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  OPERATIONS RESEARCH - REVISION 1) A company has factories F1, F2, and F3 which supply to warehouses W1, W2, and W3. Weekly factory capacities are 200, 160, and 90 units respectively. Weekly warehouse requirements are 180, 120 and 150 units respectively. Unit shipping costs (in rupees) are as follows: W1 W2 W3 Supply F1 16 20 12 200 F2 14 8 18 160 F3 26 24 16 90 Demand 180 120 150 450 Determine the optimal   distribution for this company to minimize total shipping cost. 2) A dairy firm has three plants located in a state. The daily milk production at each plant is as follows: Plant 1: 6 million litres Plant 2: 1 million litres Plant 3: 10 million litres Each day, the firm must fulfil the needs of its four distribution centres. Minimum requirement at each centre is as follows: Distribution centre 1: 7 million litres Distribution centre 2: 1 million litres Distribution centre 3: 2 million litres Cost in hundreds of rupees of shipping one million litre from each plant to each distribution centre is given in the following table: Distribution Centre    P    l   a   n   t  D1 D2 D3 D4 P1 2 3 11 7 P2 1 0 6 1 P3 5 8 15 9 Find the initial basic feasible solution for the given problem using the Vogel ’ s Approximation Method. 3) Explain in brief the three methods for obtaining an initial basic feasible solution for a transportation problem.  4) With reference to a transportation problem explain the following terms: i)   Feasible solution ii)   Basic feasible solution iii)   Optimal solution iv)   Non-degenerate basic feasible solution 5) Two companies are competing for the market share of a similar product. The payoff matrix in terms of their advertisement plan is shown below: Competitor B  No Advertising Medium Advertising Heavy Advertising    C   o   m   p   e   t   i   t   o   r       A   No Advertising 10 5 -2 Medium Advertising 13 12 13 Heavy Advertising 16 14 10 Suggest the optimal strategies for the firms and the net outcome thereof. 6) Use the graphical method in solving the following game and find the value of the game. Player B Player A B1 B2 B3 B4 A1 2 2 3 -2 A2 4 3 2 6 7) Define the following terms: i) Maximin and Minimax ii) Payoff Matrix iii) Pure and Mixed strategies iv) Saddle point v) Two-person zero-sum game . 8) What are assumptions made in the theory of games?  9) A television repairman finds that the time spent on his jobs has an exponential distribution with a mean of 30 minutes. If he repairs sets in the order in which they came in, and if the arrival of sets follows a Poisson ’ s distribution approximately with an average rate of 10 per 8-hour day, what is the repairman ’ s expected idle time each day? How many jobs are ahead of the TV set just brought in to the shop? 10) A road transport company has one reservation clerk on duty at a time. He handles information of bus schedules and makes reservations. Customers arrive at the rate of 8 per hour, and the clerk can service 12 customers on an average per hour. After stating your assumptions, answer the following: a)   What is the average number of customers waiting for the service of the clerk? b)   What is the average time a customer has to wait before getting service? c)   The management is contemplating to install a computer system to handle the information and reservations. This is expected to reduce the service time from 5 to 3 minutes. The additional cost of having the new system works out to Rs.50 per day. If the cost of goodwill of having to wait is estimated to be 12 paise per minute spent waiting before being served, should the company install the computer system? Assume 8 hours working day. 11) A warehouse has only one loading dock manned by a three-person crew. Trucks arrive at the loading dock at an average rate of 4 trucks per hour, and the arrival rate is Poisson distributed. The loading of a truck takes 10 minutes on an average, and can be assumed to be exponentially distributed. The operating cost of a truck is Rs.200 per hour and the members of a loading crew are paid @Rs.60 each per hour. Would you advise the truck owner to add another three-person crew? 12) What do you understand by i) queuing discipline ii) arrival process and iii) the service process? 13) Give two examples to illustrate the applications of queuing theory in business and industry. 14) Briefly explain the Kendall’s  notation used in Queuing Theory. 15) The production department for a company requires 3,600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs.360, and the cost carrying is 25% of the investment in inventories. The price is Rs.100 per kg. The Purchase Manager wishes to determine an ordering policy for raw materials. Can you suggest a suitable one?  16) Each unit of an item costs a company Rs.40. The annual holding costs are 18% of unit cost for interest charges, 1% for insurance, 2% for allowance for obsolescence, Rs.2 for warehouse overheads, Rs.1.50 for damage loss, and Rs.4 for miscellaneous costs. Annual demand for the item is constant at 1,000 units, and each order cost Rs.100 to place. Calculate the EOQ and the total costs associated with stocking the item. 17) Discuss the various costs involved in an inventory model. 18) What are the various assumptions in the Economic Order Quantity formula? 19) What are factors involved in the inventory problem analysis? 20) Explain the functional roles of inventory. 21) What are the main considerations in the formulation of an inventory policy? Quiz 1.   The initial solution of a transportation problem can be obtained by applying any known method. However, the only condition is that a.   The solution be optimal b.   The rim conditions are satisfied c.   The solution not be degenerate d.   All of the above 2.   The solution to a transportation problem with m-rows (supplies) and n-columns (destinations) is feasible if the number of positive allocations are: a.   m + n b.   m x n c.   m + n  –  1 d.   m + n + 1 3.   When the total supply is equal to the total demand in a transportation problem, the problem is said to be a.   Balanced b.   Unbalanced c.   Degenerate d.   None of the above
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