Unformatted text preview: h jk demand for product j ! J in week k ! K f g j fixed cost of placing an order or the grand order cost additional fixed cost of including product j ! J in an order that is placed c jkm total holding cost of product j ! J when the order arrives at the beginning of week k ! K and is to be used during the next m weeks " 1 if an order that arrives at the beginning of week k ! K
a kmn $
for the next m weeks satisfies the inventory needs of week n ! K
#
$ 0 if not
%
DECISION VARIABLES X k " 1 if a grand order is placed (and arrives) at the beginning of week k ! K $
#
$
% 0 if not
" 1 if an order for product j ! J is received at the beginning of week k ! K
Y jkm $
and has inventory for the next m weeks
#
$ 0 if not
%
2 of 8 pages IOE 491, Service Operations Management
Winter, 2012, IOE Dept, U. Michigan Name Place your name on all pages now! a) Formulate the first term of the objective function which is to minimize the total fixed cost of placing orders or the total grand ordering cost. This should depend on the decision variable X k Min
" f X k k !K b) Formulate the second term of the objective function which minimizes the total additional fixed costs of including each product in the orders that are placed. This should depend on the Y jkm decision variables. Min " g j " " Y jkm j !J m k !K c) Formulate the final term of the objective function which captures the inventory holding cost. This too should depend on the Y jkm decision variables. Min " " " c jkmY jkm m k !K j !J d) Formulate the constraint that stipulates that we cannot place an order for item j ! J in period k ! K for any length of time unless we have placed a grand order in period k ! K . s.t.
"j # J ; k # K ; m...
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 Winter '08
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 Operations Management, the00, IOE Dept

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