Doctoral Thesis Green Lot-Sizing

Defended on Thursday, 3 October 2013


The lot-sizing problem concerns a manufacturer that needs to solve a production planning problem. The producer must decide at which points in time to set up a production process, and when he/she does, how much to produce. There is a trade-off between inventory costs and costs associated with setting up the production process at some point in time. Traditionally, the lot-sizing model focuses solely on cost minimisation. However, production decisions also affect the environment in many ways. In this dissertation, the classic lot-sizing model is extended into several different directions, in order to take various environmental considerations into account.

First, items that are returned from customers are included in the lot-sizing problem, within the context of reverse logistics. These items can be remanufactured to fulfil customer demand. In another extension, a minimum is imposed on the size of a production batch, in order to reduce the pollution associated with producing many small batches. Furthermore, a lot size model is considered in which there is a maximum on the amount of pollutants, such as carbon dioxide. This model can also be seen as a bi-objective lot-sizing problem. The mathematical models that arise from these extensions are fundamentally harder to solve than the classic lot-sizing problem. Several approaches to solving these problems are developed, based on mathematical optimisation techniques such as mixed integer programming, dynamic programming and fully polynomial time approximation schemes.


green; lot-sizing; production planning; reverse logistics; mixed integer programming; bi-objective optimisation; fully polynomial time approximation scheme; FPTAS; carbon emissions; batch production; dynamic programming

Time frame

2007 - 2010

Preferred reference

M. Retel Helmrich, Green Lot-Sizing, Promotor:Prof. dr. Albert Wagelmans,


Mathijn Jan Retel Helmrich
Mathijn Jan Retel Helmrich

Supervisory Team

Albert Wagelmans
Professor of Econometrics (Management Science)
  • Promotor
Wilco van den Heuvel
Associate Professor of Opereations Research
  • Copromotor
  • Daily Supervisor
Raf Jans
Raf Jans
  • Copromotor
  • External Member Supervisory Team

Committee Members

Stéphane Dauzère-Pérès
Rommert Dekker
Professor of Econometrics (Operations Research and Informatics)
Steef van de Velde
Dean RSM & Professor of Management and Technology