A multi-stage stochastic programming approach in master production scheduling

Abstract

a b s t r a c tMaster Production Schedules (MPS) are widely used in industry, especially within Enterprise Resource Planning (ERP) software. The classical approach for generating MPS assumes infinite capacity, fixed processing times, and a single scenario for demand forecasts. In this paper, we question these assumptions and consider a problem with finite capacity, controllable processing times, and several demand scenarios instead of just one. We use a multi-stage stochastic programming approach in order to come up with the maximum expected profit given the demand scenarios. Controllable processing times enlarge the solution space so that the limited capacity of production resources are utilized more effectively. We propose an effective formulation that enables an extensive computational study. Our computational results clearly indicate that instead of relying on relatively simple heuristic methods, multi-stage stochastic programming can be used effectively to solve MPS problems, and that controllability increases the performance of multi-stage solutions.

A review of discrete-time optimization models for tactical production planning

“…Uncertainty in the production environment is addressed by 39 references which employ different modeling approaches. Stochastic programming models are considered with distinct approaches, such as two-stage stochastic programming (Leung et al, 2006;Nagar and Jain, 2008;Schütz and Tomasgard, 2011;Wu, 2011;Zanjani et al, 2011) or multi-stage stochastic programming (Brandimarte, 2006;Denizel et al, 2010;Guan and Miller, 2008;Guan et al, 2009;Guan and Philpott, 2011;Koerpeoglu et al, 2011;Nagar and Jain, 2008;Zanjani et al, 2010b). Other stochastic programming proposals are presented by Karabuk (2008), Kim and Xirouchakis (2010), Sodhi and Tang (2009), Tempelmeier and Herpers (2011) and Tempelmeier (2007).…”

“…Automobile industry 1 Koerpeoglu et al (2011) Plastic industry 1 Lang and Shen (2011) Poultry industry 1 Lu and Qi (2011) Remanufacturing of printers and copy cartridges 1 Wei et al 2011TOTAL 18…”

Hybrid fuzzy-stochastic approach for multi-product, multi-period, and multi-resource master production scheduling problem: case of a polyethylene pipe and fitting manufacturer

“…Supriyanto and Noche [32] proposed a methodology for MPS problems in which uncertainty was considered under fuzzy information. K orpeo glu et al [33] used a multi-stage stochastic programming approach, considering several demand scenarios. Also, Mula et al [34] reviewed production planning under uncertainty.…”

An Inventory-Theory-Based Inexact Multistage Stochastic Programming Model for Water Resources Management

“…However, TSP can only take recourse actions at the second stage to correct any infeasibility, and thus, it can hardly reflect the dynamic variations of system conditions, especially for multistage problems with a sequential structure. To address such a dynamic characteristic, a lot of multistage stochastic programming (MSP) methods were proposed as extensions of dynamic stochastic optimization approaches [13,[22][23][24][25][26][27][28]. MSP was improved upon the conventional TSP methods by permitting revised decisions in each time stage based on the information of sequentially realized uncertain events [29].…”