UBC Theses and Dissertations
Till cash management model Sick, Gordon Arthur
This thesis develops a model for the management of till cash (currency and coin) of a branch for a Vancouver area credit union. The model is developed in two parts. First, a model is estimated to forecast cash demand and then a cash order algorithm is developed. Two statistical models are developed to estimate cash demand. The first employs Box-Jenkins time series techniques. This model fails because the cash flow data are non-stationary, exhibiting both a growth trend and high autocorrelations at large lags. In the second model, a growth trend for real weekly cash flows is first estimated, incorporating an asymptotic capacity constraint. The real cash flow trend is converted to a nominal trend and used as the weight in a linear weighted least squares model for daily cash flows, in which the explanatory variables are dummy variables to indicate days of the week, months of the year, incidence of pay days, etc. The consistency of the resulting forecast model is also discussed. To develop a cash order algorithm, steady state models are first considered. These models are generally based on stationary cash demand, constant delivery lag times for orders and other assumptions that are inappropriate in this till cash management setting. To relax the steady state assumptions a general dynamic programming framework is developed for the cash management model that allows for either penalty costs for cash-outs (cash shortages) or a chance constraint involving the probability of a cash-out. Because of non-stationarity of the cash flows the dynamic program cannot be solved directly, but an approximate solution is obtained using a simulation technique. The resulting algorithm is tested on historical data and the results are discussed briefly.