Mémoire
| Résumé : | In this Master’s thesis, we analyse a problem in product pricing under a modelof single-minded customer behaviour, determined by a bundle and a budget.A bundle is a subset of products, a given customer wants to purchase, andhe is willing to pay at most his budget. The single-mindedness of the clienttranslates into him purchasing if and only if the total price of his bundleis at most his budget. The objective is to maximise to total profits and weassume that supply is unlimited. This problem is known under Single-MindedBundle Pricing Problem (SMBPP). It has been introduced only recently inthe literature of algorithmic pricing.After a brief literature review on product pricing, we note that most ofthe research on the SMBPP is dedicated to complexity results and approx-imation. We therefore contribute to a missing piece of literature of exactmethods. We find that the problem can be described very intuitively by abilinear objective in the prices and purchase decisions under bilinear con-straints for every customer. We formulate this as a mixed-integer nonlinearprogram (MINLP). We linearise the formulation in two different ways to ob-tain two mixed-integer linear programs (MILP) that can be solved exactly byusing branch-and-bound methods. We next set up a semi-definite programthat allows to construct the best convex reformulation of the SMBPP.We prove some properties of our formulations and compare our modelstheoretically. We then deduce valid inequalities by exploiting the problemstructure and formulate their respective separation problems. When possi-ble, separation algorithms are suggested. This work concludes by extensivenumerical experiments to support our theoretical results and to evaluate theperformance of our exact methods. |
