Moving economic lot size

The process of the sliding economic lot size (English least-unit-cost-method, LUC) is a heuristic process of dynamic lot size determination . It aims to minimize unit costs.

In the case of constant demand quantities (stationary case), the average costs are minimal depending on the quantity, precisely when the optimal lot size is produced. If one transfers this property to the dynamic case, one obtains the procedure of the sliding economic lot size. Sigfrid Gahse was the first to publish this method (1965), Walter Trux followed soon after (1968).

formula

Calculation of the unit costs in the selected production period and demand period . : Changeover costs or batch costs [GE] : Net requirement of the product in period t : Storage cost rate : Period ${\displaystyle k_{ij}}$ ${\displaystyle i}$ ${\displaystyle j}$
${\displaystyle k_{ij}={\frac {A+lk\sum _{t=i}^{j}B_{t}\cdot (t-i)}{\sum _{t=i}^{j}B_{t}}}}$
${\displaystyle A}$
${\displaystyle B_{t}}$ ${\displaystyle \lbrack {\tfrac {\text{ME}}{\text{Periode}}}\rbrack }$
${\displaystyle lk}$ ${\displaystyle \lbrack {\tfrac {\text{GE}}{{\text{ME}}\cdot {\text{Periode}}}}\rbrack }$
${\displaystyle t}$

method

Starting from the production period , the system searches for the demand period for which the unit costs are minimal. It starts with and . In the first iteration, this is only increased until the unit costs are greater than the unit costs of . If this is the case, the first iteration is canceled and the first batch size is found. In the next iteration step, the period is assigned the value from the previous iteration and the value of the demand periods remains. ${\displaystyle i}$ ${\displaystyle j}$ ${\displaystyle k_{ij}}$ ${\displaystyle i=1}$ ${\displaystyle j=1}$ ${\displaystyle j}$ ${\displaystyle k_{ij}}$ ${\displaystyle k_{i(j-1)}}$ ${\displaystyle k_{i(j-1)}}$
${\displaystyle i}$ ${\displaystyle j}$ ${\displaystyle j}$

Conflict of goals

Cost history for batch production

You made with fewer, larger lots, then the reduced set-up costs , the increase for up storage costs . Conversely, more lots lead to lower storage costs, but higher set-up costs.

example

For periods 1 to 6, the following requirements arise in pieces:

Periods	1	2	3	4th	5	6th
Required quantity	50	10	80	40	5	70

The setup costs are A = 200 euros, the storage cost rate . ${\displaystyle 10{\tfrac {\text{Euro}}{{\text{Stück}}\cdot {\text{Periode}}}}}$

Solution with the help of a table

Production period i	Demand period j	Unit cost ${\displaystyle k_{ij}}$
1	1	${\displaystyle {\tfrac {200}{50}}=4}$ (local minimum)
1	2	${\displaystyle {\tfrac {300}{60}}=5}$ (Cancellation)
2	2	${\displaystyle {\tfrac {200,00}{10}}=20}$
2	3	${\displaystyle {\tfrac {1000}{90}}=11,1}$ (local minimum)
2	4th	${\displaystyle {\tfrac {1800}{130}}=13,8}$ (Cancellation)
4th	4th	${\displaystyle {\tfrac {200}{40}}=5}$ (local minimum)
4th	5	${\displaystyle {\tfrac {250}{45}}=5,6}$ (Cancellation)
5	5	${\displaystyle {\tfrac {200}{5}}=40}$
5	6th	${\displaystyle {\tfrac {900}{75}}=12}$ (The End)

This followed the lot sizes: , , , and total cost of . ${\displaystyle x_{1}=50}$ ${\displaystyle x_{2}=90}$ ${\displaystyle x_{4}=40}$ ${\displaystyle x_{5}=75}$ ${\displaystyle 2300\ {\text{GE}}}$

See also

• Silver-meal heuristic
• Period adjustment
• Procedure by Groff

literature

• Sigfrid Gahse : Warehouse disposition with electronic data processing systems, Neue Betriebswirtschaft, Issue 1, 1965, page 4
• Sigfrid Gahse : Optimal order quantities, IBM specialist literature Form 81533, April 1967
• Walter Trux : Purchasing and warehouse disposition with data processing, Verlag modern industry, Munich, 1968
• Sigfrid Gahse : Systems of Integrated Data Processing - Purchasing, Verlag modern industry, Munich, 1972, page 115 ff.
• Karl-Werner Hansmann : Industrial Management. 7th, completely revised and enlarged edition. Oldenbourg, Munich et al. 2001, ISBN 3-486-25676-9 , p. 307.
• Karl Kurb : Production planning and control in Enterprise Resource Planning and Supply Chain Management. 6th, completely revised edition. Oldenbourg, Munich et al. 2005, ISBN 3-486-57578-3 , p. 118.
• Peter Mertens : Integrated information processing. Volume 1: Operational Systems in Industry. 17th, revised edition. Gabler, Wiesbaden, ISBN 978-3-8349-1645-7 , p. 81.
• Horst Tempelmeier : Material logistics. Models and algorithms for production planning and control and supply chain management. 4th, revised and expanded edition. Springer, Berlin et al. 1999, ISBN 3-540-66288-X , p. 158.
• Rainer Weber: Contemporary materials management with storage. Flexibility, readiness to deliver, inventory reduction, cost reduction - the German Kanban (= contact & study. 266). 9th, revised edition. Expert-Verlag, Renningen 2009, ISBN 978-3-8169-2903-1 , p. 97.