Methods for parts procurement quantity determination where demand is uncertain for the product in which the parts are used

Claim 1

A stochastic method for determining, over a series of time periods, parts procurement requirements for products, certain said parts used in a plurality of products, wherein actual demand for said products is unknown, said method adapted to meet a specified service level for all products and to minimize expected excess part inventories, the method having inputs comprising, lists of parts for each said product, prices for said parts, and forecasts of demands for each said product in each time period, the method comprising computer implemented steps of: a. deriving a first cumulative demand D' ci ,t for each part c i through a current time period t, and a second cumulative demand D ci ,t for each part c i through a time period t-1, added to the demand for each part in current time period t, modified by a specified volume fraction of actual demand for each part in period t that is to be satisfied in period t, each cumulative demand expressed by a mean and standard deviation; b. determining a minimum cumulative procurement quantity q'* ci ,t for each part through time period t that meets said specified service level, from a demand distribution function F Dci ,t from said second cumulative demand; c. finding a factor (λ), for each part, at said determined minimum cumulative procurement quantity, that satisfies equation 6 t : ##EQU14## where: c i is part i, P ci is the cost of part i, t is the time period, q' ci ,t is the cumulative procurement of part i up to period t, F D'ci ,t (q' ci ,t) is the cumulative distribution function of the random variable q' ci ,t, * means, at optimality, λ t is the LaGrange Multiplier for time period t, ƒ Dci ,t (q' ci ,t) is the density function of the random variable q' ci ,t, F Dci ,t (q' ci ,t) is the cumulative distribution function of the random variable q' ci ,t, i means for all i, i.e., i=1,2, . . . d. employing a maximum value factor (λ) found in step c to derive for each part, a new cumulative procurement quantity from equation 6 t over all time periods through t, and based thereon, an overall service level for each part, said overall service level for each part determined by taking the product of cumulative demand distribution functions for all parts, as determined from said second cumulative demands, evaluated at said new cumulative procurement quantity; e. finding if said new cumulative procurement quantities for all parts provide a service level equal to said specified service level, and, if not, revising said factor (λ), and repeating steps d and e employing the revised factor (λ) until said specified service level is achieved; and f. employing resultant procurement quantities that enable achievement of the service level for acquisition of said parts.