# IE426 – Case studies – Production planning

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```					IE426 – Case studies – Production planning
An aluminium production plant will start operations in January 2009. The fac-
tory has a maximum production capacity of 109 ton/month, with a production
cost of 1,000\$/ton and sales price of 2,200\$/ton. A further section of the plant is
in general not in use, but it can be useful for a little extra production; it can be
activated at the beginning of each month and can produce up to 15 ton/month,
which is however not as proﬁtable due to poorer technology: its production cost
is 1100\$/ton.
We are in charge of planning production for the next few years, and have a
fairly accurate estimate of the monthly aluminium demand (in tons):

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Demand 128 131 119 105 98 90 92 101 106 110 130 115
These monthly demands are ﬂexible in that they can be satisﬁed in later
months. However, due to contractual terms the aluminium loses 5% of its value
for each month it is sold late.
The plant has an inventory with virtually unlimited capacity. It is empty on
December 31, 2008, and has a maintenance cost of 20\$/ton/month. The company
needs a production plan that maximizes total proﬁt, taking into account the loss
due to delay and the inventory cost.

1. Determine the production plan for year 2009, taking into no account the
following years. For each month, report the quantity of demand that was
satisﬁed on time and with one or more months of delay. Also, report when
the extra capacity was needed.
2. Determine the production plan for 2009 through 2011. Does the solution
change? Report the same data as Problem 1.
3. Determine the production plan from 2009 on, not considering a ﬁnal year.
Does there exist a year when production stabilizes? What is the diﬀerence
in the usage of inventory and extra production and in the on time demands
between the ﬁrst year and the ﬁnal year? Report the same data as Problem
1, for all years up to the “stabilization” year.

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