Version 0.13.0 implements three variants explicitly analyzed in:
U. Wemmerlöv (1983), The Part-Period Balancing Algorithm and Its Look Ahead-Look Back Feature: A Theoretical and Experimental Analysis of a Single Stage Lot-Sizing Procedure, Journal of Operations Management 4(1), 23-39.
DOI: https://doi.org/10.1016/0272-6963(83)90023-2
The public strategies are:
Wemmerlöv rewrites the ordinary PPB balance as
\[\left| A-h\sum_{j=1}^{T}(j-1+\nu)d_{k+j-1} \right|. \]
The paper derives a positive correction factor and reports that the practical limiting value
\[\nu=0.5 \]
can be used with only a small empirical penalty relative to item-specific values.
WemmerlovModifiedPartPeriodBalancingSolver therefore exposes this recommended fixed correction explicitly rather than silently changing the existing classical PartPeriodBalancingSolver.
The modified LALB procedure in Figure 4 locally adjusts a tentative PPB lot.
Suppose a replenishment in k tentatively covers T periods and the next replenishment is therefore planned for k+T.
Before moving the next replenishment one period forward, the algorithm checks
\[h T d_{k+T} \le A. \]
The two-period local cost comparison is
\[h\{\nu d_{k+T}+(1+\nu)d_{k+T+1}\} \]
versus
\[h\{(T+\nu)d_{k+T}+\nu d_{k+T+1}\}. \]
When moving the next replenishment forward is cheaper, the tentative current lot is enlarged by one period.
If Look-Ahead does not move the replenishment, the final requirement already inside the tentative lot is tested against moving it into the next batch:
\[h\{(T-1+\nu)d_{k+T-1}+\nu d_{k+T}\} \]
versus
\[h\{\nu d_{k+T-1}+(1+\nu)d_{k+T}\}. \]
If the shifted pattern is cheaper, the tentative lot is shortened by one period.
The original analysis is for stationary ordering and holding costs. These strategies therefore use the library's stationary-cost guard.
For LALB, ULSAlgorithms additionally requires strictly positive period demand. The paper's local formulas contain explicitly identified adjacent requirements; rather than inventing a zero-demand preprocessing convention, the current implementation rejects such instances.
The corrected PPB strategy without LALB continues to support zero-demand periods.
Wemmerlöv evaluates four variants separately:
The study reports statistically significant average improvements from both the correction factor and LALB, while also warning that Look-Back can perform poorly in constant or near-constant demand environments. The library therefore keeps all variants public instead of assuming one universally dominates the others.
1.17.0 