# Supply Chain Distribution Optimization] Harvard Case Solution & Analysis

Distribution Pattern that would minimize cost:

C1 should be supplied through Brighton while C2 should be provided through New Castle, the demand of C3 should be delivered to London.On the other hand, C4 should be distributed through Liverpool, 20000 tons for C5 should be circulated from London whereas the remaining 40000 tons should be transported through Exeter channel and finally, London depot should be used for delivering the C6.

The objective function was to minimize the cost, on the other hand, the decision variable is the variable that is in control of the entity and the decision variable in the linear programming is the channel of distribution through which the units have to be delivered. The constraints are the demand and the capacity that the company can achieve. Company cannot manufacture more than its capacity and should only produce the required amount of units to match the demand of the products.

Steps:

• Firstly, the objective function is described in the solver i.e. minimization of total distribution cost.
• The changing variable cells are the factors that can be changed or varied in order to find the optimal cost and distribution pattern.
• Then, the constraints are selected, the constraints are the maximum capacity of the company which it can pursue and the other constraint is demand which it can be fulfilled. The company can only produce units less than its capacity and the company should have to produce units that are equal to the demands.

Supply-Chain-Distribution-Optimization-Harvard-Case-Solution-Analysis
Harvard Case Solution & Analysis"]

Objective Function:

Minimization of total cost = number of units delivered to customers*cost per unit in tones

50000*1+10000*1+40000*0.2+35000*1+60000*1+20000*1> 325000

Decision Variable:

Ci= Customer’s preferences over the selected factories and depots

(i= C1, C2, C3, C4 for Liverpool, Brighton, New Castle, London and Exeter)

C4= Customer’s preference for Liverpool cost utilization

C1= Customer’s preference for Brighton cost utilization

C2 = Customer’s preference for New Castle cost utilization

C3 = Customer’s preference for London cost utilization

C5 = Customer’s preference for London and Exeter cost utilization

C6 = Customer’s preference for London cost utilization

(C+1)i= Excluding Preferences from Ci to (C+1)i

(i= C1, C2, C3, C4 for Liverpool, Brighton, New Castle, London and Exeter)

C4= Customer’s preference for Liverpool cost utilization

C1= Customer’s preference for Brighton cost utilization

C2 = Customer’s preference for New Castle cost utilization

C3 = Customer’s preference for London cost utilization

C5 = Customer’s preference for London and Exeter cost utilization

C6 = Customer’s preference for London cost utilization

Constraints:

(Customer’s preference for Liverpool+ Customer’s preference for Brighton+ Customer’s preference for New Castle+ Customer’s preference for Birmingham+ Customer’s preference for London+ Customer’s preference for Exeter=Total customer’s preferences for all the factories and depots) = (All customer’s preferences for Liverpool+ All customer’s preferences for Brighton+ All customer’s preferences for New Castle+ All customer’s preferences for Birmingham+ All customer’s preferences for London+ All customer’s preferences for Exeter)

(50000, 10000, 40000, 35000, 60000, 20000) = (35000, 50000, 10000, 0, 80000, 40000)

All customers’ preferences for Liverpool, Brighton, New Castle, Birmingham, London and Exeter <= The total capacity required for each factory and depot

(35000, 50000, 10000, 0, 80000, 40000) <= (150000, 200000, 70000, 50000, 100000, 40000).................

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