Abstract:
This article explains how one can apply the logistics OPTIPRO model to provision spare parts to a pre-assigned desired operational availability. OPTIPRO is a versatile logistics model computer programmed and designed by the Dr. Joseph E. Brierly. The model offers unique capability to selectively emphasize provisioning factors appropriate to highly specialized situations. Unit spare part cost may be inconsequential for some situations where volume or weigh is of more importance as in space travel. For obvious reasons, operational availability of a space vehicle is more important than cost of and ease of reordering parts for a long-term space journey since limited ability exists for receiving spare parts in outer space. For land fleets spare parts are normally much easier to reorder. So, operational availability is tied directly to the timing on ordering and receiving spare parts.
The article assumes stockage demands are Poisson distributed. System operational availability is viewed as an overall constraint. One preselects the operational availability desired. OPTIPRO computes optimal spare parts provisioning relative to the factors considered relevant such as storage capacity, cost of line replaceable units (LRUs), failure rates of LRUs, mean time to repair an LRU, and weight and volume of a required spare part.
The article proves that under fairly unrestricted conditions optimal spare parts are independent of weighting factors. Said another way, one obtains the same optimal provisioning regardless of whether one considers a factor, such as part maintainability twice as important as volume or weight of the spare part. Weighting of factors is irrelevant because optimal spare parts are determined only by whether a factor is considered or not. This is a dramatic result that is proven in this article. In essence, the situation is like a Boolean operator, which can only assume values zero or one. Either a factor is considered or not considered. If it is considered than weighting of factors have no impact on optimal provisioning to availability.
This article on Optimal Provisioning uses several fine references. The Advanced Calculus book by David V. Widder was a well-known text book on Probability and Statistics that was used at Wayne State University in Advanced Calculus courses for a number of years when Dr. Brierly was a graduate student there. Similarly, An Introduction to Probability Theory and Its application by Dr. William Feller was also a standard textbook on Probability theory during that same period used in many universities including Wayne State University. Bernie Price was a colleague of Dr. Joseph Brierly working for the US Army who motivated Dr. Brierly to put the problem of optimizing availability on a solid mathematical basis. Both Bernie Price and Dr. Joseph Brierly were members of the US Army Logistics Support Technical Working Group during the early 1980s when this article was first conceived.
