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GATE ME Industrial Engineering Previous Year Questions

60 solved GATE ME questions on Industrial Engineering, drawn from 11 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.

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Industrial Engineering: model the system, then optimize the objective

Define the decision variables, constraints, and objective function before solving. These selected foundations connect work study, inventory models, scheduling, linear programming, and quality control. They are not a complete syllabus; simulation, facility layout, and advanced scheduling heuristics need separate study.

Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.

Before you start

  • Basic algebra, inequalities, and graphical plotting of linear equations.
  • Mean, standard deviation, and the concept of a normal distribution.

Concepts to revise before solving

Work study: time and motion

Observed time is the directly measured cycle time. Normal time = observed time x performance rating. Standard time = normal time x (1 + allowance fraction), where allowances account for fatigue, personal needs, and delays. Methods study precedes time study: improve the method before measuring it.

Check yourself: Have you applied both the performance rating and allowances?

Inventory: EOQ model

Economic Order Quantity: EOQ = √(2DC_o/C_c), where D is annual demand, C_o is ordering cost per order, and C_c is carrying cost per unit per year. Total cost is minimized at EOQ, where annual ordering cost equals annual carrying cost. The model assumes constant demand, instantaneous replenishment, and no stockouts.

Check yourself: Are the assumptions (constant demand, no shortages) valid for this problem?

Scheduling and sequencing

For n jobs on 2 machines, Johnson's rule minimizes makespan: assign jobs with smaller processing time on machine 1 to the front, and jobs with smaller processing time on machine 2 to the back. PERT uses three time estimates (optimistic a, most likely m, pessimistic b): expected time = (a + 4m + b)/6, variance = ((b - a)/6)².

Check yourself: Have you identified the critical path before computing project duration?

Linear programming

A linear program maximizes or minimizes a linear objective subject to linear inequality constraints. The feasible region is a convex polygon (in 2D). The optimal solution lies at a vertex of the feasible region. The simplex method moves between adjacent vertices. Dual variables give shadow prices for constraints.

Check yourself: Have you checked all vertices of the feasible region for the optimum?

Quality control: control charts

X-bar and R charts monitor process mean and variability. Control limits are set at ±3 standard deviations from the process mean (for X-bar chart). A process is 'in control' when all points fall within control limits with no non-random patterns. Cp = (USL - LSL)/(6σ) measures process capability; Cp ≥ 1.33 is commonly targeted.

Check yourself: Are you distinguishing specification limits (design) from control limits (process)?

Mistakes to avoid

Using EOQ when demand is highly variable.
EOQ assumes constant, known demand. For variable demand, use safety stock models or dynamic lot sizing.
Confusing critical path duration with the sum of all activity durations.
The critical path is the longest path through the network; parallel activities overlap in time.
Setting control limits equal to specification limits.
Control limits are calculated from process data (±3σ); specification limits come from design requirements. They are independent.

Original teaching example · not a PYQ

Work through the reasoning

Original example: annual demand D = 10 000 units, ordering cost C_o = 200 per order, carrying cost C_c = 5 per unit per year. Assume constant demand and no shortages. Find the EOQ and total annual inventory cost (ordering + carrying).

  1. EOQ = √(2DC_o/C_c) = √(2 x 10000 x 200/5) = √(800000) ≈ 894.4 units.
  2. Number of orders per year = D/EOQ = 10000/894.4 ≈ 11.18.
  3. Annual ordering cost = (D/EOQ) x C_o = 11.18 x 200 ≈ 2236.
  4. Annual carrying cost = (EOQ/2) x C_c = 447.2 x 5 ≈ 2236.
  5. Total cost = 2236 + 2236 = 4472. At EOQ, ordering cost equals carrying cost.

EOQ ≈ 894 units; total annual inventory cost ≈ 4472.

Try it before reading the answer

Three activities in a PERT network have the following estimates (a, m, b) in days: A(2, 5, 8), B(3, 6, 15), C(4, 7, 10). Compute the expected time for each activity.

Show answer and reasoning

A: 5.0 days; B: 7.0 days; C: 7.0 days.

Expected time = (a + 4m + b)/6. A: (2 + 20 + 8)/6 = 30/6 = 5.0. B: (3 + 24 + 15)/6 = 42/6 = 7.0. C: (4 + 28 + 10)/6 = 42/6 = 7.0.

Go deeper with free learning resources

Supplemental reading, not an official GATE reading list or an endorsement of these notes.

Apply this to the previous-year questions

Previous-year questions by year

This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE ME papers. Questions can carry more than one subject tag; counts are not marks weightage.

