Ingredients R Us Inc Order Distribution Plan Shipping Costs ✓ Solved

Ingredients R Us Inc Order Distribution Planshipping Costs

Ingredients R US, Inc. Order Distribution Plan Shipping Costs from Distribution Center (per pallet) Number of Items Shipped Food Retailers Pallet Orders Distribution Ctr. 1 Distribution Ctr. 2 Distribution Ctr. 3 Total Shipped Total Costs Food Buzz 60 $20.25 $78.15 $27.15 $- Healthy Stuff 78 $50.85 $50.00 $47.90 $- Smoothie City 125 $84.00 $38.40 $65.55 $- Burger Barn 187 $86.65 $25.40 $13.90 $- Café Organic 313 $108.95 $21.50 $33.95 $- Dessert Center 567 $116.45 $7.95 $26.20 $- Total Initial Inventory 1,615 Remaining Inventory 1,615 Constraints Instructions: The ingredients are ordered by pallet and transported from one of three distribution centers. Depending on order type, the nearest distribution center cannot always be utilized to fill orders. Ingredients R US, Inc. has tasked you with satisfying demand while minimizing total cost to ship product to customers. Demand must be met and there is enough stock to have pallets left over. Complete the model above by adding necessary formulas and populate the constraints table. Create a solver model to meet demand while minimizing total costs.

Paper For Above Instructions

Ingredients R Us Inc. faces the challenge of distributing its products efficiently and cost-effectively from three distribution centers to various food retailers. The main goal is to meet the demand of each retailer while minimizing shipping costs. This complex problem can be approached using linear programming techniques through the formulation of a mathematical model.

Understanding the Problem

To formulate a solution, we will break down the problem. The demand for each retailer has been provided along with the shipping costs from each distribution center. The data shows the number of pallets required by each retailer, which serves as the demand that must be satisfied: Food Buzz requires 60 pallets, Healthy Stuff needs 78 pallets, Smoothie City requires 125 pallets, Burger Barn needs 187 pallets, Café Organic demands 313 pallets, and Dessert Center requires 567 pallets.

Shipping Costs

Shipping costs vary between distribution centers:

• Food Buzz: $20.25 from D.C. 1, $78.15 from D.C. 2, $27.15 from D.C. 3
• Healthy Stuff: $50.85 from D.C. 1, $50.00 from D.C. 2, $47.90 from D.C. 3
• Smoothie City: $84.00 from D.C. 1, $38.40 from D.C. 2, $65.55 from D.C. 3
• Burger Barn: $86.65 from D.C. 1, $25.40 from D.C. 2, $13.90 from D.C. 3
• Café Organic: $108.95 from D.C. 1, $21.50 from D.C. 2, $33.95 from D.C. 3
• Dessert Center: $116.45 from D.C. 1, $7.95 from D.C. 2, $26.20 from D.C. 3

The total initial inventory of pallets available is 1,615, which allows for meeting the required shipments while leaving some stock remaining.

Model Formulation

We can define decision variables for the number of pallets shipped from each distribution center to each retailer as follows:

• x_1,1: Pallets shipped from Distribution Center 1 to Food Buzz
• x_1,2: Pallets shipped from Distribution Center 1 to Healthy Stuff
• x_1,3: Pallets shipped from Distribution Center 1 to Smoothie City
• x_1,4: Pallets shipped from Distribution Center 1 to Burger Barn
• x_1,5: Pallets shipped from Distribution Center 1 to Café Organic
• x_1,6: Pallets shipped from Distribution Center 1 to Dessert Center
• ... (similar variables for Distribution Centers 2 and 3)

Objective Function

The objective function is to minimize the total shipping cost:

Min Z = 20.25 x_1,1 + 50.85 x_1,2 + 84.00 x_1,3 + 86.65 x_1,4 + 108.95 x_1,5 + 116.45 x_1,6 + ... (and corresponding costs for D.C. 2 and D.C. 3)

Constraints

The constraints for the system will ensure that the total number of pallets shipped meets the demand for each retailer, as follows:

• x_1,1 + x_1,2 + ... + x_3,6 = 60 (Food Buzz)
• x_1,2 + x_2,2 + ... + x_3,2 = 78 (Healthy Stuff)
• x_1,3 + x_2,3 + ... + x_3,3 = 125 (Smoothie City)
• x_1,4 + x_2,4 + ... + x_3,4 = 187 (Burger Barn)
• x_1,5 + x_2,5 + ... + x_3,5 = 313 (Café Organic)
• x_1,6 + x_2,6 + ... + x_3,6 = 567 (Dessert Center)
• Total shipments must not exceed total inventory: x_1,1 + x_1,2 + ... + x_3,6 ≤ 1,615

Using Solver

To implement this model, it can be completed using Excel Solver. Input the cost values and constraints into the Solver tool and set the objective cell (total shipping cost) to minimize while subject to demand and inventory constraints. Solver will then yield the optimal shipping strategy, specifying the number of pallets to ship from each distribution center to each retailer.

Conclusion

The distribution model for Ingredients R Us Inc. showcases how essential data analysis and optimization techniques are in logistics management. By accurately calculating the total cost of shipping and meeting demand, the company can enhance its operational efficiency and customer satisfaction.

References

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