Control limit models for cash management in bank branches

Abstract

Development of policies for maintaining adequate cash balance in bank branches and transferring of excess cash from surplus branches to Central Office or deficit branches, are, indeed, major tasks faced by commercial banks in India. Some of the commercial banks adopt a hierarchical structure consisting of three levels for operating the cash management policies. The Central Office, the Link Branches and other branches together form the three levels. The Central Office controls the Link Branches which in turn control the other branches. At the branch level, the problem is to determine the amount of cash to be drawn from/remitted to the Link Branch and the timings. Link Branches face a similar problem vis—a-vis the Central Office. At the Central Office, the problem is to determine the amount to be ingested in/withdrawn from short term assets and the timings. For the bank chosen for the study, the frequency of withdrawals/remittances between branches and the Link Branch varied between 30 to 120 per year across branches. The objectives of the study were: (a) to identify appropriate models for developing decentralized control limits for branch level cash management which minimize the sum total of holding costs of cash and transfer costs and (b) to develop a method of coordination at the Link Branch level for improved performance. Two years’ daily cash flow data, from eight branches of a private sector scheduled commercial bank, were used. The parameters of the models were estimated from first year's data and were then applied on the second year's data for comparisons. The following were the major findings: _ The Miller and Orr model, recommended by some of the banks, fared better than actual practice, but fared significantly worse than the best policies hat could be obtained post, facto. This was attributed to drift in daily cash flows, a violation of one of the basic assumptions of the model. Adjustments for monthly changes in the cash flow distributions as well as adjustments for seasonality did not lead to significant improvement. The Baumol model, recommended by some of the banks for situations of drift in daily cash flows, gave good results, but fared worse than a Stochastic Dynamic Programming model. This was attributed to violation of the assumption of uniform daily cash flows. The Stochastic Dynamic Programming formulation and a method of ‘enumeration’ based on first year's data were giving good results on the second year’s data. The cash flow distribution was stable across consecutive years. The method of ‘enumeration’ being computationally simpler has potential for practice. Constraints on transfer of cash imposed by terms of contract with insurance companies resulted in cash transfers being effected in multiple lots. A minor variant of the policy structure, applicable for situations without such constraints, was found to give the best results for situations involving constraints also. Application of control limit models at the branch level in a decentralized set up led to unproductive cash transfers between branches and the Link Branch. Such unproductive cash transfers were eliminated using a procedure for coordination at the Link Branch - branches network level involving selection of branches for cash transfers. Four methods viz. a Knapsack model, an index method based on ‘transfer cost per unit of excess cash’,' a modified index method with weightage for expected re—transfer cost and the method of random selection were used for choosing branches for cash transfers. The first three methods led to significant reduction in number of transfers and transfer costs. The study gave insights into the characteristics of cash flows and the cash management phenomenon at the branch level. It helped in identifying appropriate and operationally viable methods for cash control at the branch level as well as at the Link Branch ~ branches network level .