Concept explainers
(a)
To determine: The optimal rotational cycle time.
Introduction:Economic order quantity refers to the approach which is used to evaluate flow and volume of order needed to fulfill consumers demand while reducing the cost per order.Such tool is used by the organization to handle andmanage operations and logistic operations.
(a)
Explanation of Solution
Optimal cycle time of the fiber store is as follows.
Apply variables of each type of items and determine optimal cycle time by the following formula.
Similarly, the modified holding cost for each of the item should be calculated by the following method.
Item | Annual Sales | Cost | |||||
A | 25,900 | 1125000 | .003 | .00063 | .000615 | 120 | 15.9285 |
B | 42,000 | 1375000 | .002 | .00042 | .000407 | 80 | 17.094 |
C | 14,400 | 825000 | .008 | .00168 | .00165 | 160 | 23.76 |
D | 46,000 | 800000 | .002 | .00042 | .000395 | 80 | 18.17 |
E | 12,500 | 450000 | .001 | .0021 | .002041 | 60 | 25.5125 |
F | 75,000 | 975000 | .005 | .00105 | .000969 | 120 | 72.675 |
G | 30,000 | 725000 | .004 | .00084 | .000805 | 20 | 24.15 |
H | 18,900 | 300000 | .007 | .00147 | .001377 | 60 | 26.0253 |
SUM | 0.008259 | 700 | 223.315 |
Put the value of each item to determine the optimal cycle time.
Hence, the optimal rotation cycle time is 2.50 per year
(b)
To determine:TheSize of the lots.
Introduction: Economic order quantity sometimes EOQ refers to the technique used by the organizations to determine the volume and frequency or order needed to fulfill the customer demand while minimizing the cost of the item.
(b)
Explanation of Solution
Determine the optimal quantity of each item by the following formula.
Same procedure will be followed to calculate optimal quantity for each item
Item | Demand | Time | Quantity (Q) |
A | 25,900 | 2.5 | 64750 |
B | 42,000 | 2.5 | 105000 |
C | 14,400 | 2.5 | 36000 |
D | 46,000 | 2.5 | 115000 |
E | 12,500 | 2.5 | 31250 |
F | 75,000 | 2.5 | 187500 |
G | 30,000 | 2.5 | 75000 |
H | 18,900 | 2.5 | 47250 |
(C)
To determine:Average annual cost of holding and setup cost at the optimal solution.
Introduction: Economic order quantity sometimes EOQ refers to the technique used by the organizations to determine the volume and frequency or order needed to fulfill the customer demand while minimizing the cost of the item.
(C)
Explanation of Solution
Procedure to find average annual cost of holding and setup cost is discussed below.
Determine the annual holding and setup cost by the following formula.
Determine the values to calculate annual holding cost for the item A by the following method
Same procedure will be followed to calculate optimal quantity for each item
Item | Setup cost (K*D/Q) | Holding Cost (H*Q/2) | Total |
A | 48 | 19.91 | 67.91 |
B | 32 | 21.37 | 53.37 |
C | 64 | 29.70 | 93.70 |
D | 32 | 22.71 | 54.71 |
E | 24 | 31.89 | 55.89 |
F | 48 | 90.84 | 138.84 |
G | 8 | 30.19 | 38.19 |
H | 24 | 32.53 | 56.53 |
SUM | 559.14 |
Hence, annual cost of holding and setup is $559.14
(d)
To determine: Contractual obligation that G might have with the fabrics that would stop them from implementing the policy mention in part (a) and (b).
Introduction:Economic order quantity sometimes EOQ refers to the technique used by the organizations to determine the volume and frequency or order needed to fulfill the customer demand while minimizing the cost of the item.
(d)
Explanation of Solution
With the responsibility or obligation, the time required to supply 3 shipments will be 4 times in a year instead of 2.5. Hence, the size of the optimal quantity will vary as the cycle time being changed to 4 times in a year.
Hence, to make shipment thrice in a year it is very much important for the firm to change its cycle time and optimal quantity of every item to remain focused in their commitment.
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Chapter 4 Solutions
Production and Operations Analysis, Seventh Edition
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