Title: Using Contingency Matrices and Tensors for Allocation in Accounting Speaker: Peter Chew Date/Time: Wednesday, February 10, 2010, 1:00 pm Location: CSRI Building/Room 90 (Sandia NM) Brief Abstract: A common task in accounting is the allocation of a total amount into shares. Owing to the discrete characteristics of money, allocation often cannot be exact; for example, if $100 is divided into thirds, the result (after rounding) could be three shares of $33.33. However, as is evident, this results in a shortfall of a cent, which for many applications is not acceptable; it may be preferable or even required that the $100 be allocated into two shares of $33.33 and one of $33.34 to exhaust an account balance. One way of looking at this problem is as the construction of a vector subject to a constraint on the vector sum. To complicate matters further, allocation may be in more than one mode. An example is an array of I payments, each on a particular date, which must be allocated first among J beneficiaries, and then allocated again to K heirs of the beneficiaries. In this case, we wish to construct a three-way I x J x K tensor of payments, where the entry at cell (i, j, k) represents the amount of the payment made to heir k of beneficiary j at time i. Just as we might wish to constrain the allocation in a vector, there may be a requirement to constrain the allocations in a tensor. We describe a real-life problem of this type that we have encountered and solved. In our case, the constraints on the tensor were (1) that the lateral slices sum to exactly the respective amounts of the periodic payments; and (2) that the horizontal vectors in the tensor sum to exactly the amounts generated by an independent system. We describe the solution to this problem, which involved modifying and developing a technique previously used for construction of contingency tables from fixed marginals (Hu and Mukerjee 2002); the computation time required is proportional to I x J X K. The solution has been implemented in production in a project which involves thousands of allocations, each into a separate payment tensor. Our approach is conservatively projected to save thousands of hours of manual labor.CSRI POC: Andy Wilson, (505) 844-1089 |