Chapter 10, Problem 29P

a

Summary Introduction

Interpretation:

Amount paid by the hotel for desert and frequency of production of desert under its current policy.

Concept Introduction: Materials Requirement Planning is a process in which planning is made for the requirement of raw material required for manufacturing of the finished product.

Explanation of Solution

Demand for desert = 30,000 per year

Production rate = 125 per day

Set up cost = $4

Cost of dessert = $0.40

Daily demand for dessert is calculated by dividing annual demand with the number of days the company can operate in the year.

  $\text{Daily}\text{Demand}\text{=}\frac{\text{Annual}\text{demand}}{\text{Number}\text{of}\text{operating}\text{days}\text{in}\text{the}\text{year}}$

  $\text{Daily}\text{Demand}\text{=}\frac{\text{30,000}\text{desserts}}{\text{365}\text{days}}$

  $\text{Daily}\text{Demand}\text{=}\text{82}\text{desserts}$

Hence, the daily demand is 82 desserts.

Calculation of holding cost.

It is given that holding cost is 300% of the cost of the dessert.

  $\begin{array}{l}\text{Annual}\text{holding}\text{cost}\text{=}\text{300\%×}\text{cost}\text{of}\text{the}\text{dessert}\\ \text{=}\frac{\text{300}}{\text{100}}\text{×}\text{\$0}\text{.40}\text{=}\text{3}\text{×}\text{\$0}\text{.40}\\ \text{=}\text{\$1}\text{.2}\text{per}\text{dessert}\text{per}\text{year}\end{array}$

Hence, the holding cost per dessert is $1.2

Calculation of total holding and ordering cost for given batch quantity.

It is given that the current batch quantity is 300 desserts.

Calculation of annual holding cost:

Annual holding cost is calculated by multiplying the holding cost with two values. First value is calculated by dividing the quantity with 2. Second value is calculated by subtracting the value attained by dividing the daily demand with the production from 1.

  $\text{Annual}\text{holding}\text{cost}\text{=}\frac{\text{Batch}\text{quantity}}{\text{2}}\text{×}\text{Holding}\text{cost×}\left(\text{1-}\frac{\text{Daily}\text{demand}}{\text{Production}\text{rate}}\right)$

  $\text{Annual}\text{holding}\text{cost}\text{=}\frac{\text{300}\text{desserts}}{\text{2}}\text{×}\text{\$1}\text{.2×}\left(\text{1-}\frac{\text{82}\text{desserts}}{\text{125}\text{desserts}}\right)$

  $\text{Annual}\text{holding}\text{cost}\text{=}150\text{desserts}\text{×}\text{\$1}\text{.2×0}\text{.344}\text{desserts}$

  $\text{Annual}\text{holding}\text{cost}\text{=}\$61.92$

Hence, the annual holding cost is $61.92

Calculation of annual ordering cost:

It is calculated by multiplying the setup cost with the value attained by dividing the annual demand with the batch quantity.

  $\text{Annual}\text{ordering}\text{cost}\text{=}\frac{\text{Annual}\text{demand}}{\text{Batch}\text{quantity}}\text{×}\text{Setup}\text{cost}$

  $\begin{array}{l}\text{Annual}\text{ordering}\text{cost}\text{=}\frac{\text{30,000}\text{desserts}}{\text{300}\text{desserts}}\text{×}\text{\$4}\\ \text{=}\text{100}\text{desserts}\text{×}\text{\$4}\\ \text{=}\text{\$400}\end{array}$

Hence, the annual ordering cost is $400.

Calculation of total cost of inventory:

It is calculated by adding the annual holding cost and annual ordering cost.

  $\begin{array}{l}\text{Total}\text{cost}\text{of}\text{inventory}\text{=}\text{Annual}\text{holding}\text{cost+}\text{Annual}\text{ordering}\text{cost}\\ \text{=}\text{\$61}\text{.92+\$400}\\ \\ \text{=}\text{\$461}\text{.9}\end{array}$

Hence, the total cost of inventory is $461.9

Calculation of frequency of dessert production:

It is calculated by dividing the annual demand with the batch quantity.

  $\text{Number}\text{of}\text{batches}\text{produced}\text{annually}\text{=}\frac{\text{Annual}\text{demand}}{\text{Batch}\text{qunatity}}$

  $\text{Number}\text{of}\text{batches}\text{produced}\text{annually}\text{=}\frac{\text{30,000}\text{desserts}}{\text{300}\text{quantity}}$

  $\text{Number}\text{of}\text{batches}\text{produced}\text{annually}\text{=}\text{100}\text{batches}$

Hence, the company will produce 100 batches.

b

Summary Introduction

Interpretation:

Order size required to minimize the total annual cost and amount of savings by using order size.

Concept Introduction: Materials Requirement Planning is a process in which planning is made for the requirement of raw material required for manufacturing of the finished product.

Explanation of Solution

Calculation of order size:

It is calculated by dividing two values and taking the square root of the attained value. First value is the multiple of annual demand and set up cost with 2. Second value is calculated by multiplying the holding cost with the value attained by subtracting the dividing value of daily demand with production rate from 1.

  $\text{Economic}\text{Order}\text{Quantity}\text{=}\sqrt{\frac{\text{2×}\text{Annual}\text{demand×}\text{Set}\text{up}\text{cost}}{\text{Holding}\text{cost}\left(\text{1-}\frac{\text{Daily}\text{Demand}}{\text{Production}\text{rate}}\right)}}$

  $\text{Economic}\text{Order}\text{Quantity}\text{=}\sqrt{\frac{\text{2×}\text{30,000}\text{desserts×}\text{\$4}}{\text{\$1}\text{.2×}\left(\text{1-}\frac{\text{82}\text{desserts}}{\text{125}\text{desserts}}\right)}}$

  $\text{Economic}\text{Order}\text{Quantity}\text{=}\sqrt{\frac{240,000}{\text{\$1}\text{.2×0}\text{.344}}}$

  $\text{Economic}\text{Order}\text{Quantity}\text{=}\sqrt{\frac{240,000}{0.4128}}$

  $\text{Economic}\text{Order}\text{Quantity}\text{=}762.5$

Hence, the economic order quantity is 762.5

Calculation of total holding cost and ordering cost for optimal order quantity:

It is given that the optimal order quantity is 762.5 desserts.

Annual holding cost is calculated by multiplying the holding cost with two values. First value is calculated by dividing the quantity with 2. Second value is calculated by subtracting the value attained by dividing the daily demand with the production from 1.

  $\text{Annual}\text{holding}\text{cost}\text{=}\frac{\text{Batch}\text{quantity}}{\text{2}}\text{×}\text{Holding}\text{cost×}\left(\text{1-}\frac{\text{Daily}\text{demand}}{\text{Production}\text{rate}}\right)$

  $\text{Annual}\text{holding}\text{cost}\text{=}\frac{\text{762}\text{.5desserts}}{\text{2}}\text{×}\text{\$1}\text{.2×}\left(\text{1-}\frac{\text{82}\text{desserts}}{\text{125}\text{desserts}}\right)$

  $\text{Annual}\text{holding}\text{cost}\text{=}381.3\text{desserts}\text{×}\text{\$1}\text{.2×0}\text{.344}\text{desserts}$

  $\text{Annual}\text{holding}\text{cost}\text{=}\$157.38$

Hence, the annual holding cost is $157.38

Calculation of annual ordering cost:

It is calculated by multiplying the setup cost with the value attained by dividing the annual demand with the batch quantity.

  $\text{Annual}\text{ordering}\text{cost}\text{=}\frac{\text{Annual}\text{demand}}{\text{Batch}\text{quantity}}\text{×}\text{Setup}\text{cost}$

  $\begin{array}{l}\text{Annual}\text{ordering}\text{cost}\text{=}\frac{\text{30,000}\text{desserts}}{762.5\text{desserts}}\text{×}\text{\$4}\\ \text{=}39.34\text{desserts}\text{×}\text{\$4}\\ \text{=}\text{\$157}\text{.37}\end{array}$

Hence, the annual ordering cost is $157.37

Calculation of total cost of inventory:

It is calculated by adding annual holding cost and annual ordering cost.

  $\begin{array}{c}\text{Total}\text{cost}\text{of}\text{inventory}\text{=}\text{Annual}\text{holding}\text{cost+}\text{Annual}\text{ordering}\text{cost}\\ \text{=}\text{\$157}\text{.38+\$157}\text{.37}\\ \text{=}\text{\$314}\text{.7}\end{array}$

Annual saving in the total cost of optimal order quantity:

It is calculated by subtracting the total cost of optimal quantity from the total cost of given batch quantity.

  $\text{Annual}\text{saving}\text{=}\text{Total}\text{cost}\text{of}\text{given}\text{batch-}\text{Total}\text{cost}\text{of}\text{optimal}\text{order}\text{quantity}$

  $\begin{array}{l}\text{Annual}\text{saving}\text{=}\$461.9-\$314.7\\ =\$147.2\end{array}$

Hence, the annual saving is $147.2

c

Summary Introduction

Interpretation:

Change in size of refrigerated pantry.

Concept Introduction: The efficiency of output is the actual productivity generated compared with the planned or effective capacity. It is usually calculated by dividing actual output by effective capacity.

Explanation of Solution

The plan to expand the capacity

The lowest inventory cost order size is 762 desserts. However, the refrigerator can only store 300 desserts. Thus, the capacity must increase 462 spaces.