GATE ME 20265 questions

  1. Set 1 Q46An objective function ZZ of primal variables (x1x_1 and x2x_2) is described below: Minimize Z=0.07x1+0.05x2Z = 0.07 x_1 + 0.05 x_2 subject to 0.1x1≥0.40.1 x_1 \geq 0.4…MCQ · +2 marks · Medium
  2. Set 1 Q47Four 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)…MCQ · +2 marks · Easy
  3. Set 1 Q60The actual demand for castings in a factory is 500500 units and 635635 units for the months of January 2026 and February 2026, respectively. The forecasted…NAT · +2 marks · Medium
  4. Set 1 Q61The 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…NAT · +2 marks · Medium
  5. Set 1 Q65The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e., optimistic (tot_o), most likely (tmt_m), and pessimistic…NAT · +2 marks · Medium

GATE ME 20253 questions

  1. Set 1 Q37Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively,…MCQ · +2 marks · Medium
  2. Set 1 Q64A 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…NAT · +2 marks · Medium
  3. Set 1 Q65A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is _____ hours…NAT · +2 marks · Medium

GATE ME 20245 questions

  1. Set 1 Q34A set of jobs U,V,W,X,Y,ZU, V, W, X, Y, Z arrive at time t=0t = 0 to a production line consisting of two workstations in series. Each job must be processed by both…MCQ · +1 marks · Medium
  2. Set 1 Q35A 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…MCQ · +1 marks · Easy
  3. Set 1 Q38A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000…MCQ · +2 marks · Medium
  4. Set 1 Q39At the current basic feasible solution (bfs) v0\mathbf{v}_0 (v0∈R5\mathbf{v}_0 \in \mathbb{R}^5), the simplex method yields the following form of a linear…MCQ · +2 marks · Hard
  5. Set 1 Q65In 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…NAT · +2 marks · Medium

GATE ME 20232 questions

  1. Set 1 Q13With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct? [figure]MCQ · +1 marks · Easy
  2. Set 1 Q14Which one of the options given represents the feasible region of the linear programming model: Maximize 45X1+60X2\text{Maximize } 45X_1 + 60X_2 X1≤45X_1 \leq 45…MCQ · +1 marks · Easy

GATE ME 202210 questions

  1. Set 1 Q21In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource isMCQ · +1 marks · Easy
  2. Set 1 Q22Which one of the following is NOT a form of inventory?MCQ · +1 marks · Easy
  3. Set 1 Q42Activities 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…MCQ · +2 marks · Medium
  4. Set 1 Q58An 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…NAT · +2 marks · Easy
  5. Set 1 Q59The product structure diagram shows the number of different components required at each level to produce one unit of the final product P. If there are 50 units…NAT · +2 marks · Medium
  6. Set 2 Q32An electric car manufacturer underestimated the January sales of car by 2020 units, while the actual sales was 120120 units. If the manufacturer uses…NAT · +1 marks · Easy
  7. Set 2 Q33The demand of a certain part is 10001000 parts/year and its cost is ₹1000₹1000/part. The orders are placed based on the economic order quantity (EOQ). The cost of…NAT · +1 marks · Medium
  8. Set 2 Q41Parts 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…MCQ · +2 marks · Medium
  9. Set 2 Q42A manufacturing unit produces two products P1 and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required,…MCQ · +2 marks · Medium
  10. Set 2 Q59A project consists of five activities (A, B, C, D and E). The duration of each activity follows beta distribution. The three time estimates (in weeks) of each…NAT · +2 marks · Medium

GATE ME 20218 questions

  1. Set 1 Q30Robot Ltd. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the…NAT · +1 marks · Medium
  2. Set 1 Q38A set of jobs A, B, C, D, E, F, G, H arrive at time t=0t = 0 for processing on turning and grinding machines. Each job needs to be processed in sequence — first…MCQ · +2 marks · Medium
  3. Set 1 Q45Activities A, B, C and D form the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given…NAT · +2 marks · Medium
  4. Set 1 Q52Consider 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…NAT · +2 marks · Medium
  5. Set 2 Q18A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical…MCQ · +1 marks · Medium
  6. Set 2 Q39A factory produces m(i=1,2,...,m)m (i = 1, 2, ..., m) products, each of which requires processing on n(j=1,2,...,n)n (j = 1, 2, ..., n) workstations. Let aija_{ij} be the amount of…MCQ · +2 marks · Medium
  7. Set 2 Q46Daily production capacity of a bearing manufacturing company is 30000 bearings. The daily demand of the bearing is 15000. The holding cost per year of keeping…NAT · +2 marks · Medium
  8. Set 2 Q53The demand and forecast of an item for five months are given in the table. | Month | Demand | Forecast | | :--- | :--- | :--- | | April | 225 | 200 | | May |…NAT · +2 marks · Medium

