# Recent questions tagged operations-research

In the Critical Path Method $(CPM)$, the cost-time slope of an activity is given by $\dfrac{\text{Crash Cost – Normal Cost}}{\text{Crash Time}} \\$ $\dfrac{\text{Normal Cost}}{\text{Crash Time – Normal Time}} \\$ $\dfrac{\text{Crash Cost}}{\text{Crash Time – Normal Time}} \\$ $\dfrac{\text{Crash Cost – Normal Cost}}{\text{Normal Time – Crash Time}}$
A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is _______(round off to $2$ decimal places).
For an assembly line, the production rate was $4$ pieces per hour and the average processing time was $60$ minutes. The $\text{WIP}$ inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by $30$ percent. As a result ... time, the $\text{WIP}$ inventory decreases by $25\%$ increases by $25\%$ decreases by $30\%$ increases by $30\%$
Two business owners Shveta and Ashok run their business in two different states. Each of them, independent of the other, produces two products $A$ and $B$, sells them at $Rs.\:2,000$ per kg and $Rs.\:3,000$ per kg, respectively, and uses Linear ... absolute value of the difference in daily (optimal) revenue of Shveta and Ashok is _________ thousand Rupees (round off to $2$ decimal places).
$\textbf{Consider two cases as below.}$ $\textbf{Case 1:}$ A company buys $1000$ pieces per year of a certain part from vendor $'X'.$ The changeover time is $2$ hours and the price is $Rs.\: 10$ per piece. The holding cost rate per part is $10\%$ per year. ... percentage reduction in the annual cost of $\text{Case 2}$, as compared to $\text{Case 1}$ is __________ (round off to $2$ decimal places).
The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship $X<Y,Z$ means that $X$ is predecessor of activities $Y$ and $Z$ ... $17$ $21$ $23$ $25$
The table presents the demand of a product. By simple three-months moving average method, the demand-forecast of the product for the month of September is ... $490$ $510$ $530$ $536.67$
A project starts with activity $A$ and ends with activity $F$ ... The minimum project completion time (in days) is _________.
A product made in two factories, $P$ and $Q$, is transported to two destinations, $R$ and $S$ ... optimized (the minimum) total transportation cost is $Y$ (in Rupees), then $(X-Y)$, in Rupees, is $0$ $15$ $35$ $105$
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. $\begin{array}{|l|l|} \hline \text{Job} & \text{Processing Time (days)} \\ \hline P & 15 \\ \hline Q & 9 \\ \hline R & 22 \\ \hline S & 12 \\ \hline \end{array}$
Two models, $P$ and $Q$, of a product, earn profits of Rs.$100$ and Rs. $80$ per piece, respectively. Production times for $P$ and $Q$ are $5$ hours and $3$ hours, respectively, while the total production time available is $150$ hours. For a total batch size of $40$, to maximise profit, the number of units of $P$ to be produced is ________.
A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts $I$ and $II$ are $Rs. 40$ ... week (minutes) I II Turning machine $12$ $6$ $6000$ Milling center $4$ $10$ $4000$ Grinding Machine $2$ $3$ $1800$
The demand for a two-wheeler was $900$ units and $1030$ units in April $2015$ and May $2015$, respectively. The forecast for the month of April $2015$ was $850$ units. Considering a smoothing constant of $0.6$, the forecast for the month of June $2015$ is $850$ units $927$ units $965$ units $970$ units
In PERT chart, the activity time distribution is Normal Binomial Poisson Beta
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 __________
A food processing company uses $25,000 \:kg$ ... charge on an annual basis is $20\%$ of the purchase price of the corn flour per $kg$. The optimal order quantity (in $kg$) is _____________
In a single-channel queuing model, the customer arrival rate is $12$ per hour and the serving rate is $24$ per hour. The expected time that a customer is in queue is _______ minutes.
The annual demand for an item is $10,000$ units. The unit cost is $Rs$. $100$ and inventory carrying charges are $14.4\%$ of the unit cost per annum. The cost of one procurement is $Rs$. $2000$. The time between two consecutive orders to meet the above demand is _______ month($s$).
In the notation $(a/b/c) : (d/e/f)$ for summarizing the characteristics of queuing situation, the letters $‘b’$ and $‘d’$ stand respectively for service time distribution and queue discipline number of servers and size of calling source number of servers and queue discipline service time distribution and maximum number allowed in system
For a canteen, the actual demand for disposable cups was $500$ units in January and $600$ units in February. The forecast for the month of January was $400$ units. The forecast for the month of March considering smoothing coefficient as $0.75$ is ________
Following data refers to the activities of a project, where, node $1$ refers to the start and node $5$ ... critical path (CP) in the network is $1$-$2$-$3$-$5$ $1$-$4$-$3$-$5$ $1$-$2$-$3$-$4$-$5$ $1$-$4$-$5$
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 _______
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 $f$ ... $0$ and $4$ $1$ and $4$ $2$ and $3$ $3$ and $1$
The total number of decision variables in the objective function of an assignment problem of size $n × n$ ($n$ jobs and $n$ machines) is $n^2$ $2n$ $2n-1$ $n$
The actual sales of a product in different months of a particular year are given below: ... $4$-month moving average method, for the month of February is _______