Period adjustment

The piece period balancing method (also cost balancing method, part period method or also part period balancing) is a heuristic method of dynamic lot size determination . It aims to balance the set-up and storage costs, as this is where the optimum cost is achieved. In contrast to the Wagner-Whitin algorithm, the result of the heuristic is not optimal in all cases.

formula

The general formula is: Since this formula does not usually work for integer values, one works with the following inequalities: ${\displaystyle A=lk\cdot \sum _{t=i}^{j}B_{t}\cdot (t-i)}$

${\displaystyle {\frac {A}{lk}}\ \geq \sum _{t=i}^{j}B_{t}\cdot (t-i)}$ and ${\displaystyle {\frac {A}{lk}}\ <\sum _{t=i}^{j+1}B_{t}\cdot (t-i)}$

${\displaystyle A}$: Retrofitting costs or batch costs [GE] : Net demand of the product in period t [ME / period] : Storage cost rate [GE] : Period
${\displaystyle B_{t}}$
${\displaystyle lk}$
${\displaystyle t}$

${\displaystyle i}$: Production period : Demand period
${\displaystyle j}$

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 set-up costs are A = 200 euros, the storage costs . ${\displaystyle 10{\tfrac {\text{Euro}}{{\text{Stück}}\cdot {\text{Periode}}}}}$

Solution with the help of a table

Production period i	Demand period j	${\displaystyle {\frac {A}{lk}}}$	${\displaystyle {\frac {A}{lk}}\ >=\sum _{t=i}^{j}B_{t}\cdot (t-i)}$	${\displaystyle {\frac {A}{lk}}\ <\sum _{t=i}^{j+1}B_{t}\cdot (t-i)}$
1	1	20th	0	${\displaystyle 0+10=10}$
1	2	20th	${\displaystyle 0+10=10}$	${\displaystyle 0+10+160=170}$ (Cancellation)
3	3	20th	0	40 (abort)
4th	4th	20th	0	5
4th	5	20th	5	${\displaystyle 0+5+140=145}$ (Cancellation)
6th	6th	20th	0	No result found

This followed the lot sizes: , , , and total cost of 950 GE. The total costs are calculated as follows: This also corresponds to the optimal solution according to the Wagner-Whitin algorithm . ${\displaystyle x_{1}=60}$ ${\displaystyle x_{3}=80}$ ${\displaystyle x_{4}=45}$ ${\displaystyle x_{6}=70}$

${\displaystyle {\text{Gesamtkosten}}=\underbrace {200+10\cdot 10} _{x_{1}}+\underbrace {200} _{x_{3}}+\underbrace {200+5\cdot 10} _{x_{4}}+\underbrace {200} _{x_{6}}=950}$

See also

• Silver-meal heuristic
• Moving economic lot size
• Procedure by Groff

literature

• Stephan Zelewski , Susanne Hohmann, Torben Hügens: Production planning and control systems. Concepts and exemplary implementations using SAP R / 3. Oldenbourg, Munich 2008, ISBN 978-3-486-58722-7 , p. 362.
• Karl-Werner Hansmann : Industrial Management. 8th, completely revised and expanded edition. Oldenbourg, Munich et al. 2006, ISBN 3-486-58058-2 , p. 310.
• 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. 120.