Processing times (including setup times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest processing time rule is ___________ (correct to two decimal places).
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 minutes is _______ (correct to two decimal places).
The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node 1 to node 6 is _______.
Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 80 per price, respectively. Production times for P and Q are 5 hour and 30 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, to maximize profit, the number of units of P to be produced is ________
Following data refers to the jobs (P, Q, R, S) which have arrived at a machine for scheduling. The shortest possible average flow time is ______ days.
For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following services rates will provide a steady finite queue length?
A product made in two factories, P and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are per the following matrix:
Factory P produces 7 units and factory Q produce 9 units of the product. Each destination requires 8 units. If the north-west corner method provides the total transportation cost as X (in Rupees) and the optimized (the minimum) total transportation cost is Y (in Rupees), then $ (x-y) $, in Rupees, is
A project start with activity A and ends with activity F. The precedence relation and duration of the activites are as per the following table:
The minimum project completion time (in days) is___________
Maximize $Z=5{x}_{1}+3{x}_{2}$,
Subject to
${x}_{1}+2{x}_{2}\le 10$,
${x}_{1}-{x}_{2}\le 8$,
${x}_{1}$, ${x}_{2}\ge 0$.
In the starting Simplex tableau, $ x_1 $ and $ x_2 $ are non-basic variable and the value of $ Z $ is zero. The value of $ Z $ in the next Simplex tableau is___________
Maximize $Z=15X_1 + 20X_2$ subject to $12X_1 + 4X_2 ≥ 36$ $12X_1 − 6X_2 ≤ 24$ $X_1, X_2 ≥ 0$ The above linear programming problem has
A project consists of 14 activities, A to N. The duration of these activities (in days) are shown in brackets on the network diagram. The latest finish time (in days) for node 10 is __________
In PERT chart, the activity time distribution is
Following data refers to the activities of a project , where, node 1 refers to the start and node 5 refers to the end of the project.
The critical path (CP) in the network is
A project consists of 7 activities. The network along with the time durations ( in days) for various activities is shown in figure.
The minimum time( in days) for completion of the project is ______.
In the notation (a/b/c) : (d/e/f) for summarizing the characteristics of queueing situation, the letters ‘b’ and ‘d’ stand respectively for
For the linear programming problem: Maximize Z = 3X_{1} + 2X_{2} Subject to – 2X_{1} + 3X_{2} ≤ 9 X_{1} – 5X_{2} ≥ – 20 X_{1}, X_{2} ≥ 0
The above problem has
The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is
Jobs arrive at a facility at an average rate of 5 in an 8 hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is 40 minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be
If there are m sources and n destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is
A component can be produced by any of the four processes I, II, III and IV. The fixed cost and the variable cost for each of the processes are listed below. The most economical process for producing a batch of 100 pieces is
A project has four activities P, Q, R and S as shown below.
The normal cost of the project is Rs. 10,000/- and the overhead cost is Rs. 200/- per day. If the project duration has to be crashed down to 9 days, the total cost (in Rupees) of the project is _______
A minimal spanning tree in network flow models involves
Consider the given project network,where numbers along various activities represent the normal tim me. The free float on activity 4-6 and the project duration, respectively, are
The total number of decision variables in the objective function of an assignment problem of size n × n (n jobs and n machines) is
The precedence relations and duration (in days) of activities of a project network are given in the table. The total float (in days) of activities e and f , respectively, are
At a work station, 5 jobs arrive every minute. The mean time spent on each job in the work station is 1/8 minute. The mean steady state number of jobs in the system is _______
Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is
A linear programming problem is shown below. Maximize 3x + 7y Subject to 3x + 7y ≤ 10 4x + 6y ≤ 8 x, y ≥ 0 It has
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below.
The critical path for the project is
If the duration of activity f alone is changed from 9 to 10 days, then the
Cars arrive at a service station according to Poisson’s distribution with a mean rate of 5 per hour. The service time per car is exponential with a mean of 10 minutes. At steady state, the average waiting time in the queue is
One unit of product P_{1} requires 3 kg of resource R_{1} and 1 kg of resource R_{2}. One unit of product P_{2} requires 2 kg of resource R_{1} and 2 kg of resource R_{2}. The profits per unit by selling product P_{1} and P_{2} are Rs. 2000 and Rs. 3000 respectively. The manufacturer has 90 kg of resource R_{1} and 100kg of resource R_{2}
The unit worth of resource R_{2}, i.e., dual price of resource R_{2} in Rs. Per kg is
The manufacturer can make a maximum profit of Rs.
Little’s law is relationship between
Simplex method of solving linear programming problem uses
The project activities, precedence relationships and durations are described in the table. The critical path of the project is
Four jobs are to be processed on a machine as per data listed in the table.
If the Earliest Due Date (EDD) rule is used to sequence the jobs, the number of jobs delayed is
Using the Shortest Processing Time (SPT) rule, total tardiness is
The expected time (${t}_{e}$) of a PERT activity in terms of optimistic time (${t}_{o}$), pessimistic time (${t}_{p}$) and most likely time (${t}_{l}$) is given by
Consider the following Linear Programming Problem (LPP):
Maximize z = 3x_{1} + 2x_{2} Subject to x_{1} ≤ 4 x_{2} ≤ 6 3x_{1} + 2x_{2} ≤ 18 x_{1} ≥ 0, x_{2} ≥ 0
Six jobs arrived in a sequence as given below:
Average flow time (in days) for the above jobs using Shortest Processing Time rule is
Consider the following PERT network:
The optimistic time, most likely time and pessimistic time of all the activities are given in the table below
The critical path duration of the network (in days) is
The standard deviation of the critical path is
In an M/M/1 queuing system, the number of arrivals in an interval of length T is a Poisson random variable (i.e. the probability of there being n arrivals in an interval of length T is $\frac{{e}^{-\lambda T}{\left(\lambda T\right)}^{n}}{n!}$). The probability density function f(t) of the inter-arrival time is given by
For the standard transportation linear programme with m sources and n destinations and total supply equaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero x_{ij} values (amounts from source i to destination j) is desired. The best upper bound for this number is
For the network below, the objective is to find the length of the shortest path from node P to node G. Let d_{ij} be the length of directed are from node i to node j.
Let s_{j} be the length of the shortest path from P to node j. Which of the following equations can be used to find s_{G} ?
Consider the Linear Programme (LP)
Max 4x + 6y
subject to
3x + 2y ≤ 6
2x +3y ≤ 6
x,y ≥ 0
After introducing slack variables s and t, the initial basic feasible solution is represented by the table below (basic variables are s = 6 and t = 6, and the objective function value is 0).
After some simplex iterations, the following table is obtained
From this, one can conclude that
The dual for the LP in Q 74 is
3u + 2v ≥ 4
2u + 3v ≥ 6
u, v ≥ 0
3u + 2v ≤ 4
2u + 3v ≤ 6
3u + 2v ≥ 6
3u + 2v ≤ 6