GATE ME 20208 questions

  1. Set 1 Q23In the Critical Path Method (CPM), the cost-time slope of an activity is given byMCQ · +1 marks · Easy
  2. Set 1 Q43For an assembly line, the production rate was 4 pieces per hour4\text{ pieces per hour} and the average processing time was 60 minutes60\text{ minutes}. The WIP inventory was…MCQ · +2 marks · Easy
  3. Set 1 Q57Two business owners Shveta and Ashok run their businesses in two different states. Each of them, independent of the other, produces two products A and B, sells…NAT · +2 marks · Medium
  4. Set 1 Q58Consider two cases as below. 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…NAT · +2 marks · Hard
  5. Set 2 Q23In Materials Requirement Planning, if the inventory holding cost is very high and the setup cost is zero, which one of the following lot sizing approaches…MCQ · +1 marks · Easy
  6. Set 2 Q33Consider the following network of activities, with each activity named A-L, illustrated in the nodes of the network. [figure] The number of hours required…NAT · +1 marks · Medium
  7. Set 2 Q43The forecast for the monthly demand of a product is given in the table below. | Month | Forecast | Actual Sales | | :---: | :---: | :---: | | 1 | 32.00 | 30.00…MCQ · +2 marks · Medium
  8. Set 2 Q57For a single item inventory system, the demand is continuous, which is 10000 per year. The replenishment is instantaneous and backorders (SS units) per cycle…NAT · +2 marks · Medium

GATE ME 20195 questions

  1. Set 1 Q27The 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 |…MCQ · +1 marks · Easy
  2. Set 1 Q64Five jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any of the five different machines (M1, M2, M3, M4 and M5).…NAT · +2 marks · Medium
  3. Set 1 Q65A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below: | Activity |…NAT · +2 marks · Medium
  4. Set 2 Q45The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship "X<Y,ZX < Y, Z"…MCQ · +2 marks · Medium
  5. Set 2 Q65The annual demand of valves per year in a company is 10,000 units. The current order quantity is 400 valves per order. The holding cost is Rs. 24 per valve per…NAT · +2 marks · Medium

GATE ME 20186 questions

  1. Set 1 Q26The time series forecasting method that gives equal weightage to each of the mm most recent observations isMCQ · +1 marks · Easy
  2. Set 1 Q61The minimum value of 3x+5y3x + 5y such that: 3x+5y≤153x + 5y \leq 15 4x+9y≤84x + 9y \leq 8 13x+2y≤213x + 2y \leq 2 x≥0,y≥0x \geq 0, y \geq 0 is _______.NAT · +2 marks · Medium
  3. Set 1 Q62Processing 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…NAT · +2 marks · Medium
  4. Set 2 Q28A 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…MCQ · +1 marks · Easy
  5. Set 2 Q45The problem of maximizing z=x1−x2z = x_1 - x_2 subject to constraints x1+x2≤10x_1 + x_2 \leq 10, x1≥0x_1 \geq 0, x2≥0x_2 \geq 0 and x2≤5x_2 \leq 5 hasMCQ · +2 marks · Medium
  6. Set 2 Q61The 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 _______. [figure]NAT · +2 marks · Easy

GATE ME 20176 questions

  1. Set 1 Q51Two 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,…NAT · +2 marks · Medium
  2. Set 1 Q52Following 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. | Job…NAT · +2 marks · Easy
  3. Set 2 Q23For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a…MCQ · +1 marks · Easy
  4. Set 2 Q48A 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…MCQ · +2 marks · Medium
  5. Set 2 Q49A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table: | Activity |…NAT · +2 marks · Easy
  6. Set 2 Q51Maximize Z=5x1+3x2Z = 5x_1 + 3x_2, subject to x1+2x2≤10x_1 + 2x_2 \leq 10, x1−x2≤8x_1 - x_2 \leq 8, x1,x2≥0x_1, x_2 \geq 0. In the starting Simplex tableau, x1x_1 and x2x_2 are…NAT · +2 marks · Medium

GATE ME 20162 questions

  1. Set 1 Q64The annual demand for an item is 10,00010,000 units. The unit cost is Rs. 100100 and inventory carrying charges are 14.4%14.4\% of the unit cost per annum. The cost of…NAT · +2 marks · Medium
  2. Set 1 Q65Maximize Z=15X1+20X2Z = 15X_1 + 20X_2 subject to 12X1+4X2≥3612X_1 + 4X_2 \geq 36 12X1−6X2≤2412X_1 - 6X_2 \leq 24 X1,X2≥0X_1, X_2 \geq 0 The above linear programming problem hasMCQ · +2 marks · Medium

Other GATE ME topics

Engineering Mathematics(269)General Aptitude(265)Manufacturing Processes(207)Thermodynamics(160)Strength of Materials(131)Theory of Machines & Vibrations(130)Fluid Mechanics(127)Heat Transfer(106)Engineering Mechanics(105)Machine Design(77)Metrology, CIM & Additive Mfg(41)Engineering Materials(37)

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