The Wilson lot size formula The Wilson lot size formula in...

The Wilson lot size formula The Wilson lot size formula in economics says that the most economical quantity $Q$ of goods (radios, shoes, brooms, whatever) for a store to order is given by the formula $Q=\sqrt{2 K M / h},$ where $K$ is the cost of placing the order, $M$ is the number of items sold per week, and $h$ is the weekly holding cost for each item (cost of space, utilities, security, and so on). To which of the variables $K, M,$ and $h$ is $Q$ most sensitive near the point $\left(K_{0}, M_{0}, h_{0}\right)=(2,20,0.05) ?$ Give reasons for your answer.

The Wilson lot size formula The Wilson lot size formula in
economics says that the most economical quantity $Q$ of goods
(radios, shoes, brooms, whatever) for a store to order is given by the
formula $Q=\sqrt{2 K M / h},$ where $K$ is the cost of placing the order,
$M$ is the number of items sold per week, and $h$ is the weekly holding
cost for each item (cost of space, utilities, security, and so on). To
which of the variables $K, M,$ and $h$ is $Q$ most sensitive near the point
$\left(K_{0}, M_{0}, h_{0}\right)=(2,20,0.05) ?$ Give reasons for your answer.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Sensitivity Analysis

Sensitivity analysis examines how changes in the input parameters of a model, such as ordering cost, demand rate, and holding cost, affect its output. In the context of the EOQ model, it assesses which variables have a larger influence on the optimal order quantity, thereby helping decision-makers understand where inaccuracies or fluctuations might have significant impacts.

Partial Derivatives and Parameter Elasticity

Using partial derivatives, one can mathematically quantify the sensitivity of the optimal order quantity to changes in each parameter of the EOQ formula. This approach helps in calculating the rate at which the order quantity changes with respect to a small change in ordering cost, demand, or holding cost, providing insight into the elasticity of the model and identifying which variable the optimal quantity is most sensitive to.

Economic Order Quantity (EOQ) Model

The EOQ model, also known as the Wilson lot size formula, helps determine the ideal order quantity that minimizes total inventory costs by balancing ordering costs against holding costs. This model finds widespread use in operations management and inventory control for optimizing stock levels and reducing overall costs.

Transcript

00:01 The wilson lot size formula economics is the most economic quantity q of goods for a store to order is given by this formula q, where case cost of placing order, m numbers, items sold per week, h is weekly holding cost for each item.

00:16 So we want to find which of the variables, k, m, and h is q most sensitive near this given point.

00:25 So for that, we're looking at the total differential, and so we are given in the book, a formula for that.

00:30 That.

00:31 This will give us a change.

00:34 And that is that dq is equal to the partial of k first at our initial point times dk, plus the partial with respect to m at our initial point times d .m.

00:55 Plus the partial derivative with respect to h at p .0 times d .h.

01:03 So the first thing i want to do, do is find what exactly these partial derivatives are.

01:07 So first starting with qk.

01:12 Here i'm going to have to use my chain rule.

01:14 So this is really just to the one -half.

01:15 So i have a one -half.

01:17 Taking the derivative of the inside, outside, i mean, 2km over h.

01:23 It's a negative one -half.

01:25 And then i multiplied by the derivative of the inside.

01:27 I am taking it with respect to k, so i'll just get 2m over h...