### [Solved] StayCool, an Indian manufacturer of Air Conditioners, has two plants – one in Mumbai and the other in Chennai

StayCool, an Indian manufacturer of Air Conditioners, has two plants – one in Mumbai and the other in Chennai. Each plant has a capacity of 250,000 units. The two plants serve the entire country, which is divided into four regional markets: the North, with a demand of 100,000 units; the East, with a demand of 50,000 units; the West, with a demand of 150,000 units; and the South, with a demand of 150,000 units. Two other potential sites for plants are Delhi and Kolkata. The variable production and transport costs (in thousands of rupees) per AC from each potential production site to each market are shown below:

Table: Transportation cost and Production capacity (‘000 Rupees) per AC at StayCool

North | East | West | South | Current Capacity | |

Chennai | 19 | 20 | 18 | 14 | 250 |

Delhi | 19 | 15 | 19 | 20 | 0 |

Kolkata | 15 | 19 | 20 | 17 | 0 |

Mumbai | 20 | 19 | 15 | 18 | 250 |

Current Demand (‘000s units) | 100 | 50 | 150 | 150 |

StayCool is anticipating a compounded growth in demand of 35% for the next year and must plan its network investment decisions carefully. An additional capacity of 150,000 units can be added any of the four plants, by incurring a one-time cost of 1.5 billion rupees. Assume that StayCool plans to meet all demand.

**a.** Provide the facility configuration model for StayCool in written form. Detail the decision variables with a clear description of each, the objective function and the constraints. Do not copy/paste from Excel.

*[Hints: The model is similar to the Home Store example in Lecture 2. The model of the Home Store example can be found in “In-class exercise 2 – Model.doc” available in BrightSpace. The binary variables (one for each plant) should be defined as:* *y**i**=1** if an additional capacity of 150,000 is added to plant* *i**;* *y**i**=0** otherwise. The capacity constraint for plant 1 (plant in Chennai) is then given by* *x**11**+**x**12**+**x**13**+**x**14**≤250+150**y**1**.**]*

**b.** Run the model with Excel Solver. Is additional capacity recommended? How much and where?

**c.** What is the optimal total cost (transportation + production + additional capacity costs) of the solution provided?

**d.** Now suppose that from some reason, the route from Mumbai to the West is no longer available. How does the optimization problem change in terms of equations? You do not need to re-run the model to find the optimal solution.

*[Hints: Think about adding a constraint with respect to the quantity shipped from Mumbai to the West, i.e.,* *x**43**,* *or changing the cost parameter* *c**43** which is now 15.]*

**e.** Suppose that the East market must be served by Kolkata due to some service level requirement. How does the optimization problem change in terms of equations? You do not need to re-run the model to find the optimal solution.

*[Hints: Think about adding constraints with respect to the quantities shipped from plants to the East, i.e.,* *x**12**,* *x**22**,* *x**32** and* *x**42**.]*

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