Price updating in combinatorial auctions for coordination of manufacturing multiagent systems

Abstract

In this work we use the paradigm of multiagent systems to solve the Job Shop problem. Job Shop problem is a particular problem of scheduling in which we try to find an schedule that optimize a objective and is subject to certain constraints. We propose a combinatorial auction mechanism to coordinate agents. The “items” to be sold are the time slots that we divide the time horizon into. In tasks scheduling problems tasks need a combination of time slots of multiple resources to do the operations. The use of auctions in which different valuations of interdependent items are considered (e.g. combinatorial auctions) is necessary. A certain time slot will be more valuated to the extent that it enables task to finish the job on time, together with the other time slot bought. Job-agents are price-takers in the model. The auctioneer fixes prices comparing the demand over a time slot of a resource with the capacity of the resource in this time slot. There are many ways to update prices (e.g. constant increase or decrease of prices, proportional to the demand, proportional to the excess of demand). Our objective is to compare the different methods of updating prices based on those of the lagrangian relaxation solving method.