This thesis deals with timing and sizing decisions for production lots, and more precisely, with mathematical models to support optimal tim- ing and sizing decisions. These models are called lotsizing models. They are characterized by the fact that production lots are determined based on a trade-offbetween production costs and customer service. Production costs can be categorized as basic production costs, which consist of material costs, labour costs, machine startup costs and over- head costs, and inventory related costs, which include costs of capital tied up in inventory, insurances and taxes. Customer service is the capability of the firm to deliver to their clients the products in the quantity they ordered at the agreed upon time and place. The costs of realizing a certain service level are usuaIly very dif- ficult to convert into money. They include costs of expediting, loss of customer goodwill, and loss of sales revenues resulting from the short- age situation.