Petkim has a contract with one of its customers, Tofaş, to supply a unique liquid chemical
product that is used by Tofaş in the manufacture of a lubricant for Doblo’s engines. Because
of the chemical process used by Petkim, batch size for the liquid chemical product must be
Tofaş has agreed to adjust manufacturing to the full batch quantities, and will order either
one, two, or three batches every three months. Since an aging process of one month is
necessary for the product, Petkim will have to make its production (how much to make)
decision before Tofaş places an order. Thus, Petkim can list the product demand alternatives
of 1000, 2000, or 3000 kgs, but the exact demand is unknown. Unfortunately, Petkim’s
product cannot be stored more than two months without degenerating into a viscous and
highly corrosive toxic compound, linked in laboratory tests to the Ebola virus.
Petkim’s manufacturing costs are $150 per kg, and the product sells at the fixed contract price
of $200 per kg. If Tofaş orders more than Petkim has produced, Petkim has agreed to absorb
the added cost of filling the order by purchasing a higher quality substitute product from As
Kimya, another chemical firm. The substitute As Kimya product, including transportation
expenses, will cost Petkim $240 per kg. Since the product cannot be stored more than two
months, Petkim cannot inventory excess production until Tofaş’s next three-month order.
Therefore, if Tofaş’s current order is less than the amount that Petkim has produced, the
excess production will be reprocessed and valued at $50 per kg.
The inventory decision in this problem is how much Petkim should produce given the costs
and the possible demands of 1000, 2000, and 3000 kgs. From historical data and an analysis
of Tofaş’s future demands, Petkim has assessed the probability distribution for demand shown
in the table below.