Multilevel uncapacitated lot sizing  Procedure of Simpson
and Erenguc
The dynamic multilevel uncapacitated lot sizing
problem (MLULSP) is solved with the "NonIncrementalPartPeriodAlgorithm"
(NIPPA) of Simpson und Erenguc. This procedure combines adjacent lots
if this leads to a cost reduction. The criterion considered is the ratio of
the holding cost increase to the setup cost decrease.
The changing of the relevant costs is computed with respect to all products
in the BOM structure..
Symbols:
d(k,t) 
demand of product k in period t 
s(k) 
setup costs of product k 
e(k) 
echelon holding costs of product k 
Pr(k,t) 
priority criterion: ratio of the increase of the
all holding costs to the decrease of all setup costs, if the production
quantity of product k in period t is shifted to the nearest earlier production
period 
The billofmaterial structure is generated with the graph
editor.
Next the end product demands d(k,t) (green
cells in the upper table).
In the lower table the setup costs s(k) and the echelon holdings costs e(k)
are entered. This can also be done in the graph editor.
During
the iterations of the algorithm the current production plan is displayedin the
upper table.
The
lower table shows the current cost ratios. Click on a cell in
the lower table to get more information about the computation of the cost ratio
displayed in the cell.
Note.: You can also apply the procedure
for a single item. This would result in a heuristic solution of the WagnerWhitinProblem.
Literature:
 Tempelmeier (1999), Kapitel D.3.4.3.4
