Journal
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Volume 212, Issue 1, Pages 81-88Publisher
ELSEVIER
DOI: 10.1016/j.ejor.2011.01.032
Keywords
Robust production planning; Random failures; Service level; First passage time; Brownian motion
Funding
- Natural Sciences and Engineering Research Council of Canada (NSERC)
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In this paper, we consider a multi-period, multi-product production planning problem where the production rate and the customer service level are random variables due to machine breakdowns. In order to determine robust production plans, constraints are introduced in the stochastic capacitated lot-sizing problem to ensure that a pre-specified customer service level is met with high probability. The probability of meeting a service level is evaluated by using the first passage time theory of a Wiener process to a boundary. A two-step optimization approach is proposed to solve the developed model. In the first step, the mean-value deterministic model is solved. Then, a method is proposed in the second step to improve the probability of meeting service level. The resulting approach has the advantage of not being a scenario-based one. It is shown that substantial improvements in service level robustness are often possible with minimal increases in expected cost. (C) 2011 Elsevier B.V. All rights reserved.
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