Topoil A Refiner In Indiana Serves Three Customers Near Nash

Topoil A Refiner In Indiana Serves Three Customers Near Nashville T

TopOil, a refiner in Indiana, serves three customers near Nashville, Tennessee, and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses transportation to deliver separately to each customer, with each truck costing $800 plus $250 per stop, totaling $1,050 per truck. TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons per year, and at the small customer, 8 tons per year. Product cost is $10,000 per ton, with a holding cost of 25%. Truck capacity is 12 tons. The assignment asks to analyze different delivery policies, costs, and inventory levels based on shipment strategies.

Paper For Above instruction

This paper evaluates the optimal transportation and inventory policies for TopOil, considering separate deliveries, consolidated shipments, and customized strategies to minimize costs and inventory holdings. The analysis integrates economic order quantity principles, transportation cost structures, and inventory management theories to derive optimal solutions under various scenarios.

Part A: Cost and Inventory Analysis for Full Truckload Delivery per Customer

The first scenario assumes TopOil ships a full truckload each time a customer is running out of stock. The demand for the large customer is 60 tons annually, requiring approximately five shipments (since each truck holds 12 tons: 60/12 = 5). The small customer demands 8 tons annually, requiring approximately one shipment (8/12 ≈ 0.67, rounded up to 1).

Transportation Cost Calculation:

Each truck costs $800 fixed plus $250 per stop. For five shipments to the large customer, total transportation cost = 5 ($800 + $250) = 5 $1050 = $5,250.

For the small customer, one shipment costs $800 + $250 = $1,050.

Holding Cost and Inventory Calculation:

Holding costs are 25% of product cost per year.

Product cost per ton is $10,000, so annual holding cost per ton = 0.25 * $10,000 = $2,500.

Since the shipments are full truckloads, inventory held is on average half the shipment size: 6 tons (half of 12-ton truck).

Inventory value per customer: 6 tons * $10,000 = $60,000.

Annual holding cost per customer: 25% * $60,000 = $15,000.

Days of Inventory Carried:

Assuming uniform demand during a year (365 days), for the large customer with 60 tons demand and one shipment at a time, the average inventory is 6 tons, and the replenishment occurs roughly every 60 days (since 60 tons/year divided by 5 shipments). Thus, days of inventory = (Inventory in tons / daily demand).

Daily demand = 60 tons / 365 days ≈ 0.164 tons/day.

Therefore, days of inventory at large customer: 6 / 0.164 ≈ 36.6 days.

Similarly, for the small customer: 8 tons/year, with approximately one shipment, and an inventory of 6 tons, days of inventory = 6 / (8/365) ≈ 273 days.

However, as demand is lower, actual inventory turnover is less frequent; but given the same shipment size, the days of inventory are higher.

Part B: Costs and Inventory for Separate Shipments to Each Customer

In this scenario, TopOil ships separately to each customer, but without consolidation. The demand remains the same—60 tons for the large and 8 tons for the small customer.

Optimal Delivery Policies:

For separate shipments, the company should aim for order quantities minimizing total costs, potentially using the Economic Order Quantity (EOQ) model, which finds the optimal order size to balance ordering costs and holding costs.

EOQ Calculation:

EOQ = sqrt((2 D S) / H)

Where D = annual demand, S = ordering cost, H = holding cost per unit per year.

S = $4,000 fixed cost per order (assuming the transportation cost is fixed and independent of shipment size for simplicity).

H = 25% of $10,000 = $2,500.

For the large customer:

EOQ = sqrt((2 60 4000) / 2500) = sqrt((480,000) / 2,500) ≈ sqrt(192) ≈ 13.86 tons.

Since truck capacity is 12 tons, this EOQ exceeds capacity, so the maximum shipment is 12 tons.

Thus, shipments are constrained by capacity, and the number of shipments = demand / shipment size.

For smaller demand like 8 tons, the EOQ would be less, but constrained by capacity.

Total Costs:

Total transportation cost = number of shipments * cost per shipment.

Number of shipments for large customer: 60 / 12 = 5.

Total transportation costs = 5 * $1,050 = $5,250.

holding costs:

Average inventory per shipment = 6 tons (half capacity).

Annual holding cost per shipment = 25% 6 $10,000 = $15,000, same as Part A.

Days of Inventory:

As in Part A, for large customers: approx. 36.6 days; for small customers, proportionally adjusted.

Part C: Aggregated Shipments to All Customers on a Single Truck

Now, TopOil considers consolidating shipments such that one truck services all customers in Nashville simultaneously, optimizing vehicle utilization and reducing costs.

Shipment Strategy:

The combined demand is 60 + 8 = 68 tons/year.

Since a truck capacity is 12 tons, the number of shipments needed for combined deliveries = ceil(68/12) ≈ 6 shipments per year.

Transportation Cost Calculation:

Each trip costs $800 + $250 for each stop, and now the stops are combined. The total fixed cost per trip remains $800, but stops increase with each customer.

Assuming one combined stop per shipment for all customers (for simplicity), the cost per shipment remains $1,050; total cost = 6 * $1,050 = $6,300.

Inventory and Storage:

The inventory held at each location is similar but may slightly increase due to combined scheduling, but for simplicity, assume the same as in previous parts.

Inventory levels are dictated by demand and replenishment frequency; for the large customer, approximately 36.6 days of inventory, and for the small customer, proportionally.

Cost and Inventory Reduction:

By consolidating, transportation costs decrease marginally, and inventory holding costs could reduce by aligning replenishment cycles.

Part D: Tailored Policy for Cost Reduction

A potential tailored policy could involve order batching that minimizes total costs. For instance, setting synchronized reorder points that align shipments for all customers, possibly reducing the number of trips from six to fewer by ordering larger quantities less frequently.

Projected Savings and Inventories:

Suppose the company reduces the number of shipments from six to four annually by increasing order quantities strategically, aiming to balance inventory holding and transportation costs.

This will increase per-shipment quantity but decrease shipment frequency, reducing fixed transportation costs, while potentially increasing inventory levels.

Cost and Inventory Impact:

Assuming order quantities are increased accordingly, carrying costs would rise proportionally, but transportation costs would decline. Calculating the precise economic balance requires simulation of demand variability, but generally, this policy can yield cost savings if the increased inventory levels remain manageable.

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Application to Amazon Inventory Strategies

Amazon’s case studies illustrate large-scale inventory and order management. The EOQ model applies to Amazon’s ordering of consumer electronics from Samsung, where the goal is to minimize combined ordering and holding costs.

For Amazon, with monthly demand D=20,000 units, unit cost $100, holding cost rate 20%, fixed order cost $4,000, the EOQ can be calculated as:

EOQ = sqrt((2 D S) / H)

= sqrt((2 20,000 4,000) / (0.20 * 100))

= sqrt((160,000,000) / 20)

= sqrt(8,000,000) ≈ 2,828 units.

If Amazon reduces order size to 2,500 units, the fixed cost needed to make this optimal increases correspondingly, or the order size would no longer be optimal unless the fixed cost decreases.

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