M.Sc Student | Melamed Michal |
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Subject | Robust Optimization of a Multi-Period Production Planning Problem under Uncertainty |

Department | Department of Industrial Engineering and Management |

Supervisors | Professor Emeritus Aharon Ben-Tal |

Professor Boaz Golany | |

Full Thesis text |

This thesis applies the *Robust
Optimization* (RO) methodology to a single-product multi-period production
planning problem in which the inventories are managed periodically over a
finite horizon. The demand for the product is uncertain and is only known to
reside within a user-defined uncertainty set while drifting around a nominal
trajectory which is assumed to follow a typical life-cycle pattern. Our work
differs from previous analyses as it measures the performance of the RO
methodology based on average performance found through a simulation study
rather than on the basis of optimal solutions value.

The objective of the research is twofold: at the operational level the objective is to determine the production quantities over the planning horizon to maximize the total profit; at the tactical level the objective is to estimate at the outset of the planning horizon the length of a profitable horizon. We consider two settings: one in which all the costs are attributed to specific quantities in specific periods, i.e., linear costs, and another in which setup costs are present.

In the linear costs
setting, we show that the average performance of the adjustable and pure online
RO methods is better than alternative methods (and more so as the level of
uncertainty grows). Moreover, these preferred methods achieved on average,
solutions that are surprisingly close to the *perfect hindsight* (PH)
profit, i.e., the objective value that would have been obtained if it was
possible to know exactly the realizations of the demand at the outset of the
horizon.

In the scenario that includes an additional fixed cost, the nominal model is a mixed integer linear programming, and so is its RC formulation when the uncertainty set is polyhedral. For this setting we examined the average performance of the pure online RO. Here, the simulation study shows that the average performance of the pure online RO follows the same trend as in the linear costs setting, namely close to the PH profit.