Distributed Auction Algorithms for the Assignment Problem with Partial Information

operations centers (MOC), in which multiple DMs with partial information and partial control over assets are involved in the development of operational level plans. The MOC emphasizes standardized processes and methods, centralized assessment and guidance, networked distributed planning capabilities, and decentralized execution for assessing, planning and executing missions across a range of military operations  Abstract—Task-asset assignment is a fundamental problem paradigm in a wide variety of applications. Typical problem setting involves a single decision maker (DM) who has complete knowledge of the weight (reward, benefit, accuracy) matrix and who can control any of the assets to execute the tasks. Motivated by planning problems arising in distributed organizations, this paper introduces a novel variation of the assignment problem, wherein there are multiple DMs and each DM knows only a part of the weight matrix and/or controls a subset of the assets. We extend the auction algorithm to such realistic settings with various partial information structures using a blackboard coordination structure. We show that by communicating the bid, the best and the second best profits among DMs and with a coordinator, the DMs can reconstruct the centralized assignment solution. The auction setup provides a nice analytical framework for formalizing how team members build internal models of other DMs and achieve team cohesiveness over time. [1]. In this vein, we are developing analytical and computational models for multi-level coordinated mission planning and monitoring processes associated with MOCs, so that they can function effectively in highly dynamic, asymmetric, and unpredictable mission environments. Two key problem areas are: 1) realistic modeling of multi-level coordination structures that link tactical, operational and strategic levels of decision making; and 2) collaborative planning with partial information and partial control of assets. In the collaborating planning problem, each DM “owns” a set of assets and is responsible for planning certain tasks. Each task is characterized by a vector of resource requirements, while each asset is characterized by a vector of resource capabilities (see Fig. 1). Multiple assets (from the same DM or multiple DMs) may be required to process a task. The degree of match between the task-resource requirement vector and asset-resource capability vector determines the accuracy of task execution. In addition, the elements of