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This research studies a cash inventory problem in an ATM Network to satisfy customerâ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

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