The production and transportation at the warehouse for a product are planned in 4-days increments. The following tables report transportation costs between production sites and warehouses, production capacity, and demand at each warehouse.

a) For the given data develop a transportation model from production sites to warehouses that minimizes total transportation cost.

b) Given the anticipated increase in demand (12%), the company is considering increasing capacity.

Adding 20000 units to any plant incurs a one-time cost of INR 400,000,000 while adding 50000 units incurs a cost of INR 800,000,000. The increases in capacity can be additive (i.e., one could decide to increase capacity at a plant by 100000 units paying double the cost of 50000 units) and capacity can be added to multiple plants.

Reformulate your transportation model adding the decision of where to increase plant capacity and by how much.

c) What would be your recommendation to the company going forward in terms of their supply chain strategy?

Table 1. Average transportation cost per unit between production sites and warehouses (in Rupees)
Production Site	Bangalore	Chennai	Hyderabad	Mangalore	Mumbai
Bangalore	0.156	2.091	3.556	2.2	6.519
Chennai	2.169	0.125	3.913	4.406	8.338
Pune	5.313	7.519	3.513	4.831	0.931
Mumbai	6.519	8.338	4.438	5.719	0.181
Delhi	13.35	13.556	9.65	14.188	8.556
Hyderabad	3.556	3.913	0.125	5.15	4.438
Dubai	8.394	10.213	6.313	8.095	2.056
Table 2. Production site capacity (in units over 4 days)
Production Site	Capacity
Bangalore	80000
Chennai	100000
Pune	120000
Mumbai	80000
Delhi	100000
Hyderabad	100000
Dubai	120000
Table 3. Demand at each warehouse (in units over 4 days)
Warehouse	Demand
Bangalore	102884
Chennai	237288
Hyderabad	145231
Mangalore	44000
Mumbai	167000