Plant location: factor rating and break-even methods

Location factors and the factor rating, location break-even and centre-of-gravity methods, with a three-site cost-volume comparison.

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Why it matters

A plant's location fixes a large share of its costs for decades: freight on raw materials and finished goods, wage levels, power and water, taxes and incentives. A wrong choice cannot be fixed by good layout or work study later. Factor rating and location break-even analysis are the two standard tools for turning a mix of hard costs and soft factors into a defensible decision.

Key ideas

Levels of the decision. Location is usually chosen in stages: the region or state (markets, raw materials, policy), then the community or town (labour, utilities, services, living conditions), then the exact site (land cost, soil, drainage, access road or rail siding, room for expansion).

Factors affecting location

  • Cost-related (tangible): raw-material and inward freight, outward freight to markets, labour wages and productivity, land and construction, power and water tariffs, taxes and subsidies.
  • Non-cost (intangible): availability of skilled labour, labour relations, community attitude, quality of life, climate, government stability and incentives (special economic zones, industrial estates), environmental clearances, proximity to suppliers and competitors.
  • Material-oriented industries (weight-losing raw materials such as cement, sugar, steel) locate near the raw material; market-oriented ones (perishable or weight-gaining products such as bakery goods, soft drinks) locate near the market.

Factor rating (weighted scoring) method

  1. List the relevant factors.
  2. Give each a weight reflecting its importance; weights usually sum to 1 (or 100).
  3. Score every site on each factor on a common scale (e.g. 0–10 or 0–100).
  4. Multiply score by weight and sum for each site.
  5. Choose the site with the highest total, after checking sensitivity: if two totals are close, small changes in weights can reverse the choice. It brings qualitative factors into a numerical comparison, but the weights and scores are subjective, so involve several assessors.

Location break-even (cost–volume) analysis

  1. Estimate the annual fixed cost F and variable cost per unit v for each site.
  2. Plot total cost TC = F + v·Q against annual volume Q for each site.
  3. Find the crossover volumes where lines intersect.
  4. For the expected volume, choose the site with the lowest total cost (or highest profit if selling prices differ between sites). Assumptions: costs are linear in volume, fixed costs are truly fixed over the range, only one product (or a fixed mix), and revenue per unit is the same at every site.

Related quantitative tools. The centre-of-gravity method locates a distribution centre at the volume-weighted average of the coordinates of the points it serves; the transportation model of linear programming chooses among sites when several plants serve several markets; the Brown–Gibson model combines objective cost measures with subjective factor ratings.

Formulas

Weighted score S_j = Σ w_i × s_ij

  • w_i = weight of factor i (Σ w_i = 1); s_ij = score of site j on factor i.

Total cost TC_j = F_j + v_j × Q

  • F_j = annual fixed cost of site j (₹/year); v_j = variable cost (₹/unit); Q = annual volume (units/year).

Crossover volume Q* = (F_B − F_A) / (v_A − v_B)

  • For two sites with F_B > F_A and v_A > v_B; below Q* site A is cheaper, above Q* site B is cheaper.

Profit_j = (p − v_j) × Q − F_j

  • p = selling price (₹/unit), used if price differs between sites.

Centre of gravity: x̄ = Σ x_i V_i / Σ V_i, ȳ = Σ y_i V_i / Σ V_i

  • (x_i, y_i) = coordinates of point i; V_i = volume shipped to or from it.

Worked examples

Example 1 (standard). Weights: labour 0.30, market access 0.25, transport 0.25, government incentives 0.20. Scores (out of 100): site P 70, 80, 60, 90; site Q 85, 60, 75, 70; site R 60, 90, 80, 50. Choose a site.

  1. S_P = 0.30 × 70 + 0.25 × 80 + 0.25 × 60 + 0.20 × 90 = 21 + 20 + 15 + 18 = 74.0.
  2. S_Q = 25.5 + 15 + 18.75 + 14 = 73.25.
  3. S_R = 18 + 22.5 + 20 + 10 = 70.5.
  4. Site P (74.0), but Q (73.25) is very close; a small shift of weight from incentives to labour would favour Q, so test the weights before deciding.

Example 2 (GATE level). Annual fixed costs and variable costs per unit: A ₹30 lakh, ₹750; B ₹50 lakh, ₹450; C ₹90 lakh, ₹250. Find the volume ranges in which each site is cheapest, and choose for 15,000 units/year.

  1. A = B: Q = (50 − 30) × 10⁵ / (750 − 450) = 20,00,000 / 300 = 6,667 units.
  2. B = C: Q = (90 − 50) × 10⁵ / (450 − 250) = 40,00,000 / 200 = 20,000 units.
  3. A = C: Q = 60,00,000 / 500 = 12,000 units (this crossover lies where B is cheaper than both, so it does not decide anything).
  4. Hence A is cheapest below 6,667 units, B between 6,667 and 20,000 units, and C above 20,000 units.
  5. At 15,000 units: TC_A = 30 + 0.0075 × 15,000 = ₹142.5 lakh; TC_B = 50 + 0.0045 × 15,000 = ₹117.5 lakh; TC_C = 90 + 0.0025 × 15,000 = ₹127.5 lakh. Choose B (₹117.5 lakh).

