CASH FLOW OPTIMIZATION IN DELIVERY SCHEDULING
Abstract The paper examines the inventory routing problem from the perspective of the present value of the cash flow associated with the distribution of a commodity such as propane. We analyze this problem for both deterministic and stochastic customer demands and validate our results on data from a real life distribution operation of propane. The analysis based on the present value of the cash flow indicates that optimization of propane deliveries based on efficiency/cost criteria alone will generate inferior solutions and it would be more advantageous for the company to set deliveries for a large percentage of the customers based on the present value of cash flow. In addition, in the case of stochastic demands, deliveries based on the cash flow consideration will tend to reduce the number of stockouts (i.e. improve both profit and service).
The monotonicity of the threshold detection probability in a stochastic accumulation process
Abstract In this paper we prove for a number of distributions that the probability for the value of the sum of the first k (but not before) of i.i.d.r.v. to exceed a given value A is monotonically increasing in the range k ∗ ( or k ∗ + 1 ) where k ∗ = max k such that kμ ≤A. We conjecture that this monotonicity property is preserved for a much larger family of distribution functions than those examined in the paper.
The Effectiveness of Two Approaches to the Teaching of High School American History
The purpose of this study was to test the effectiveness of studies in depth utilizing selected materials which had been developed for teaching high school American history.