10. Quantitative Layout Models and Optimization

Introduction: From Arrangement to Model-Based Design

Facilities layout is often introduced as the physical arrangement of departments, workstations, storage areas, service points, aisles, and supporting facilities. At an advanced level, however, layout planning is a decision problem involving competing objectives, uncertain data, operational constraints, and substantial financial consequences. A layout may reduce material movement but increase congestion; shorten travel distance but limit future expansion; improve departmental adjacency but create safety or supervision difficulties. Quantitative layout models provide a disciplined way to expose and evaluate these trade-offs.

The central idea is to represent a facility mathematically. Departments or activities are treated as entities, possible locations as positions, and movement or interaction requirements as numerical relationships. The planner then seeks an arrangement that minimizes cost, distance, risk, or another objective while satisfying practical constraints. Quantitative models do not replace engineering judgment. Rather, they make assumptions explicit, permit alternatives to be compared consistently, and support defensible managerial decisions.

This chapter develops assignment, quadratic assignment, graph-based, distance-based, cost, and multi-criteria models. It also examines heuristic solution methods, sensitivity analysis, digital applications, and the interpretation of model results in real facilities.

Learning Objectives

After studying this chapter, the student should be able to:

1. Formulate layout decisions using assignment, distance, flow, and cost variables.

2. Distinguish between linear assignment and quadratic assignment models.

3. Construct relationship graphs and convert qualitative closeness requirements into analytical inputs.

4. Evaluate layouts using rectilinear, Euclidean, aisle, and path-based distances.

5. Apply heuristic methods such as pairwise exchange, construction algorithms, and improvement search.

6. Incorporate constraints, uncertainty, safety, flexibility, and multiple criteria into layout analysis.

7. Interpret sensitivity analysis and recognize the limitations of mathematical optimization.

8. Recommend a layout alternative using quantitative evidence and managerial judgment.

10.1 The Analytical Representation of a Layout

A layout model normally contains four elements: facilities or departments, candidate locations, interaction requirements, and an objective function. Let departments be indexed by i and j, and locations by k and l. A binary assignment variable may be defined as:

xᵢₖ = 1 if department i is assigned to location k; otherwise xᵢₖ = 0.

If every department occupies exactly one location and every location receives one department, the basic assignment constraints are:

Σₖ xᵢₖ = 1 for every department i,

Σᵢ xᵢₖ = 1 for every location k.

These constraints describe a one-to-one assignment. Real facilities may require unequal areas, multiple modules, reserved spaces, corridors, fire exits, clean zones, or fixed departments. Such requirements must be added as constraints or handled during solution evaluation.

The interaction between departments may be measured by material flow, people movement, information exchange, service frequency, communication intensity, or risk exposure. A flow matrix F = [fᵢⱼ] records the intensity of movement between departments i and j. A distance matrix D = [dₖₗ] records the distance between locations k and l. A cost matrix may assign a cost per unit of flow and distance, or may include handling, installation, relocation, and operating costs.

The widely used load-distance measure is:

LD = Σᵢ Σⱼ fᵢⱼ dᵢⱼ,

where dᵢⱼ is the distance between the assigned locations of departments i and j. If the cost per unit movement varies, the objective becomes:

C = Σᵢ Σⱼ fᵢⱼ cᵢⱼ dᵢⱼ,

where cᵢⱼ is the unit handling cost. In practice, the objective may also contain fixed costs, congestion penalties, safety costs, and future-change costs.

Important Terminology

A department is any organizational or operational unit requiring space. A location is a candidate position within the facility. Flow is the quantity of movement or interaction between two units during a defined period. Adjacency means that two units share a boundary or are positioned sufficiently close for a specified purpose. A relationship chart expresses desired closeness, often using ratings such as A, E, I, O, U, and X. A layout alternative is a complete or partial assignment of departments to locations. The objective function measures the performance criterion being minimized or maximized. A feasible solution satisfies all specified constraints; an infeasible solution violates at least one.

10.2 Assignment Models: Useful Structure and Restricted Scope

The linear assignment model assigns departments to locations when the contribution of assigning a department to a location can be calculated independently of other assignments. Its general form is:

Minimize Z = Σᵢ Σₖ cᵢₖ xᵢₖ,

subject to the one-to-one assignment constraints and xᵢₖ ∈ {0,1}.

