Recent questions tagged 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...

Four jobs are on order in a factory. As on day $20$ of the production calendar, the corresponding due date and work remaining to complete these jobs (in days) are given i...

The actual demand for castings in a factory is $500$ units and $635$ units for the months of January $2026$ and February $2026$, respectively. The forecasted demand for J...

The inventory holding cost of an item is ₹ $0.50$ per unit per month and the ordering cost per order is ₹ $550$. A stockist needs to supply $10000$ units of the item per ...

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...

​​​​​​Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, arePer...

A company uses $3000$ units of a part annually. The units are priced as given in the table below. It costs ₹ $150$ to place an order. Carrying costs are $40$ percent of t...

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...

​​​​​A set of jobs $\text{U, V, W, X, Y, Z}$ arrive at time $t=0$ to a production line consisting of two workstations in series. Each job must be processed by both workst...

​​​​​A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson dist...

​​​​A company orders gears in conditions identical to those considered in the economic order quantity $\text{(EOQ)}$ model in inventory control. The annual demand is $800...

​​​​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 factory produces $m (i= 1,2,\cdots, m)$ products, each of which requires processing on $n(j = 1,2,\cdots, n)$ workstations. Let $a_{ij}$ be the amount of processing ti...

The demand and forecast of an item for five months are given in the table.$$\begin{array}{|cl|cI|cI|}\hline&\textbf{Month} & \textbf{Demand} & \textbf{Forecast} \\ \hline...

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...

The forecast for the monthly demand of a product is given in the table below:$\begin{array}{|c|c|c|} \hline \textbf{Month} & \textbf{Forecast} & \textbf{Actual Sales} \\ ...

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...