Campus Units

Industrial and Manufacturing Systems Engineering, Bioeconomy Institute (BEI)

Document Type


Publication Version

Accepted Manuscript

Publication Date


Journal or Book Title

Computers & Industrial Engineering



First Page


Last Page


Research Focus Area(s)

​Operations Research




A stochastic lot-sizing and scheduling problem with demand uncertainty is studied in this paper. Lot-sizing determines the batch size for each product and scheduling decides the sequence of production. A multi-stage stochastic programming model is developed to minimize overall system costs including production cost, setup cost, inventory cost and backlog cost. We aim to find the optimal production sequence and resource allocation decisions. Demand uncertainty is represented by scenario trees using moment matching technique. Scenario reduction is used to select scenarios with the best representation of original set. A case study based on a manufacturing company has been conducted to illustrate and verify the model. We compared the two-stage stochastic programming model to the multi-stage stochastic programming model. The major motivation to adopt multi-stage stochastic programming models is that it extends the two-stage stochastic programming models by allowing revised decision at each period based on the previous realizations of uncertainty as well as decisions. Stability test and weak out-of-sample test are applied to find an appropriate scenario sample size. By using the multi-stage stochastic programming model, we improved the quality of solution by 10–13%.


This is a manuscript of an article published as Hu, Zhengyang, and Guiping Hu. "A Multi-stage Stochastic Programming for Lot-sizing and Scheduling under Demand Uncertainty." Computers & Industrial Engineering 119 (2018): 157-166. DOI: 10.1016/j.cie.2018.03.033. Posted with permission.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Copyright Owner

Elsevier Ltd.



File Format


Available for download on Wednesday, May 01, 2019

Published Version