Chapter 10, Problem 30P

a

Summary Introduction

Interpretation:

Calculation of value of safety stock:

Concept Introduction: Inventory management is the process of managing the company’s stock so that there are no stock-outs. It includes ordering, storing, managing the stock.Stock keeping unit is the service or product identification code, which is a machine-readable bar code. It helps the company to track the product.

Explanation of Solution

Safety stock is calculated by subtracting the demand value from the reorder point. Demand value is the multiple of daily demand of 25 units and the lead time is 4 days.

  $\begin{array}{l}\text{Safety}\text{Stock}\text{=}\text{Reorder}\text{point}\text{-}\text{Demand}\\ \text{=}\text{120}\text{units-}\text{(25}\text{units×}\text{4days)}\\ \text{=}\text{120}\text{units-}\text{100}\text{units}\\ \text{=}\text{20}\text{units}\end{array}$

Hence, the safety stock is 20 units.

b

Summary Introduction

Interpretation:

Service level provided by reorder point.

Concept Introduction: Inventory management is the process of managing the company’s stock so that there are no stock-outs. It includes ordering, storing, managing the stock. Stock keeping unit is the service or product identification code, which is a machine-readable bar code. It helps the company to track the product.

Explanation of Solution

The service level for all the three stock keeping units.

Stock keeping unit 1:

It is calculated by adding two values. First value is the multiple of daily demand and lead-time and second value is the multiple of Z, standard deviation, and square root of lead time. However, the z value is unknown in the equation. Thus, the equation should be remodeled to find the value of Z.

  $\text{Reorder}\text{point}\text{=}\left(\begin{array}{l}\left(\text{Demand×}\text{Lead}\text{time}\right)\text{+}\\ \text{(Z×}\text{Demand×}\text{Standard}\text{deviation}\text{during}\text{leadtime)}\end{array}\right)$

  $\text{120}\text{units=}\text{(25}\text{units×}\text{4}\text{days)+(Z}\text{×}\text{25}\text{units×}\text{1}\text{day)}$

  $\text{120}\text{units=}\text{100}\text{units+(Z}\text{×}\text{25}\text{units×}\text{1}\text{day)}$

  $\text{120}\text{units-}\text{100}\text{units=}\text{Z}\text{×}\text{25}\text{units}$

  $\frac{\text{20units}}{\text{25}\text{units}}\text{=}\text{Z}$

  $Z=0.8$

From the normal distribution table, service value is 0.7881 or 78.81%.

Stock keeping unit 2:

It is calculated by adding two values. First value is the multiple of daily demand and lead-time and second value is the multiple of Z, standard deviation, and square root of lead time. However, the z value is unknown in the equation. Thus, the equation should be remodeled to find the value of

  $\text{Reorder}\text{point}\text{=}\left(\begin{array}{l}\left(\text{Demand×}\text{Lead}\text{time}\right)\text{+}\\ \text{(Z×}\text{Demand×}\text{Standard}\text{deviation}\times \sqrt{\text{leadtime}}\text{)}\end{array}\right)$

  $\text{120}\text{units=}\text{(25}\text{units×}\text{4}\text{days)+(Z}\text{×}\text{25}\text{units×}\sqrt{4\text{day}s}\text{)}$

  $\text{120}\text{units=}\text{(25}\text{units×}\text{4}\text{days)+(Z}\text{×}\text{25}\text{units×}\text{2}\text{days}\text{)}$

  $\text{120}\text{units-}\text{100}\text{units=}\text{Z}\text{×}\text{2}\text{days}$

  $\frac{\text{20units}}{\text{2}\text{days}}\text{=}\text{Z}$

  $Z=10$

From the normal distribution table, service value is 0.9772 or 97.72%.

Stock keeping unit 3:

It is calculated by adding two values. First value is the multiple of daily demand and lead time and second value is the multiple of Z with the square root of value A. Value A is the sum attained by multiplying standard deviation during demand and the lead time and the value attained by multiplying standard deviation during demand and the lead time and the value attained by multiplying standard deviation during lead-time and square of demand. However, the z value is unknown in the equation. Thus, the equation should be remodeled to find the value of Z.

  $\text{Reorder}\text{point}\text{=}\left(\begin{array}{l}\left(\text{Demand×}\text{Lead}\text{time}\right)\text{+}\\ \left(\text{Z×}\sqrt{\begin{array}{l}\left[\begin{array}{l}{\text{(Standard}}^{}\\ \text{×}\text{Lead}\text{time}\end{array}\right]\\ \left[\begin{array}{l}{\text{(Standard}}^{}\\ \text{×Demand}\end{array}\right]\end{array}}\right)\end{array}\right)$

  $\text{120}\text{units}\text{=100}\text{units}\left(\left(\text{Z×}\sqrt{\begin{array}{l}\left[\text{(25}\text{units)}\times 4day\right]\\ \left[\begin{array}{l}\text{(625}\text{units)}\\ \text{×1}\text{day}\end{array}\right]\end{array}}\right)\right)$

  $\text{120}\text{units}\text{=100}\text{units}\left(\left(\text{Z×}\sqrt{\begin{array}{l}\left[\text{(25}\text{units)}\times 4day\right]\\ \left[\begin{array}{l}\text{(625}\text{units)}\\ \text{×1}\text{day}\end{array}\right]\end{array}}\right)\right)$

  $\text{120}\text{units-100}\text{units}\text{=}\text{Z}\text{×}\sqrt{\text{100}\text{units+625}\text{units}}$

  $\text{20}\text{units}\text{=}\text{Z}\text{×}\sqrt{\text{725}\text{units}}$

  $\text{20}\text{units}\text{=}\text{Z}\text{×}\text{26}\text{.93}\text{units}$

  $\text{Z}\text{=}\frac{\text{20}\text{units}}{\text{26}\text{.93}\text{units}}$

  $\text{Z}\text{=}0.74$

From the normal distribution, service value is 0.7704or77.04%.