Zadaće optimizacije u lancima opskrbe

master's thesis

• Title (english): Optimization tasks in supply chains
• Author: Ana Nedić
• Mentor: Marko Vrdoljak (mentor)
• Committee member: Marko Vrdoljak (predsjednik povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Zoran Vondraček (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Strateške odluke poput određivanja lokacija novih objekata, poput tvornica, skladišta i trgovina su ključne za učinkovito i optimalno upravljanje lancem opskrbe. Za dani skup potencijalnih lokacija skladišta te skup trgovina, problem određivanja lokacija skladišta je odrediti lokacije skladišta tako da ukupan trošak dodjeljivanja trgovina skladištima, uz zadovoljavanje potražnje bude minimalan. U ovom radu ćemo predstaviti optimizacijske modele za tri važna problema određivanja lokacija skladišta, započevši s problemom P-medijana. Potom ćemo taj model proširiti kako bismo uključili dodatne faktore poput kapaciteta skladišta i fiksnih troškova. Završit ćemo s općenitijim modelom u kojem se prilikom određivanja lokacija skladišta u obzir uzimaju svi dijelovi distribucijskog sustava, to jest tvornice i trgovine. Pri rješavanju ovih problema koristit ćemo metodu Lagrangeove relaksacije. Ideja te metode je doći do relaksiranog problema kojeg je jednostavnije riješiti, nego originalni problem. Do relaksiranog problema dolazimo eliminiranjem jednog ili više uvjeta originalnog problema na način da se pripadne funkcije uvjeta pomnože Lagrangeovim multiplikatorima i potom dodaju funkciji cilja.

Abstract (english)

Strategic decisions like determining the location of facilities such as factories, warehouses and retailers are critical to the effective and efficient supply chain management. Given a set of potential locations for warehouses and a set of retailers, the warehouse location problem is to find the location of warehouses in such a way that the total cost for assigning retailers to warehouses, while satisfying the demand is minimized. In this thesis, optimization models for three important warehouse location problems will be presented, beginning with the P-Median Problem. We then extend this model in order to incorporate additional factors, such as warehouse capacities and fixed costs. We conclude by giving a more general model where all levels of the distribution system, plants and retailers, are taken into account when deciding warehouse locations. In order to solve these problems, we will use the Lagrangian relaxation method. The idea of this method is to obtain a relaxed problem, which is easier to solve than the original problem. This is done by eliminating one or more of the original problem constraints and adding these constraints, multiplied by Lagrangian multiplier, to the objective function.

• Keywords: optimizacijski modeli; P-medijan; lokacija skladišta; metoda Lagrangeove relaksacije; Lagrangeovi multiplikatori
• Keywords (english): optimization models; P-Median Problem; warehouse location problem; Lagrangian relaxation method; Lagrangian multiplier
• Language: croatian
• URN:NBN: urn:nbn:hr:217:701554
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-11-02 13:38:47