Labro is a Portuguese producer of olive oil. It is interested in establishing two new tasting stands for its products in hypermarkets located in the Central Alentejo region.
From a preliminary analysis, the hypermarkets available to host them are in the following locations (one tasting stand per hypermarket): Alandroal, Borba, Evora, Mour ´ ao, Portel, Redondo, Sousel, ˜ Vendas Novas, Viana do Alentejo and Vila Vic¸osa. The oil mill plant has three warehouses, which are located in the towns of Borba, Mourao and ˜ Redondowhich, respectively, and can be used for distributing the oil products to the two tasting stands. The following data are available:
• fj costs (in €/year) for opening and managing tasting stand j ;
• average daily amount of oil rj (expressed as a number of packages of 12-litre bottles) needed to supply the tasting stand if it is located at hypermarket j ;
• average daily availability di of oil (for 12-litre bottles) at warehouse i.
Formulate the location problem by considering that:
(a) each tasting stand will be supplied with a daily door-to-door connection,
(b) the average daily transport cost grows linearly with the number of cases of 12-litre oil bottles transported and
(c) 220 working days should be considered per year.