Here, cᵢₖ may represent the cost of placing department i at location k. Examples include distance from a fixed receiving dock, installation cost, environmental suitability, or expected service time. The model is computationally efficient and can be solved exactly using methods such as the Hungarian algorithm or integer programming software.

Its principal limitation is independence. If the cost of placing department i at location k depends on where department j is placed, the linear assignment model is inadequate. For example, the value of assigning machining to a particular location depends on the location of assembly if material flow between the two is significant. This interaction leads to the quadratic assignment problem.

Assignment models remain valuable as submodels. They can assign machines to predesigned cells, offices to standardized rooms, or service functions to fixed zones. They are also useful in staged planning, where the broad layout is determined first and detailed assignment is performed subsequently.

10.3 Quadratic Assignment and Interaction-Based Optimization

The quadratic assignment problem (QAP) explicitly considers the interaction between pairs of assignments. Its standard objective is:

Minimize Z = Σᵢ Σⱼ Σₖ Σₗ fᵢⱼ dₖₗ xᵢₖ xⱼₗ.

The product xᵢₖxⱼₗ equals 1 only when department i is assigned to location k and department j to location l. The model therefore calculates the total flow-weighted distance generated by the complete arrangement.

QAP is especially appropriate when:

• material flow between departments is substantial;
• the number of departments is moderate but interactions are numerous;
• travel distance is a major operating cost;
• adjacency decisions cannot be evaluated independently;
• the facility has a relatively stable product or process structure.

The model is computationally difficult because the number of possible arrangements grows factorially with the number of departments. Even medium-sized problems may be impractical to solve through complete enumeration. Exact methods, including branch-and-bound and mixed-integer formulations, can provide optimal solutions for smaller instances. For larger instances, planners generally use heuristics or metaheuristics.

A key managerial issue is the quality of the data. A precise optimization applied to unreliable flow estimates may produce a misleading answer. Flow matrices should distinguish average volume from peak volume, account for empty travel where relevant, and state the time horizon. If product mix changes substantially, a single flow matrix may not represent actual operations.

10.4 Distance, Flow, and Cost: Selecting the Right Measure

Distance is not a universal concept. The straight-line or Euclidean distance between two centroids is easy to calculate but may be unrealistic when walls and aisles restrict movement. Rectilinear distance is commonly used in block layouts:

dᵢⱼ = |xᵢ − xⱼ| + |yᵢ − yⱼ|.

It is appropriate where movement follows orthogonal aisles. Euclidean distance is:

dᵢⱼ = [(xᵢ − xⱼ)² + (yᵢ − yⱼ)²]¹ᐟ²,

and may be suitable for open movement or preliminary analysis. Actual travel distance is obtained from the shortest feasible path through the aisle network. This path-based measure is more realistic for warehouses, hospitals, airports, and factories with restricted access.

A load-distance score is useful for comparing alternatives, but it is not necessarily a monetary cost. A movement of hazardous chemicals, fragile components, or high-value products may require a much larger penalty than an equivalent movement of ordinary materials. A cost model can incorporate handling rates, labor time, equipment usage, damage risk, and energy consumption.

For example, suppose three department pairs have flows of 80, 40, and 20 loads per day, distances of 10, 5, and 15 metres, and unit movement costs of 2, 3, and 1 monetary unit per load-metre. The total movement cost is:

(80 × 10 × 2) + (40 × 5 × 3) + (20 × 15 × 1) = 2,400 monetary units per day.

This calculation is simple, but it demonstrates why a high-flow pair may deserve priority even if another pair has a greater physical distance.

10.5 Graph-Based Models and Relationship Analysis

A facility can be represented as a weighted graph. Departments are nodes, and desired relationships are edges. The edge weight may represent flow, communication intensity, safety separation, or a closeness rating. A high-weight edge indicates that the connected departments should be close; a negative or exclusionary relationship indicates that separation is preferred.

The relationship diagram is particularly useful when reliable numerical flow data are unavailable. Systematic Layout Planning traditionally converts activity relationships into closeness requirements and then develops block layouts. Quantitative graph models extend this logic by assigning numerical weights to edges and evaluating the degree to which a layout preserves important relationships.

One useful objective is:

Maximize S = Σᵢ Σⱼ wᵢⱼ aᵢⱼ,

where wᵢⱼ is the relationship weight and aᵢⱼ indicates whether departments i and j are adjacent or within a defined distance. A penalty may be added for violating an X relationship or placing incompatible activities too close.

