The supply chain approach to planning and procurement management

Hewlett-Packard Journal, Feb, 1997 by Gregory A. Kruger

The supply chain approach models stochastic events influencing a manufacturing organization's shipment and inventory performance in the same way that a mechanical engineer models tolerance buildup in a new product design. The objectives are to minimize on-hand inventory and optimize supplier response times.

This paper describes the processes and equations behind a reengineering effort begun in 1995 in the planning and procurement organizations of the Hewlett-Packard Colorado Springs Division. The project was known as the supply chain project. Its objectives were to provide the planning and procurement organizations with a methodology for setting the best possible plans, procuring the appropriate amount of material to support those plans, and making up-front business decisions on the costs of inventory versus supplier response time (SRT),(*) service level to SRT objectives, future demand uncertainty, part lead times, and part delivery uncertainty. The statistical modeling assumptions, equations, and equation derivations are documented here.

Basic Situation

Consider a factory building some arbitrary product to meet anticipated customer demand. Since future demand is always an uncertainty, planning and procurement must wrestle with the task of setting plans at the right level and procuring the appropriate material. The organization strives to run the factory between two equally unattractive scenarios: not enough inventory and long SRTs, or excessive inventory but meeting SRT goals. In fact, more than one organization has found itself with the worst of both worlds--huge inventories and poor SRTs.

The supply chain project focused on characterizing the various stochastic events influencing a manufacturing organization's shipment and inventory performance, modeling them analogously to the way a mechanical engineer would model a tolerance buildup in a new product design.

Problem Formulation

For a particular product, a factory will incur some actual demand each week, that is, it will incur demand [D.sub.i] in week i, for i = 1, 2, 3, ... From a planning and procurement perspective, the problem is that looking into the future the [D.sub.i] are unknown.

Let [P.sub.i] be the plan (or forecast) for week i in the future. Now for each week, the actual demand can be expressed as the planned demand plus some error: [D.sub.i] = [P.sub.i] [e.sub.i].

The MRP (material requirements planning) system, running at intervals of R weeks, evaluates whether to order more material to cover anticipated demand, and if the decision is to order, how much to order. Given a lead time of L weeks to take delivery of an order placed to a supplier now for some part, the material in the supply pipeline must cover real demand for the next L R weeks. By supply pipeline we mean the quantity of the part already on hand at the factory plus the quantity in orders placed to the supplier and due for delivery over the next L weeks.

For simplicity, assume for the remainder of this discussion that we are dealing with a part unique to one product and used only once in building the product. We will remove these constraints later but for now it will help to focus on the key concepts.

Define X to be the unknown but actual demand the factory will experience for this part over the next L R weeks:

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In statistical terminology, X is a random variable, that is, we cannot say with certainty the value it will take next, but with some assumptions about the nature of the planning errors ([e.sub.i]), the distribution of X can be characterized. Specifically, we will make the assumption that the [e.sub.i] are distributed according to the Gaussian (normal) distribution with mean zero and variance [[Sigma].sup.2] (see Fig. 1). The assumption that the mean of the [e.sub.i] is zero says that our plans are unbiased, that is, the factory is not consistently overestimating or underestimating future demand. Thus, the average of the differences between the plan and the actual demand over a reasonable period of time would be about zero. The normal distribution is symmetric, so we are saying there is equal probability in any week of actual demand being above or below plan. The variance measures how large the planning errors can get in either direction from zero.

[Figure 1 ILLUSTRATION OMITTED] We would like to know both the expected value of X and its variance. Knowing these two values will form the basis for the ultimate decision rules for replenishment order sizes placed to the supplier for our part.

We will use the following notation: E(x) represents the expected value of the random variable x, and V(x) represents the variance of the random variable x.

Before launching into the derivation of the expected value of the real demand over the next L R weeks, note that L itself is a random variable. When an order is placed with the supplier, delivery does not always come exactly on the acknowledgment date. There is some uncertainty associated with when the replenishment order will arrive. Like the planning errors, we will assume that the delivery errors are normally distributed about zero. Thus: