Case 9: Baseball Card Emporium Demand Data 6000 Units Annual

Case 9 2 Baseball Card Emporiumdatar6000unitsannual Demand

This assignment involves calculating the economic order quantity (EOQ), total costs, and transportation-related expenses for Baseball Card Emporium based on given data such as annual demand, inventory costs, and different transportation modes. The main goal is to analyze which transportation alternative—motor carrier or air carrier—is more cost-effective while considering inventory, ordering, and transit costs.

Paper For Above instruction

The Baseball Card Emporium faces the challenge of optimizing its inventory management and transportation strategies to minimize costs while fulfilling a consistent annual demand of 6,000 units. To achieve this goal, the analysis employs the classic Economic Order Quantity (EOQ) model, integrated with transportation cost considerations for motor and air carriers. This comprehensive approach ensures that the company adopts the most economical and efficient approach for its operations, balancing inventory costs, order costs, and transportation expenses.

Calculation of EOQ (Question 1)

The EOQ formula is given by:

Q = √(2RA / VW)

where:

- R = Annual demand = 6,000 units

- A = Ordering cost per order = $75

- V = Unit value = $96

- W = Unit weight in pounds = 50 pounds

Calculating Q in units:

Q = √(2  6,000  75 / (96 * 50))


= √(900,000 / 4,800)


= √187.5


≈ 13.69 units

Since EOQ typically requires whole units, approximate EOQ is 14 units.

To determine EOQ in pounds, multiply units by weight per unit:

Q in pounds = 14 units * 50 lbs = 700 lbs

Total Cost Without Transportation (Question 2)

Total Annual Cost (TAC) excluding transportation costs combines ordering costs and holding costs:

TAC = (½)  Q  V  W + (A  R) / Q

Calculating:

Holding cost per unit per year = V  W  Inventory carrying rate = 96 * 0.3125 (since 30% of unit value) = 30


(Note: For simplicity, we use the given inventory carrying cost rate of 30%)

Alternatively, directly using provided data:

- Inventory carrying cost per unit per year = $29

- Calculated holding cost per cycle = Q/2 * inventory cost per unit

- Ordering cost per cycle = A

Total cost:

TAC = (½)  14  50  30 + (75  6,000) / 14


= (0.5)  14  1,500 + (450,000) / 14


= 7 * 1,500 + 32,142.86


= 10,500 + 32,142.86


= $42,642.86

Total Cost with Motor Carrier Transportation (Question 3)

Motor carrier introduces transit time (MTT = 4 days). Additional costs include transit inventory and transportation costs.

Transit inventory is calculated as:

Transit inventory = (Q  Y  MTT) / OC

Where:

- Y = inventory carrying cost rate = 18%

- MTT = motor transit time = 4 days

- OC = order cycle in days = (Q / R) * 365

Order cycle:

OC = (Q  365) / R = (14  365) / 6000 ≈ 0.852 days

Transit inventory:

Transit inventory = (14  0.18  4) / 0.852 ≈ (14 * 0.72) / 0.852 ≈ 10.08 / 0.852 ≈ 11.83 units

Additional transportation costs per cycle include:

Motor freight rate = $1.20 per unit


Total transportation cost per cycle:


= Q  freight rate = 14  1.20 = $16.80

Total annual transportation cost:

Transportation cost:


= (Q  freight rate)  (R / Q) = 16.80  (6000 / 14) ≈ 16.80  428.57 ≈ $7,200

Therefore, total costs with motor carrier:

TIC motor = TAC + transportation costs + transit inventory costs


= 42,642.86 + 7,200 + (transit inventory cost)


- Transit inventory cost:


= 11.83 units * $96 = approximately $1,135.68

Total:

TIC motor ≈ 42,642.86 + 7,200 + 1,135.68 ≈ $50,977.54

Total Cost with Air Carrier Transportation (Question 4)

Similarly, air carrier introduces a transit time of 1 day, influencing transit inventory and costs.

Transit inventory:

Transit inventory = (Q  Y  ATT) / OC


= (14  0.18  1) / 0.852 ≈ 2.97 units

Transportation cost:

Air freight rate = $2.50 per unit


Total transportation cost per cycle:


= 14 * 2.50 = $35

Annual transportation cost:

= 35  (6000 / 14) ≈ 35  428.57 ≈ $15,000

Total transportation costs including transit inventory:

Transit inventory cost:


= 2.97 units * $96 ≈ $285.12


Total:


= 42,642.86 + 15,000 + 285.12 ≈ $57,927.98

Comparison and Recommendations (Question 5)

The analysis presents a detailed comparison between the two transportation modes. The motor carrier, despite longer transit times, yields a lower overall total cost (~$50,977.54) compared to the air carrier (~$57,927.98). The significant cost difference primarily stems from lower freight rates and the relatively moderate impact of transit inventory costs for motor transportation.

Given these calculations, Baseball Card Emporium should opt for the motor carrier transportation mode. It provides a more economical solution with total costs approximately $7,000 less than using air transportation. Besides cost savings, motor carriers often provide flexible scheduling and capacity, further favoring their selection in this context.

Conclusion

This comprehensive cost analysis underscores the importance of integrating inventory management with transportation costs to make optimal logistical decisions. Employing EOQ reduces inventory costs, and factoring in transit times and transportation costs refines the decision-making process. The findings clearly favor the motor carrier option for Baseball Card Emporium’s logistics, balancing cost efficiency with reliability.

References

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