Graph models are valuable in offices, hospitals, laboratories, retail facilities, and service systems where communication, supervision, and customer convenience may matter as much as material flow. Their weakness is that closeness ratings can be subjective. A rating should therefore be supported by evidence, such as travel frequency, communication records, safety analysis, or interviews with process owners.

10.6 Multi-Criteria Layout Optimization

Most layout decisions involve several objectives. A manufacturing manager may seek low handling cost, safe separation, short lead time, ease of supervision, low investment, and flexibility for expansion. No single measure captures all of these concerns.

A weighted-sum model can be written as:

Maximize V = w₁P₁ + w₂P₂ + ... + wₘPₘ,

where Pₖ is a normalized performance score and wₖ is the importance weight, with Σwₖ = 1. Typical criteria include load-distance performance, investment cost, safety, flexibility, accessibility, environmental impact, and implementation disruption.

Normalization is essential because criteria use different units. A cost measured in currency cannot be added directly to a safety score unless values are converted to a common scale. Min–max normalization, target-based scoring, or utility functions may be used. Weights should be established through management workshops, analytic hierarchy process comparisons, swing weighting, or other structured methods.

A weighted score should not conceal unacceptable performance. Safety, legal compliance, fire access, and environmental requirements should normally be treated as constraints rather than merely low-weight criteria. Multi-criteria analysis is most effective when it presents a small set of non-dominated alternatives rather than claiming that one mathematically superior solution is universally correct.

The Pareto concept is important. An alternative is Pareto-dominated if another alternative is at least as good on every criterion and strictly better on one. A Pareto frontier contains alternatives for which improving one criterion requires sacrificing another. Managers can then select from the frontier according to strategic priorities.

10.7 Solution Methods: Exact Optimization and Heuristics

Exact optimization is appropriate when the model is sufficiently small, the data are credible, and the value of certainty justifies computational effort. Integer programming solvers can handle assignment, capacity, precedence, and fixed-location constraints. However, exact models may become difficult when departments have unequal shapes, aisle geometry, alternative process routes, and uncertain demand.

Heuristics seek good solutions efficiently rather than proving optimality. A common method is pairwise exchange. Starting from an initial layout, the planner exchanges two departments and recalculates the objective. If the result improves, the exchange is accepted. The process continues until no tested exchange improves the score. This is a local search method and can become trapped in a local optimum.

A practical pairwise exchange procedure is:

1. Create a feasible initial layout.

2. Calculate its flow-distance or multi-criteria score.

3. Select two departments and exchange their positions.

4. Reject the exchange if it violates a hard constraint.

5. Recalculate the score and retain the exchange if improvement occurs.

6. Continue until a complete search produces no improvement.

Other approaches include construction heuristics, which place the most strongly related departments first; improvement algorithms, which modify an existing arrangement; simulated annealing, which occasionally accepts inferior moves to escape local optima; tabu search, which prevents cycling; genetic algorithms, which evolve populations of layouts; and ant-colony or other swarm methods. These methods can be useful for large QAP-type problems, but their outputs should be tested for feasibility, repeatability, and managerial plausibility.

A strong practice is to use several initial layouts and several heuristic runs. If very different solutions produce similar objective values, the decision may be robust. If small changes in initial conditions produce large differences, additional analysis is required.

10.8 Constraints That Change the Mathematical Problem

Real layout planning rarely permits unrestricted permutation. Important constraints include:

• fixed locations for docks, utilities, exits, columns, or hazardous equipment;
• minimum and maximum area requirements;
• required adjacency or required separation;
• department shapes and aspect-ratio limits;
• aisle width and emergency access;
• material-handling equipment turning radii;
• clean-room, temperature, vibration, or contamination controls;
• precedence or one-way flow requirements;
• workforce access, ergonomics, and supervision;
• expansion reserves and phased construction constraints.

A model that ignores these conditions may produce an impressive numerical score but an unusable layout. Hard constraints should be represented explicitly whenever possible. Soft constraints can be represented through penalties, but penalty values must be calibrated. An excessively low penalty may allow unacceptable violations; an excessively high penalty may prevent useful trade-offs.

10.9 Sensitivity and Robustness Analysis

Optimization results should never be accepted solely because they are optimal under one set of assumptions. Sensitivity analysis asks how the recommended layout changes when assumptions change.

Important tests include:

• increasing or decreasing major flows;
• changing unit handling costs;
• using peak rather than average demand;
• altering criteria weights;
• adding a new department or product family;
• changing available space or expansion requirements;
• imposing temporary closures or equipment failure;
• modifying distance assumptions from centroid to path distance.

If a layout remains strong across these changes, it is robust. If its ranking changes frequently, management should avoid overcommitting to a precise result and may prefer a flexible alternative.

Scenario analysis is particularly useful for uncertain demand. For example, a facility may evaluate low, expected, and high-volume scenarios. A layout can then be scored using expected value, worst-case performance, or regret. The regret of an alternative is the difference between its performance and that of the best alternative under a given scenario.

Weight sensitivity is also important in multi-criteria models. If a recommendation changes when the safety weight moves from 0.25 to 0.30, the decision should be discussed as preference-sensitive rather than presented as an objective fact.

10.10 Applied Case: Reconfiguring an Electronics Assembly Facility

Background

The following is an illustrative case. A medium-sized electronics assembly facility contains receiving, component storage, surface-mount technology (SMT), manual insertion, testing, final assembly, finished-goods storage, and shipping. The existing arrangement developed incrementally as products and equipment were added.

Situation and Problem

Material frequently travels backward through the building. The production manager believes that handling effort, lead time, and congestion can be reduced, but the facility must retain fixed receiving and shipping docks. Testing requires environmental control, and finished goods must remain separated from incoming components. Three product families account for most volume, but their monthly proportions vary.

The improvement team first constructed a department-to-department flow matrix using monthly pallet and tote movements. It then measured actual aisle routes rather than straight-line distances. Safety and environmental restrictions were treated as hard constraints. The team considered three alternatives: the existing layout, a flow-oriented block layout, and a flexible layout reserving space beside final assembly for future testing equipment.

Analysis

The flow-oriented alternative produced the lowest expected load-distance score because receiving, storage, SMT, insertion, testing, assembly, and shipping were placed in a forward sequence. However, it required relocating a utility connection and left little room for expansion. The flexible alternative had a slightly higher expected movement score but reduced projected relocation cost under the high-growth scenario.

A multi-criteria model used four normalized criteria: movement cost, implementation investment, safety and compliance, and flexibility. Safety was treated partly as a constraint and partly as a scored criterion for alternatives that met the minimum standard. Management assigned the largest weight to movement cost but tested the result under several weight combinations.

Pairwise exchange was used to improve both proposed block layouts. Several exchanges reduced movement cost, but one apparently attractive exchange was rejected because it narrowed an emergency aisle below the required width. The team also tested peak-volume flows. Under peak demand, congestion near testing became the dominant issue, and the flexible alternative performed better than its average-demand score suggested.

Approach and Solution

The recommended solution combined the flow sequence of the second alternative with the expansion reserve of the third. Storage was divided into incoming and production-support zones. Testing was positioned close to assembly but separated from high-traffic receiving routes. A one-way material route was marked through the central aisles, and shipping access was preserved. The model did not dictate the final answer; it identified the critical trade-off between minimum current travel and future adaptability.

Outcome

The case illustrates that the best managerial decision may not be the alternative with the lowest single-period load-distance value. When uncertainty, safety, implementation cost, and future equipment are included, a slightly less efficient current layout may create greater long-term value.

Learning Points

The most important lessons are that data definitions must be agreed before optimization, path distances are preferable where access is restricted, hard safety constraints cannot be traded away for low movement cost, and sensitivity analysis can reveal the strategic value of flexibility.

10.11 Digital Tools, Analytics, and Emerging Practice

Computer-aided layout systems can generate block layouts, calculate distances, visualize flows, and compare alternatives. Simulation adds a dynamic perspective by representing queues, travel variability, equipment failures, batch sizes, and peak demand. A layout that performs well in a static load-distance model may produce congestion when realistic variability is introduced.

Digital twins can connect layout models with operational data from warehouse-management systems, manufacturing-execution systems, sensors, and indoor positioning platforms. Such systems may update flow assumptions as demand changes. Optimization algorithms can then search for revised layouts or routing policies.

Artificial intelligence and machine learning can support demand forecasting, flow estimation, image-based space analysis, and heuristic search. Their usefulness depends on data quality and explainability. A recommendation that cannot be traced to understandable flows, constraints, and assumptions is difficult to govern. AI should therefore support, not replace, engineering review and stakeholder accountability.

10.12 Limitations, Risks, and Professional Governance

Quantitative layout models can create false precision. Flow estimates may reflect temporary conditions, costs may omit indirect effects, and relationship ratings may reflect the influence of one department rather than the system as a whole. Optimization may also encourage planners to minimize measurable travel while neglecting worker fatigue, accessibility, noise, privacy, learning effects, or organizational change.

Common mistakes include using centroid distances in obstructed layouts, double-counting flows, ignoring empty travel, treating all departments as equal in area, confusing adjacency with efficient process flow, and reporting an optimum without documenting assumptions. Another mistake is to optimize before confirming the process design. If routing, product mix, or technology is still changing, a highly detailed layout model may be premature.

Professional practice requires transparent assumptions, version-controlled data, documented constraints, stakeholder review, and validation through walk-throughs or simulation. Layout decisions should respect occupational health and safety obligations, accessibility requirements, environmental controls, privacy, and fair treatment of workers. A cost reduction that transfers excessive walking, lifting, noise, or exposure to employees is not a sound optimization.

Best-Practice Framework for Managers

A disciplined layout study normally follows this sequence:

1. Define the decision horizon, scope, and success measures.

2. Map processes and identify departments, flows, fixed features, and constraints.

3. Collect and validate movement, area, cost, and demand data.

4. Select an appropriate distance and objective model.

5. Develop a relationship graph and generate feasible alternatives.

6. Apply exact or heuristic optimization as appropriate.

7. Evaluate alternatives using cost, safety, flexibility, and implementation criteria.

8. Conduct scenario and sensitivity analysis.

9. Validate promising alternatives through simulation, stakeholder review, and physical or digital walk-throughs.

10. Implement in phases, monitor results, and revise the model as operating conditions change.

The best layout is therefore not simply the one with the smallest mathematical objective. It is the one that performs well under realistic conditions, complies with non-negotiable requirements, supports organizational strategy, and remains adaptable as the facility evolves.

Chapter Summary

Quantitative layout planning represents departments, locations, flows, distances, costs, and constraints in a formal decision model. Linear assignment models are suitable when assignment costs are independent, whereas quadratic assignment models capture the interaction between department pairs and locations. Graph-based models express adjacency and closeness requirements, while load-distance and cost models quantify movement performance. Multi-criteria models are necessary when safety, flexibility, investment, accessibility, and environmental considerations accompany cost objectives.

Exact optimization can solve smaller and well-defined problems, but heuristics and metaheuristics are often necessary for complex layouts. Constraints must reflect actual space, access, safety, environmental, and expansion requirements. Sensitivity and scenario analysis reveal whether a recommendation is robust or dependent on uncertain assumptions. Digital tools, simulation, digital twins, and AI can extend analysis, but professional judgment and transparent governance remain essential. Effective layout optimization combines mathematical discipline with operational realism.

Key Terms

Assignment model: A model that assigns entities to locations while minimizing or maximizing a measurable objective.

Quadratic assignment problem: A layout problem in which the cost depends on pairs of simultaneous assignments.

Flow matrix: A table showing movement or interaction quantities between departments or activities.

Distance matrix: A table containing distances between candidate locations.

Load-distance score: The sum of flow multiplied by the distance associated with each movement.

Relationship graph: A network in which nodes represent departments and weighted edges represent desired relationships.

Adjacency: The condition in which two departments share a boundary or are sufficiently close.

Objective function: The mathematical expression that a model seeks to minimize or maximize.

Feasible solution: A solution that satisfies all hard constraints.

Hard constraint: A requirement that cannot be violated.

Soft constraint: A preference that may be violated subject to a penalty or trade-off.

Pairwise exchange: A heuristic that improves a layout by exchanging the positions of two departments.

Local optimum: A solution that cannot be improved by a specified set of nearby changes.

Metaheuristic: A general search strategy designed to explore complex solution spaces efficiently.

Normalization: Converting measures with different units to a comparable scale.

Pareto frontier: A set of alternatives for which improvement in one criterion requires sacrifice in another.

Sensitivity analysis: Examination of how results change when assumptions or parameters vary.

Robustness: The ability of a layout recommendation to remain effective under changing conditions.

Path distance: The shortest feasible travel distance through the actual aisle or access network.