Common mistakes

  • Using weights that do not sum to 1 for some sites and not others, or scoring sites on different scales.
  • Reading only pairwise crossovers: always check which line is lowest in each range (the A–C crossover above is irrelevant).
  • Forgetting to convert lakh to rupees consistently between F and v.
  • Treating break-even analysis as complete: it ignores intangible factors, so combine it with factor rating.
  • Choosing the highest weighted score without testing how close the runner-up is.

For GATE PI

Expect short numericals: weighted factor scores, crossover volume between two or three sites, the cheapest site for a given volume, and sometimes a centre-of-gravity location. One-mark questions test location factors and the assumptions of each method. Practise sketching the total-cost lines quickly to see which site is lowest in each range.

Quick check

  1. Site X: F = ₹10 lakh, v = ₹200/unit; site Y: F = ₹16 lakh, v = ₹150/unit. Crossover volume?
  2. Which site is cheaper above that volume?
  3. Weights 0.6 and 0.4; a site scores 7 and 9. Weighted score?
  4. Name one weakness of the factor rating method.

Answers: 1. 6,00,000/50 = 12,000 units; 2. Y (lower variable cost); 3. 4.2 + 3.6 = 7.8; 4. Weights and scores are subjective, so results depend on who sets them.

Interview questions

All Work Systems and Facility Design interview questions

Try answering each one aloud before you open it.

  1. 1.What is the factor rating method in plant location selection?Concept

    The factor rating method is a quantitative technique used to evaluate multiple location options for a plant. It involves identifying key factors that affect location decisions, assigning weights to these factors based on their importance, and scoring each location option against these factors. The location with the highest weighted score is typically chosen.

  2. 2.Explain the break-even method in the context of plant location.Concept

    The break-even method is used to determine the point at which total costs of operating at different locations are equal. It involves calculating fixed and variable costs for each location and identifying the production volume at which the total cost for each location is the same. This helps in comparing the cost-effectiveness of different locations based on expected production volumes.

  3. 3.Why is the factor rating method preferred over other methods in some cases?Application

    The factor rating method is preferred because it allows for a comprehensive evaluation of both quantitative and qualitative factors. It is flexible and can be customized to include any number of factors relevant to the decision, making it suitable for complex decisions where multiple criteria must be considered.

  4. 4.What are the limitations of the break-even method in plant location decisions?Application

    The break-even method primarily focuses on cost factors and does not consider qualitative factors such as labor availability, infrastructure, or market access. It assumes that costs are linear and constant, which may not be realistic. Additionally, it requires accurate cost data, which may not always be available.

  5. 5.How does the factor rating method incorporate qualitative factors in decision-making?Application

    In the factor rating method, qualitative factors are included by assigning them weights based on their perceived importance. Each location is then scored on these factors, allowing decision-makers to consider aspects like community acceptance, quality of life, and environmental impact alongside quantitative factors.

  6. 6.What happens if the weights assigned to factors in the factor rating method are inaccurate?Application

    If the weights are inaccurate, the final decision may be skewed, leading to a suboptimal location choice. It is crucial to carefully assess and assign weights to reflect the true importance of each factor to ensure a balanced and effective decision-making process.

  7. 7.Describe a scenario where the break-even method might not be suitable for plant location selection.Application

    The break-even method might not be suitable in scenarios where qualitative factors are critical, such as when a company is entering a new market and needs to consider brand presence, customer proximity, or regulatory environment. In such cases, focusing solely on cost may overlook important strategic considerations.

  8. 8.Find the crossover volume for two plant locations: A has fixed costs of ₹50 lakh per year and variable cost ₹500 per unit; B has fixed costs of ₹30 lakh per year and variable cost ₹700 per unit.Numerical

    Set the total costs equal: 50,00,000 + 500Q = 30,00,000 + 700Q, so 20,00,000 = 200Q and Q = 10,000 units per year. Below 10,000 units B (lower fixed cost) is cheaper; above it A (lower variable cost) is cheaper. The choice then depends on the expected volume, and qualitative factors should still be checked.

  9. 9.With A (₹50 lakh fixed, ₹500 per unit) and B (₹30 lakh fixed, ₹700 per unit), which location should a company choose for 15,000 units a year?Numerical

    Total cost at A = 50,00,000 + 500 × 15,000 = ₹1.25 crore; at B = 30,00,000 + 700 × 15,000 = ₹1.35 crore. A is ₹10 lakh a year cheaper, as expected because 15,000 units is above the 10,000-unit crossover where the lower variable cost starts to win.

  10. 10.How can sensitivity analysis be applied to the factor rating method?Application

    Sensitivity analysis can be applied by varying the weights and scores of the factors to see how changes affect the overall ranking of location options. This helps in understanding the robustness of the decision and identifying which factors have the most influence on the final outcome.

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