Myopic and stationary solutions for stochastic cash balance problems

This paper presents constructive solutions to stochastic cash balance problems. The model studied is in a periodic review framework with convex holding and shortage costs levied both in the beginning and at the end of each period. Transaction costs are linear, with the possibility of unequal fixed and proportional parts for orders and disposals. Optimal myopic solutions are presented for convex and linear costs. The application of an integral of the cumulative demand distribution yields simple formulae for solving the exact values of the policy parameters. The logistic distribution is used to obtain results readily applicable in day-to-day decision-making. Approximations of the Wilson formula type are developed and compared with earlier contributions. Conditions for the optimality of myopic policies are also presented. Stationary solutions are developed, and compared with myopic results in order to evaluate the amount of suboptimality. The stationary distribution and the optimal policy are given for the bilateral exponential demand distribution case. All results have been programmed and tested against the local finance market data.