leftover inventory at the end of the season will be donated to a charity organization for free. The demand is lost when Green does not have inventory. Whole's production cost is $10 per unit. Demand(units) Probability 100 0.2 200 0.3 300 0.2 400 0.3 1. Given the current information, how many units of products should Green stock to satisfy demand? What is the associated profit for Whole and Green and for the supply chain in total?

Answer 1

1.

The units of products which Green should stock is the average demand, which is equal to  

ᎠiᏢ i=1

Where D is the demand and P is the probability.

=100 x 0.2 + 200 x 0.3 +300 x 0.2 + 400 x 0.3

= 20+ 60+ 60+ 120

=260

Profits for Whole = Sale - Cost

Cost price = $ 10 per unit

Selling price = $15 per unit

Profit per unit = $15-1$0

= $5

Thus net profit = number of units sold x profit per unit

= 260 x 5

=$1300

Profits of Green

Whenever there is a demand profit per unit is $45 - $15 which is selling price - purchase price

=$30

Whenever there is no demand and leftover inventory

there will be a loss of $15 or profit of -$15

So,

When actual demand is 100, leftover inventory = 260-100 = 160 units

when actual demand is 200, leftover inventory = 260-200 = 60 units

When actual demand is 300, leftover inventory NIL

when actual demand is 400, leftover inventory NIL

So the net profits would be

(30x100 -15x160)x0.2 + (30x200 -15x60)x0.3 + (30x260 -15x0)x0.2 + (30x260 -15x0)x0.3

=120 + 1530 + 1560 + 2340

= $5,550

Total Supply chain profit = profit of Green + profit of Whole

= 5,550 + 1,300

=$6,850

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