1. Project on: Inventory Management using Linear Programming in Hotel
submitted in partial fulfillment
for
Masters of Science
By: Heral Kevrani
I10MA045
Under Supervision of
Prof. Nita H. Shah
Professor,
Gujarat University,
Ahmedabad, Gujarat
Dr. Ranjan Kumar Jana
Assistant Professor,
S.V.N.I.T.
Surat, Gujarat

2. Overview of the Talk Inventory System Inventory in Hotel Management
Model for the Rooms
Models for the Restaurant
Proposed Model
Change in Single Constraint
Change in pair of Constraints
Conclusion

3. Inventory System
The word “inventory” says that any kind of resource that has economic value and is maintained to fulfill the present and future needs of the organization.
Two types of decisions need to be made are:
How much should be added to inventory?
When should the inventory be replenished?
It means those time and quantity elements are the variables which affect all the costs.

4. Inventory in Hotel Management
Hotels are constantly working to offer the best customer experience and service.
They need proper systems in place to manage the items necessary for efficient service at affordable charges.

5. Problem Statement
There are mainly two problems of the hotel which have to manage.
The number of rooms.
The inventories of the restaurant.

6. Rooms Electronic Inventory Tube-lights Bulbs Fans Hair dryer
Television
Refrigerator
A.C.
Bed-linen
Bed-sheets
Towel
Napkins
Curtains
Bed-mattress
Inventory
Wooden
A set of table-chair
cupboard
Dressing table
A small table
Doors
A set of bed
A sofa set
Toiletries
Shampoo
Soap
Conditioner
Shower Gel
Shower Cap
Toilet-paper
A bottle of water

7. Utensils & Electronics
Restaurant
Utensils & Electronics
Refrigerator
Oven
Grinder, Blender, Mixer
Utensils
Grocery
Oil
Butter & Cheese
Flour
Rice & Beans
Sauces
Vegetable & Fruits
Spices & Drinks
Water bottle
Cold drinks
Buttermilk, Ice-cream
Spices
Desserts
Dinnerware
Serving crockery
Food crockery
Glassware
Add-ins
Napkin & Tablecloth

8. Assumptions of Models The hotel is:
at a tourist place.
a non-alcoholic
pure vegetarian.
All the needed equipment like: table, chairs, curtains, decorative items, reservation desk, electronic items, etc are available in the restaurant.
Known budget for the different inventories of the rooms.
The manager had already decided types and the amount of inventories required.

9. Following notations are used for further models:

12. Model for the Rooms The hotel has 3 kinds of rooms:
Non-A.C. Rooms
A.C. Rooms
Deluxe rooms
The model had been created using the data of from the Federation of Hotel & Restaurant Association of India, (FH&RA).
This model has 68 rooms and approximately 46 rooms were occupied every day.

13. Model for the Rooms

14. Solution of Model for the Rooms
Solving this problem in MATLAB, we get
The profit is Rs. 2,36,58,900 for the first year of the Hotel. So, the gross revenue is:
2,36,58,900 – [1,04,75,000+20,60,000+11,70,500] =99,53,400

15. Analysis of next four year data

16. Models for Restaurant
There will be four models for the restaurant of inventory which are as following:
Model 2: Utensils & Electronic Inventory of the Kitchen
Model 3: Grocery of the Kitchen
Model 4: Drinks and Spices
Model 5: Dinnerware

17. Model 2: Utensils & Electronic Inventory of the Kitchen
Refrigerator
Utensils
Grinder & Mixer
First Constraint
Second Constraint

18. Model 3: Grocery of the Kitchen
Second Constraint
First Constraint
Third Constraint

19. Model 3: Grocery of the Kitchen

20. Model 4: Drinks and Spices

21. Model 5: Dinnerware

22. Model 5: Dinnerware

23. New model of Restaurant
With these models overall optimization of the restaurant inventory is not attended. Therefore, we need to take-up single model to attain the objective with all the constraints and minimum number of variables.

24. One should simplify the variables to be merged and declare them as new variables of the restaurant of the hotel:
Number of Refrigerators + Ovens + Grinders, Mixers and Blenders require in the kitchen
Number of Kg of Flour + Rice and beans require for each month
Number of Kg of sauces + Spices and Salt require for each month
Number of Bottles/cups/glasses of Water + Cold- drink (200 ml) + Buttermilk, Ice-cream require for a month
Number of sets of Add-ins + Napkins and Tablecloths require in the Restaurant
Number of sets of Glassware + Food Crockery + Serving Crockery require in each month

25. Now, the new notations for the restaurant inventories are:

27. Model 2: Utensils & Electronic Inventory of the Kitchen

28. Model 3: Grocery of the Kitchen

29. Model 4: Drinks and Spices

30. Model 4: Drinks and Spices

31. Model 5: Dinnerware

32. Model 5: Dinnerware

34. When some of the constraints have the same combination of variables twice, one should consider only one of them. In this new model, all the variables are covered in these constraints. Finally, the new model will be:

36. The minimum cost of this new model is Rs. 7, 74,131.67 per month.

37. Additional Constraints of new model

38. Solution for the new model
It is clear that additional constraint in new model can’t make any difference in the result.

39. Decreasing the constraint’s Budget by 20%

40. Increasing the constraint’s Budget by 20%

41. Decreasing the constraint’s Budget by 40%

42. Increasing the constraint’s Budget by 40%

43. Decreasing the budget at the rate of 20% in a pair of constraints

44. Increasing the budget at the rate of 20% in a pair of constraints

45. Decreasing the budget at the rate of 40% in a pair of constraints

46. Increasing the budget at the rate of 40% in a pair of constraints

47. Conclusion Responsible for decrease the cost of the new model
The cost will decrease the most when first constraint is involved in it.
Whenever first constraint will decrease, the cost will decrease (for single constraint).
Whenever first constraint is decreasing with any other constraint the cost will decrease, except for the one case (pair of constraints).
In all the analysis, it comes to know that the third constraint is most sensitive.
It means that whenever a large change (more than 20 %) in third constraint is happening, the uncertainty of its output increases.

48. Conclusion Responsible for increase the cost of the new model
Whenever a fifth constraint is increasing its cost by 20 % and the rate of other constraint is decreasing than the cost of the objective function will always increase.
The fifth constraint have spices and drinks as decision variables.

49. Conclusion
Either first or sixth constraint increases the cost by the rate of 40% .
First and sixth constraint includes electronic inventory, utensils, spices & sauces and desserts.

50. References
Indian Hotel Industry Survey , Federation of Hotel & Restaurant Associations of India, 2012.
J. K. Sharma, Operation Research Theory and Application (2nd Edition), Macmillian India Ltd, 2003.
Naddor, E. Inventory System, Robert E. Krieger Publishing Co., Malabar, Florida, 1982.
Natarajan A.M., Balasubramani P., Operation Research, Pearson Education India, 2006.
N.H.Shah, R.M. Gor and H.Soni, Operation Research, Prentice-hall of India Private Limited, New Delhi, 2008.
Panneerselvam R., Operations Research, (2nd Edition), PHI Learning Private Limited, Noida, 2006.
Pizam, A. International Encyclopedia of Hospitality Management, Second Edition, Elsevier Ltd., Burlington, 2010.
e-reference:

51. THANK YOU