A service plan can work in every demand scenario when assignments are changed between scenarios, yet have no single assignment that works in all of them. The difference is when the assignment must be chosen and what information is available at that moment.
The short answer is to test the actual commitment. If service groups must keep one centre, use the same assignment in every scenario. If reassignment is genuinely available, specify a rule that uses information available before the decision. Several successful scenario maps do not by themselves establish either a fixed plan or an executable adaptive policy.
We will build a complete original three-group example, prove the fixed-plan failure and test several repairs. The groups, capacities and demand units are fictional. This is an educational allocation model, not a recommendation to move residents, change school boundaries or alter an operating service. The Urban Planning root supplies the wider place-and-service context.
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ROUTE 1 · CHAPTERS 1–7
Define scenarios and assignments
Preserve the unit, whole-group rule and complete fixed-plan case analysis.
ROUTE 2 · CHAPTERS 8–14
Compare commitment and adaptive information
Separate scenario witnesses, average demand and executable policies.
ROUTE 3 · CHAPTERS 15–21
Test capacity repairs and changed actions
Prove repairs, compare split demand and retain the actual uncertainty set.
ROUTE 4 · CHAPTERS 22–28
Preserve routes, evidence and objectives
Check interpolation, eligibility, group meaning and the operational record.
ROUTE 5 · CHAPTERS 29–34
Practise and continue
Repair a report, solve a changed case and follow verified planning routes.
Chapter contents
Define scenarios and assignments · Chapters 1–7
1. Define the commitment before calculating capacity
2. Keep capacity and demand on the same basis
3. Preserve the two supplied scenarios
4. Construct a feasible plan for the first scenario
5. Construct a feasible plan for the second scenario
Compare commitment and adaptive information · Chapters 8–14
8. Read the order of the decisions in ordinary language
9. Separate an average-demand plan from a robust one
10. Make an adaptive rule explicit
11. Show that one movable group is enough here
12. Ask whether the information arrives in time
13. Notice when the available observation cannot distinguish scenarios
Test capacity repairs and changed actions · Chapters 15–21
15. Repair the fixed plan by adding capacity deliberately
16. Prove the smallest total capacity addition in this example
17. Consider a third centre without claiming it is cheaper
18. Change the rule to permit split demand
19. Keep fixed fractions separate from fixed amounts
20. Do not replace the scenario set with unrelated combinations
Preserve routes, evidence and objectives · Chapters 22–28
22. Explain when endpoint checks suffice for a fixed assignment
23. Add route eligibility before trusting a capacity repair
24. Keep demand groups separate from representative map points
25. Record how much reassignment an adaptive plan actually needs
26. Do not confuse a scenario with a forecast probability
Practise and continue · Chapters 29–34
29. Try an independent changed-capacity example
30. Check the transfer from both directions
31. Compare a changed information rule independently
32. Choose a learner route from loads to commitments
CHAPTER 1 OF 34 · Define scenarios and assignments
1. Define the commitment before calculating capacity
Imagine two existing community-service centres, East and West. Each can serve ten demand units in the period under study. Three groups, A, B and C, need service. Initially every group can use either centre under the supplied route and eligibility assumptions.
The planning rule assigns each whole group to one centre. A group’s demand cannot be divided between centres in this first model. We require every group to be served without exceeding either capacity.
This rule is an important input, not an inevitable feature of every service. Another arrangement might allocate individual appointments or allow split demand. We will examine that change later. For now, an assignment means a centre choice for each named group, and a fixed assignment must retain those choices across every scenario being tested.
CHAPTER 2 OF 34 · Define scenarios and assignments
2. Keep capacity and demand on the same basis
A capacity of ten is meaningful only if it uses the same service unit and time window as demand. Ten appointments per session cannot automatically be compared with ten households or ten visits per week.
Our fictional units are deliberately abstract but consistent. Each listed demand amount consumes that many units of its assigned centre’s capacity during the same model period. There are no waiting lists, carryovers, cancellations or partial completions.
For a real study, the unit might require distinctions between different services, staffing needs or appointment durations. Such distinctions can turn one scalar capacity into several constraints. Do not put incompatible activities into one total merely because the arithmetic becomes simpler. A clear unit ledger is the first protection against calling a plan feasible when its demand and capacity figures describe different tasks.
CHAPTER 3 OF 34 · Define scenarios and assignments
3. Preserve the two supplied scenarios
In scenario One, demand is nine units for A, two for B and two for C. In scenario Two, it is two for A, nine for B and two for C.
| Fictional scenario | Group A | Group B | Group C | Total demand |
|---|---|---|---|---|
| One | 9 | 2 | 2 | 13 |
| Two | 2 | 9 | 2 | 13 |
The total is thirteen in both cases, below the combined centre capacity of twenty. The scenarios differ in where the larger demand occurs.
These are two allowed states of the model. We have not assigned probabilities or claimed that they exhaust the real future. Their role is to make the logical distinction visible. Adding another scenario later changes the set of conditions a plan must satisfy; it does not merely add another decorative row to a report.
CHAPTER 4 OF 34 · Define scenarios and assignments
4. Construct a feasible plan for the first scenario
In scenario One, assign A to East and B together with C to West. East serves nine units. West serves two plus two, or four units. Both remain within ten.
The assignment serves every group and respects the whole-group rule. It therefore provides a feasible witness for this scenario. The unused capacity is one unit at East and six at West.
Do not combine those seven spare units into a freely movable resource. They are located at particular centres, and assignments create the local loads. A centre can be overloaded while another has spare capacity. This is why total demand below total capacity is a necessary first check but does not establish every proposed assignment. The witness must show which demand is placed at each centre.
CHAPTER 5 OF 34 · Define scenarios and assignments
5. Construct a feasible plan for the second scenario
In scenario Two, keep A at East and B at West, but put C with A. East now serves two plus two, or four units. West serves nine. Both again remain within ten.
This is a second feasible witness, but it is not the same assignment as the first. