Question

In: Operations Management

Alfred Muller &Co. produces wheat flour for large bakeries. It has four mills and five markets....

Alfred Muller &Co. produces wheat flour for large bakeries. It has four mills and five markets. The capacities of each mill, demands from each market and transportation cost of sending a ton of flour from a mill to a market are given in the table given below. The company seeks to develop a plan to minimize transportation costs.

a) Determine the objective function and constraints.

b) Find the minimum cost and the amounts of flour sent from each mill to the markets using Excel Solver.

From Mills	To Markets					Supply (Tons)
From Mills	Market 1	Market 2	Market 3	Market 4	Market 5	Supply (Tons)
Mill 1	$80	$70	$75	$50	$40	75000
Mill 2	$60	$65	$80	$70	$60	60000
Mill 3	$50	$85	$60	$85	$70	65000
Mill 4	$70	$55	$50	$75	$85	50000
Demand (Tons)	70000	60000	30000	50000	40000

Expert Solution

The cost Matrix is:

The Volume Matrix is:

Here each associated cell shows the shipped between a pair of mill and market.

Supplied is the sum of all volume from a Mill to all the markets

Demand Satisfied is the sum of all volumes to a market from all the mills

Minimized cost is the total cost associated. It can be calculated by multiplying each shipment volume with associated cost. This can be determined by applying the formula SUMPRODUCT from the cost cells and volume cells.

The formula used for Supplied, Demand and Minimized cost has been mentioned in the screenshot.

Objective Function:

We have to minimize the cost. The total shipment cost has been found using the SUMPRODUCT formula.

Constraints:

A mill can send maximum the capacity of it. Hence supplied should not exceed the capacity.

A market should accept at least the demand. Also sending extra materials also adds to the cost. Here we have to minimize the cost. Hence requirement satisfied should be equal to the demand.

Solver Parameters:

As this is a transportation problem, we will solve this using SimplexLP.

Optimal Solution:

	To Market
From Mills	Market 1	Market 2	Market 3	Market 4	Market 5
Mill 1	0	0	0	35000	40000
Mill 2	5000	40000	0	15000	0
Mill 3	65000	0	0	0	0
Mill 4	0	20000	30000	0	0

The total cost of shipment = $13,150,000

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keosha answered 1 day ago

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