In markets where suppliers experience learning by doing over time or, more generally, economies of scale in production, buyers are auctioning off longer-term contracts with an eroding price policy. Under an eroding price contract, the buyer initially competitively awards production to the lowest-bid supplier via an auction. Before the auction takes place, the buyer makes it clear to the suppliers that, if chosen, a sequence of price reductions will be mandatory in subsequent periods. In this thesis, we mainly study the design of the optimal eroding price contract in a two period setting under three different model settings : (1) Every supplier faces a new cost in each period (NLI model), (2) The supplier who wins the auction in the first period locks-in his cost for the future, and the buyer makes the future payment based on the winning supplier's current bid (LI1), and (3) The supplier who wins the auction in the first period locks-in his cost for the future, and the buyer makes the future payment based on the winning supplier's actual cost (LI1). Under NLI setting, the magnitude of the cost reduction due to learning by doing is common knowledge, while the magnitude is uncertain under LI1 and LI2 settings. We also study the optimal reserve prices in sequential independent auctions under NLI setting. We go on to compare the performance of the eroding price policy against sequential independent auctions (without or with the optimal reserve prices) under the above model settings. Via analytical and numerical comparisons, we find that even in the presence of learning by doing/economies of scale in production, a buyer is often better off running sequential auctions with a reserve price, rather than limiting competition and contracting with a single supplier in the hopes of extracting a better future price.

The diploma thesis is focused on inventory management in a production company with an emphasis on optimizing company´s stock level. There has been made an analysis of the current status of selected group of inventory, and of the use of the existing information system. Based on this analysis and theoretical knowledge of inventory management, two measures have been designed. They should help to increase efficiency of purchasing and to reduce inventory and costs.