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Minimizing Cost Shipping Strategy

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Question: Develop your capability in applying your skills and knowledge in a hypothetical situation and to build your problem solving and report writing skills.

Answer: Problem Formulation: The main objective of this study is to determine an optimal solution to minimize the shipping cost. In this study, the company taken into consideration produces mandarins at three plants (named as Plant 1, Plant 2 and Plant 3) which will be either shipped directly to customers (two customers are listed, namely, Customer 1 and Customer 2) or to warehouses (two warehouses, namely, Warehouse 1 and Warehouse 2) from where it was shipped to customers (two customers are listed, namely, Customer 1 and Customer 2). Thus, the main objective of this study is to minimize the shipping cost

Let P1, P2 and P3 represents the three plants from which mandarins are produced and W1 and W2 represents the two warehouses and C1 and C2 represents two customers respectively.

Pij represents mandarins shipped from Plant i to Plant j

Therefore, the objective function is

Minimize Z = 3*P12 + 3*P13 + 6*P1W1 + 7*P1W2 + 15 * P1C1 + 15 * P1C2 + 2 *P23 + 3*P21 + 5*P2W1 + 6*P2W2 + 16 * P2C1 + 16 * P2C2 + 3*P31 + 2*P32 + 7*P3W1 + 6*P3W2 + 14 * P3C1 + 15 * P3C2 + 3*W12 + 6*W1C1 + 8 * W1C2 + 3*W21 + 7*W2C1 + 7 * W2C2 + 4 * C12 + 4 * C21

Subject to the constraints

ΣP1j + ΣP1Wk + ΣP1Ck < = 350

ΣP2j + ΣP2Wk + ΣP2Ck < = 400

ΣP3j + ΣP3Wk + ΣP3Ck < = 450

ΣC2Wk + ΣPiC2< = 480

ΣC2Wk + ΣPiC2< = 460

P1, P2, P3, C1, C2, W1 and W> = 0

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Problem Solving: The problem is solved using excel solver and the output screenshot of the workings is given below

Select the cell that contains the objective function and place it in the "Set Objective" box

Set Objective.jpg

Add the constraints by clicking Add Icon

Add Constraints.jpg

Add the constraints one by one by clicking Add Icon and after adding the last constraints click Ok icon to return back to main menu
In "Select a Solving Method", select the option "Simplex LP" and click Solve

The Solver output is given below

Solver Output.jpg

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The formula used to frame the linear programing problem is given below

Linear Programming Problem.jpg

Discussion: This study mainly focus on minimizing the shipping cost to the company that produces mandarins in their three plants.
The simplex linear programming problem method was used to solve this problem and the minimum shipping cost was found to be 18470 (in thousands of dollars)

This minimum shipping cost is obtained by shipping mandarins from

Plant 1 to Plant 2 → 200 mandarins

Plant 1 to Plant 3 → 200 mandarins

Plant 1 to Warehouse 1 → 50 mandarins

Plant 1 to Warehouse 2 → 100 mandarins

Plant 1 to Customer 1 → 200 mandarins

Plant 1 to Customer 2 → 200 mandarins

Plant 2 to Plant 1 → 200 mandarins

Plant 2 to Plant 3 → 200 mandarins

Plant 2 to Customer 1 → 80 mandarins

Plant 2 to Customer 2 → 60 mandarins

Plant 3 to Plant 1 → 150 mandarins

Plant 3 to Plant 2 → 200 mandarins

Thus, the minimum shipping cost is 18470 (in thousands of dollars)

Recommendation: Further the study can be improved by increasing the demand and capacity of the Mandarins which will certainly help the management to use the simulation techniques from which they can have a better idea of their further demands for mandarins.

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