A cash transportation vehicle routing problem with combinations of different cash denominations

Abstract

This paper investigates a new cash transportation problem, which is a variant of the capacitated vehicle routing problem. To better satisfy the demands of customers (e.g., banks, large retailers, shopping centers, automated teller machines, etc.), the combination of different cash denominations (i.e., $100, $50, $20, etc.) is considered. The robbery risk, which is measured by both the amount of cash being carried and the distance covered by the vehicle carrying the cash, is limited by a risk threshold. The problem is formulated as mixed‐integer linear programming to minimize the total cost, which consists of the total travel cost and the total penalties due to the unmet expected demand of customers. A combined hybrid tabu search metaheuristic is proposed to solve this problem. Tabu search is adopted for determining routing decisions while three methods, namely the exact method, the greedy method, and the mixed method, are proposed to be embedded within the tabu search to determine the denomination combination strategy. The numerical studies show that the proposed method makes a good tradeoff between the solution quality and the computation time. Experimental results also reveal the effects of the unit penalty and the risk threshold.