AN OPTIMIZATION-BASED HEURISTIC FOR A CAPACITATED LOT-SIZING MODEL IN AN AUTOMATED TELLER MACHINES NETWORK | Science Publications

Journal of Mathematics and Statistics

AN OPTIMIZATION-BASED HEURISTIC FOR A CAPACITATED LOT-SIZING MODEL IN AN AUTOMATED TELLER MACHINES NETWORK

Supatchaya Chotayakul, Peerayuth Charnsetthikul, Juta Pichitlamken and John Kobza

DOI : 10.3844/jmssp.2013.283.288

Journal of Mathematics and Statistics

Volume 9, Issue 4

Pages 283-288

Abstract

This research studies a cash inventory problem in an ATM Network to satisfy customer’s cash needs over multiple periods with deterministic demand. The objective is to determine the amount of money to place in Automated Teller Machines (ATMs) and cash centers for each period over a given time horizon. The algorithms are designed as a multi-echelon inventory problem with single-item capacitated lot-sizing to minimize total costs of running ATM network. In this study, we formulate the problem as a Mixed Integer Program (MIP) and develop an approach based on reformulating the model as a shortest path formulation for finding a near-optimal solution of the problem. This reformulation is the same as the traditional model, except the capacity constraints, inventory balance constraints and setup constraints related to the management of the money in ATMs are relaxed. This new formulation gives more variables and constraints, but has a much tighter linear relaxation than the original and is faster to solve for short term planning. Computational results show its effectiveness, especially for large sized problems.

Copyright

© 2013 Supatchaya Chotayakul, Peerayuth Charnsetthikul, Juta Pichitlamken and John Kobza. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.