IE426 – Case studies – Production planning

Document Sample
IE426 – Case studies – Production planning Powered By Docstoc
					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.