Digital twin: A digital representation of a physical facility linked to operational data.

Review Questions

Short Answer Questions

1. Why is a quadratic assignment model more suitable than a linear assignment model for many facility-layout problems?

2. Distinguish between Euclidean, rectilinear, and path-based distance.

3. What is the purpose of a relationship graph in layout planning?

4. Define a hard constraint and give one layout example.

5. Why is sensitivity analysis necessary after obtaining an optimized layout?

Long Answer Questions

1. Explain the formulation, assumptions, and limitations of the quadratic assignment problem.

2. Discuss how flow, distance, and unit handling cost are combined to evaluate a layout.

3. Describe the role of heuristics in solving large layout optimization problems.

4. Explain how multi-criteria layout models can incorporate safety, flexibility, investment, and movement cost.

5. Discuss the professional and ethical risks of relying exclusively on mathematical layout optimization.

Analytical / Application Questions

1. A facility has four departments and four candidate locations. Explain how you would construct the flow and distance matrices and calculate the load-distance score for a proposed assignment.

2. Two layout alternatives have nearly identical movement costs, but one offers more expansion space and the other requires less implementation investment. Design a multi-criteria evaluation approach and explain how you would test the recommendation.

3. A heuristic produces different layouts when started from different initial arrangements. What analyses would you perform before recommending one layout to management?

22. Multiple Choice Questions with Answers

Question 1

Which feature distinguishes a quadratic assignment model from a linear assignment model?

A. It requires every department to occupy exactly one location.

B. It considers interaction costs between pairs of assignments.

C. It can be used only when departments have equal areas.

D. It excludes distance from the objective function.

Correct Answer: B. It considers interaction costs between pairs of assignments.

Question 2

Which distance measure is generally most appropriate when movement is restricted by actual aisles and access routes?

A. Euclidean centroid distance

B. Straight-line distance

C. Path-based shortest feasible distance

D. Randomized distance

Correct Answer: C. Path-based shortest feasible distance

Question 3

In a load-distance calculation, a department pair with high flow should normally receive priority because it

A. always has the largest physical area.

B. contributes strongly to total movement burden.

C. must be placed at the facility boundary.

D. cannot be included in a graph model.

Correct Answer: B. contributes strongly to total movement burden.

Question 4

What is the principal purpose of a relationship graph?

A. To express desired closeness or separation between activities

B. To calculate employee wages

C. To replace all facility constraints

D. To determine equipment depreciation

Correct Answer: A. To express desired closeness or separation between activities

Question 5

Which statement best describes a hard layout constraint?

A. It is a preference that can always be ignored.

B. It is a requirement that cannot be violated in a feasible solution.

C. It is a criterion used only after implementation.

D. It is a weight assigned to a soft objective.

Correct Answer: B. It is a requirement that cannot be violated in a feasible solution.

Question 6

A pairwise exchange heuristic improves a layout by

A. exchanging two department locations and retaining beneficial changes.

B. enumerating every possible layout without evaluation.

C. removing all safety constraints from the model.

D. assigning every department to the same location.

Correct Answer: A. exchanging two department locations and retaining beneficial changes.

Question 7

Why is normalization needed in a weighted multi-criteria model?

A. To ensure that all departments have equal area

B. To convert criteria with different units to comparable scores

C. To eliminate the need for management weights

D. To guarantee a globally optimal solution

Correct Answer: B. To convert criteria with different units to comparable scores

Question 8

If a layout recommendation changes substantially when flow estimates change slightly, the recommendation is

A. necessarily infeasible.

B. highly robust.

C. sensitive to assumptions and requires further analysis.

D. automatically the global optimum.

Correct Answer: C. sensitive to assumptions and requires further analysis.

Question 9

Which alternative is Pareto-dominated?

A. One that is better on every criterion than all others

B. One for which another alternative is at least as good on every criterion and better on one

C. One that satisfies all hard constraints

D. One located on the Pareto frontier

Correct Answer: B. One for which another alternative is at least as good on every criterion and better on one

Question 10

Why should safety and legal requirements generally be treated as constraints rather than merely low-weight criteria?

A. Because they may not be traded away for movement-cost improvement

B. Because they always increase material flow

C. Because they eliminate the need for simulation

D. Because they make all alternatives identical

Correct Answer: A. Because they may not be traded away for movement-cost improvement