Recent questions and answers in Operations Research

An objective function $Z$ of primal variables ( $x_{1}$ and $x_{2}$ ) is described below:\[\begin{array}{ll}\text { Minimize } Z= & 0.07 x_{1}+0.05 x_{2} \\\text { subjec...

The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e., optimistic ( $t_{o}$ ), most likely ( $t_{m}$ ), and pessimistic ( $t_{p...

A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity $D$ is _________ hours (answer i...

​​​​At the current basic feasible solution $\text{(bfs)}$ $v_{0}\left(v_{0} \in \mathbb{R}^{5}\right)$, the simplex method yields the following form of a linear programmi...

In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each...

Which one of the options given represents the feasible region of the linear programming model:$$\begin{gathered}\text { Maximize } 45 X_1+60 X_2 \\X_1 \leq 45 \\X_2 \leq ...

An electric car manufacturer underestimated the January sales of car by $20$ units, while the actual sales was $120$ units. If the manufacturer uses exponential smoothing...

Parts $P1 – P7$ are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completio...

A manufacturing unit produces two products $P1$ and $P2$. For each piece of $P1$ and $P2$, the table below provides quantities of materials $\text{M1, M2}$ and $M3$ requi...

A project consists of five activities $\text{(A, B, C, D and E)}$. The duration of each activity follows beta distribution. The three time estimates (in weeks) of each ac...

In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource ispositivenegativezeroinfinity

Activities $A$ to $K$ are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is ...

An assignment problem is solved to minimize the total processing time of four jobs ($1,2,3$ and $4$) on four different machines such that each job is processed exactly by...

A set of jobs $\text{A, B, C, D, E, F, G, H}$ arrive at time $t= 0$ for processing on turning and grinding machines. Each job needs to be processed in sequence first on ...

Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of $12$ jobs/hour. The process time of the worksta...

Consider the following network of activities, with each activity named $\textbf{A – L}$, illustrated in the nodes of the network.The number of hours required for each act...

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 Cos...

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.$\begi...

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.$\begi...

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 __________

In PERT chart, the activity time distribution isNormalBinomialPoissonBeta

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 ____...

In the notation $(a/b/c) : (d/e/f)$ for summarizing the characteristics of queuing situation, the letters $‘b’$ and $‘d’$ stand respectively forservice time distribution ...

A minimal spanning tree in network flow models involvesall the nodes with cycle/loop allowedall the nodes with cycle/loop not allowedshortest path between start and end n...