Chapter 12, Problem 28P

a)

Summary Introduction

To determine: The Economic order quantity.

Introduction: Inventory management is the process of ordering, storing and using inventory of the company such raw material, components and finished goods. It governs the flow of goods from manufacturers to warehouse and to the point of sale. The key function is to maintain record of flow of new or returned products which enters or leaves the company.

Answer to Problem 28P

The economic order quantity for vendor A is 336.07 units and for vendor B is 335.08 units.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Annual}\text{demand,D}=8\text{00}\times \text{12}\text{units}\\ =\text{9,600}\text{units}\\ \text{Order}\text{cost,S}=\text{\$50}\text{per}\text{order}\\ \text{Annual holding cost}=50\%\text{of}\text{purchase}\text{price}\end{array}$

Vendor 1
Quantity	Price
1-499	$17.00
500-999	$16.75
1,000+	$16.50
Vendor 2
1-399	$17.10
400-799	$16.85
800-1,199	$16.60
1,200+	$16.25

Formula:

$\text{EOQ,Q}=\sqrt{\frac{\text{2DS}}{\text{H}}}$

Where

$\begin{array}{c}\text{D}=\text{Demand}\\ \text{S}=\text{Ordering}\text{cost}\\ \text{H}=\text{Holding}\text{cost}\end{array}$

Calculation of Economic order quantity:

For vendor 1 with quantity 1-499:

$\begin{array}{l}=\sqrt{\frac{\text{2}\times 9\text{,600}\times \text{50}}{0.5\times 17}}\\ =336.07\text{units}\end{array}$

EOQ is calculated by multiplying 2, 9600 and 50 and dividing the resultant $0.5\times 17$ and taking square root which gives 336.07 units.

Same calculation procedure follows for the rest of the quantities and the result is,

D	9600
S	$50.00
Vendor 1
Quantity	Price	H	EOQ
1-499	$17.00	$8.50	336.07
500-999	$16.75	$8.38	338.57
1,000+	$16.50	$8.25	341.12
Vendor 2
1-399	$17.10	$8.55	335.08
400-799	$16.85	$8.43	337.56
800-1,199	$16.60	$8.30	340.09
1,200+	$16.25	$8.13	343.74

Working:

Based on the above calculation, the EOQ for vendor A is 336.07 units and for vendor B is 335.08 units.

Hence, the economic order quantity for vendor A is 336.07 units and for vendor B is 335.08 units.

b)

Summary Introduction

To determine: The quantities to be ordered and supplier to be selected.

Answer to Problem 28P

Vendor 2 should be selected at 1,200 units of ordering quantities

Explanation of Solution

Given information:

$\begin{array}{c}\text{Annual}\text{demand,D}=8\text{00}\times \text{12}\text{units}\\ =\text{9,600}\text{units}\\ \text{Order}\text{cost,S}=\text{\$50}\text{per}\text{order}\\ \text{Annual holding cost}=50\%\text{of}\text{purchase}\text{price}\end{array}$

Vendor 1
Quantity	Price
1-499	$17.00
500-999	$16.75
1,000+	$16.50
Vendor 2
1-399	$17.10
400-799	$16.85
800-1,199	$16.60
1,200+	$16.25

Formula:

$\text{Total}\text{cost}=\text{PD}+\frac{\text{Q}}{\text{2}}\times \text{H+}\frac{\text{D}}{\text{Q}}\times \text{S}$

Calculation of ordering quantities:

D	9600
S	$50.00
Vendor 1
Quantity	Price	H	EOQ	Holding cost	Ordering cost	Purchase cost	Total cost
336	$17.00	$8.50	336.07	$1,428.00	$1428.6	$163,200.00	$166056.57
500	$16.75	$8.38	338.57	$2,093.75	$960.0	$160,800.00	$163853.75
1000	$16.50	$8.25	341.12	$4,125.00	$480.0	$158,400.00	$163005.00
Vendor 2
335	$17.10	$8.55	335.08	$1,432.13	$1432.8	$164,160.00	$167024.96
400	$16.85	$8.43	337.56	$1,685.00	$1200.0	$161,760.00	$164645.00
800	$16.60	$8.30	340.09	$3,320.00	$600.0	$159,360.00	$163280.00
1200	$16.25	$8.13	343.74	$4,875.00	$400.0	$156,000.00	$161275.00

Table 1

Working:

Based on the above calculations it can be inferred that Vendor 2 can be selected because the total cost is least at 1,200 ordering quantities (refer table1).

Hence, vendor 2 should be selected at 1,200 units of ordering quantities.

c)

Summary Introduction

To determine: The total cost for most economic order quantities.

Answer to Problem 28P

The optimum ordering quantity is 1200 units and total annual cost is $161275.00.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Annual}\text{demand,D}=8\text{00}\times \text{12}\text{units}\\ =\text{9,600}\text{units}\\ \text{Order}\text{cost,S}=\text{\$50}\text{per}\text{order}\\ \text{Annual holding cost}=50\%\text{of}\text{purchase}\text{price}\end{array}$

Vendor 1
Quantity	Price
1-499	$17.00
500-999	$16.75
1,000+	$16.50
Vendor 2
1-399	$17.10
400-799	$16.85
800-1,199	$16.60
1,200+	$16.25

Calculation of total cost:

Table 1 provides the calculation for total cost.

Hence, the optimum ordering quantity is 1200 units and total annual cost is $161275.00.

d)

Summary Introduction

To determine: The factors to be considered besides total cost.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Annual}\text{demand,D}=8\text{00}\times \text{12}\text{units}\\ =\text{9,600}\text{units}\\ \text{Order}\text{cost,S}=\text{\$50}\text{per}\text{order}\\ \text{Annual holding cost}=50\%\text{of}\text{purchase}\text{price}\end{array}$

Vendor 1
Quantity	Price
1-499	$17.00
500-999	$16.75
1,000+	$16.50
Vendor 2
1-399	$17.10
400-799	$16.85
800-1,199	$16.60
1,200+	$16.25

Factors to be considered besides total cost:

Apart from making decision based on total cost some other factor also have to be considered for making decisions to avoid uncertainty. Some other factors like perishability of the chemicals, the environment in which the chemicals are stored, storage space to handle 1,200 pounds of chemical have to be taken into account.