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Multi-level uncapacitated lot sizing - Procedure of Simpson and Erenguc

The dynamic multi-level uncapacitated lot sizing problem (MLULSP) is solved with the "Non-Incremental-Part-Period-Algorithm" (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..


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 bill-of-material 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 Wagner-Whitin-Problem.


- Tempelmeier (1999), Kapitel D.

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