Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: FoodBank South Africa is an non-profit organisation formed to establish a national network of community foodbanks in urban and rural areas of South Africa, with all participants working towards the common goal of eliminating hunger and food insecurity. FoodBank Cape Town was the first of these community foodbanks launched in South Africa on 2 March 2009. The operations of FoodBank Cape Town include sourcing food and redistributing it to agencies (social services organisations running feeding programmes). Currently the majority of the food is sourced from the retail sector and then redistributed to approximately two hundred agencies. The logistics involved in both sourcing and distributing food are vital to the efficient functioning of FoodBank Cape Town. Since the costs associated with these logistics operations are very high, streamlining these operations has been identified as a priority area for efficiency improvement. The focus in this thesis is on the distribution logistics involved, specifically focussing on a facility location problem according to which FoodBank Cape Town can establish local distribution depots to which it delivers food and from which the agencies collect food assigned to them. A mixed-integer programming model is formulated for the above facility location problem and small test instances of the problem are solved using different exact and approximate solution methods in order to identify a suitable solution methodology for the full (large-scale) FoodBank Cape Town facility location problem. The full facility location problem is solved approximately by means of a meta-heuristic solution method in the more highly constrained instances, while an exact method is selected for solving the lesser constrained instances. The problem is first solved based on the distances between the warehouse and the depots as well as the distances between the agencies and the depots, for the twenty four instances where 17 to 40 depots are located. The model is then developed further to incorporate the cost of distribution. This cost-based facility location model is solved with a view to minimise the cost of food distribution from the warehouse to the depots and the cost of food distribution incurred by each agency to collect food from its assigned depot. A basic vehicle routing technique is applied to the cost-based facility location solution and the associated costs of the distribution are updated. This cost-based solution updating process is performed iteratively until the solution converges. Since the cost of food distribution depends on the vehicle fleet composition used, a vehicle fleet composition comparison of possible FoodBank Cape Town vehicles is performed to determine the most desirable vehicle fleet composition to be used for the distribution of food to depots. The results of the FoodBank Cape Town facility location problem and vehicle fleet composition comparison are presented and recommendations are made to FoodBank Cape Town regarding the preferred number of depots, the location of these depots and the preferred vehicle fleet composition. / AFRIKAANSE OPSOMMING: FoodBank South Africa is ’n nie-winsgewende organisasie wat ten doel het om ’n nasionale netwerk van gemeenskapsvoedselbanke in stedelike en landelike gebiede van Suid-Afrika op die been te bring, waarin al die deelnemers die gemeenskaplike doel nastreef om honger en voedselonsekerheid te elimineer. Foodbank Cape Town was die eerste van hierdie gemeenskapsvoedselbanke in Suid-Afrika en is op 2 Maart 2009 gestig. Die take van Foodbank Cape Town sluit in die versameling van voedsel en die verspreiding daarvan aan agentskappe (gemeenskapsorganisasies wat voedingsprogramme bestuur). Die oorgrote meerderheid voedsel is tans uit die kleinhandelsektor afkomstig en word aan ongeveer tweehonderd agentskappe versprei. Die logistiek wat met hierdie versamelings- en verspreidingsprosesse gepaard gaan, is sentraal tot die doeltreffende funksionering van FoodBank Cape Town. Aangesien die kostes verbonde aan hierdie logistieke prosesse baie hoog is, is hierdie aktiwiteite as ’n prioriteitsarea vir verbetering geidentifiseer. Die fokus in hierdie tesis val op die logistiek verbonde aan die verspreiding van voedsel deur FoodBank Cape Town, en meer spesifiek op die probleem van die plasing van ’n aantal lokale verspreidingsdepots waar FoodBank Cape Town voedsel kan aflewer en waar die agentskappe dan voedsel wat aan hulle toegeken is, kan gaan afhaal. ’n Gemengde heeltallige-programmeringsmodel word vir die bogenoemde plasingsprobleem geformuleer en klein gevalle van die model word deur middel van beide eksakte en benadere oplossingstegnieke opgelos om sodoende ’n geskikte oplossingsmetode vir die volle (grootskaalse) Food- Bank Cape Town plasingsmodel te identifiseer. Die volle plasingsmodel word aan die hand van ’n metaheuristiese oplossingstegniek benaderd opgelos vir hoogsbeperkte gevalle van die model, terwyl minder beperkte gevalle van die model eksak opgelos word. Die plasingsmodel word eers met die oog op die minimering van afstande tussen die pakhuis en verspreidingsdepots sowel as tussen die verspreidingsdepots en agentskappe vir die vier-en-twintig gevalle van die plasing van 17 tot 40 verspreidingsdepots opgelos. Die model word dan verder ontwikkel om ook die koste van die verspreiding van voedsel in ag te neem. Die koste-gebaseerde plasingsmodel word opgelos met die doel om die voedselbankkoste van voedselverspreiding vanaf die pakhuis na die lokale verspreidingsdepots sowel as die agentskapkoste van die afhaal van voedsel vanaf verspreidingsdepots te minimeer. ’n Basiese voertuigroeteringstegniek word op die koste-gebaseerde plasingsmodel toegepas en die verspreidingskoste word dienooreenkomstig aangepas. Hierdie aanpassingsproses van die koste-gebaseerde oplossing word herhaal totdat die oplossing konvergeer. Aangesien die koste van voedselverspreiding afhang van die voertuigvlootsamestelling, word ’n vergelyking tussen moontlike vlootsamestellings vir FoodBank Cape Town getref om die mees geskikte samestelling van voertuie vir die verspreiding van voedsel te vind. Die resultate van die FoodBank Cape Town verspreidingsdepot-plasingsprobleem en vlootsamestellingsvergelyking word aangebied en ’n aanbeveling word aan FoodBank Cape Town gemaak in terme van ’n geskikte aantal verspreidingsdepots, waar hierdie depots geleë behoort te wees, en ’n geskikte voertuigvlootsamestelling vir die verspreiding van voedsel.