Production and Operations Analysis, Seventh Edition
Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 4, Problem 45AP

(a)

Summary Introduction

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)

Expert Solution
Check Mark

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.

  T*=  j=1 n K j j=1 n H' j ×λ j Where,Kj= Ordering Cost H'j= Modified holding cost λj= Total demand per year Determine the variables for each 8 items given in the table by the following method.Modified holding rate, H'=H(1-λP)Where, H= Holding cost λ= Total demand per year P= Production units per years On putting the above values in the formula H'= (.03+.18)×.03(1-25,9004,500×250)= $0.000615

Similarly, the modified holding cost for each of the item should be calculated by the following method.

    Item Annual Sales Productivity per day ×250CostHolding Cost H=0.18+0.03×costModified Holding Cost H'=H(1-DProduction rate)Ordering cost K=20×setup timeH×D
    A25,9001125000.003.00063.00061512015.9285
    B42,0001375000.002.00042.0004078017.094
    C14,400825000.008.00168.0016516023.76
    D46,000800000.002.00042.0003958018.17
    E12,500450000.001.0021.0020416025.5125
    F75,000975000.005.00105.00096912072.675
    G30,000725000.004.00084.0008052024.15
    H18,900300000.007.00147.0013776026.0253
    SUM0.008259700223.315

Put the value of each item to determine the optimal cycle time.

  T*=  2×700 223.315=2.50

Hence, the optimal rotation cycle time is 2.50 per year

(b)

Summary Introduction

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)

Expert Solution
Check Mark

Explanation of Solution

Determine the optimal quantity of each item by the following formula.

  Qj=λj× T*where, λj= total demand per year T*= optimal cycle time Qj= optimal quantity of each item Determine the value for the first itme A by the following method.QA= 25,900×2.50= 64750

Same procedure will be followed to calculate optimal quantity for each item

    ItemDemand TimeQuantity (Q)
    A25,9002.564750
    B42,0002.5105000
    C14,4002.536000
    D46,0002.5115000
    E12,5002.531250
    F75,0002.5187500
    G30,0002.575000
    H18,9002.547250

(C)

Summary Introduction

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)

Expert Solution
Check Mark

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.

  G (Qj)=Kj×λjQj×H'×Qj2

Determine the values to calculate annual holding cost for the item A by the following method

  G (Qj)= 120×25,90064750+.000615×64,7502= 48+19.91=67.91

Same procedure will be followed to calculate optimal quantity for each item

    ItemSetup cost (K*D/Q)Holding Cost (H*Q/2)Total
    A4819.9167.91
    B3221.3753.37
    C6429.7093.70
    D3222.7154.71
    E2431.8955.89
    F4890.84138.84
    G830.1938.19
    H2432.5356.53
    SUM559.14

Hence, annual cost of holding and setup is $559.14

(d)

Summary Introduction

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)

Expert Solution
Check Mark

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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