operations-research

An objective function Z of primal variables (x₁ and x₂) is described below: Minimize Z = 0.07 x₁ + 0.05 x₂ subject to 0.1 x₁ ≥ 0.4 0.1 x₂ ≥ 0.6 0.1 x₁ + 0.2 x₂ ≥ 2.0 0.2 x₁ + 0.1 x...

A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000 gears, the cost per or...

At the current basic feasible solution (bfs) $\boldsymbol{v_0}$ ($\boldsymbol{v_0} \in \mathbb{R}^5$), the simplex method yields the following form of a linear programming problem...

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

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 completion time requi...

A factory produces m (i = 1,2,..., m) products, each of which requires processing on n (j = 1, 2, ..., n) workstations. Let aij be the amount of processing time that one unit of th...

A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic o...

Maximize $$\,\,\,\,\,\,\,\,\,Z = 5{x_1} + 3{x_2}$$ Subject to $$\,\,\,\,\,\,\,\,\,\,{x_1} + 2{x_2} \le 10,$$ $$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\...

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,...

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 _______ mi...

Maximize $$\,\,\,\,Z = 15{x_1} + 20{x_2}$$ Subject to $$\eqalign{ & 12{x_1} + 4{x_2} \ge 36 \cr & 12{x_1} - 6{x_2} \le 24 \cr & \,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr} $$ The...

For the linear programming problem: $$\eqalign{ & Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr & Subject\,\,to\,\,\,\, - 2{x_1} + 3{x_2} \le 9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...

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

The total number of decision variables in the objective function of an assignment problem of size $$n\,\, \times \,\,n$$ ($$n$$ jobs and $$n$$ machines) is

A minimal spanning tree in network flow models involves

If there are $$m$$ sources and $$n$$ destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is

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

A linear programming problem is shown below. $$\eqalign{ & Maximize\,\,\,\,3x + 7y \cr & Subject\,\,to\,\,\,3x + 7y \le 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4x...

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 $$...

Simplex method of solving linear programming problem uses

Little’s law is relationship between

Consider the following Linear Programming problem $$(LLP)$$ Maximize: $$Z = 3{x_1} + 2{x_2}$$ $$\,\,$$ Subject $$\,\,$$ to $$\eqalign{ & \,\,\,\,\,\,\,{x_1} \le 4 \cr & \,\,\,\,\,\...

Consider the Linear programme $$(LP)$$ Max $$4x$$ + $$6y$$ Subject to $$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,3x + 2y \le 6 \cr & \,\,\,\,\,\,\,\,\,\,\,2x + 3y \le 6 \cr & \,\,\,\,\,\,...

The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter tak...

A company has two factories $${S_1},$$ $${S_2}$$ and two warehouses $${D_1},$$ $${D_2}$$ . the supplies from $${S_1}$$ and $${S_2}$$ are $$50$$ and $$40$$ units respectively. Wareh...

Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points of the feasible region are $$...

A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a ‘first come first served’ queue discipline. Breakdowns occur on an ave...

A company produces two types of toys: $$P$$ and $$Q.$$ Production time of $$Q$$ is twice that of $$P$$ and the company has a maximum of $$2000$$ time units per day. The supply of r...

The supply at three sources is $$50, 40$$ and $$60$$ units respectively whilst the demand at the four destinations is $$20, 30, 10$$ and $$50$$ units. In solving this transportatio...

In a single server infinite population queuing model, arrivals follow a Poisson distribution with mean $$\lambda = 4$$ per hour. The service times are exponential with mean service...

At a production machine, parts arrive according to a Poisson process at the rate of $$0.35$$ parts per minute. Processing time for parts have exponential distribution with mean of...

The cost of providing service in a queuing system increases with

If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that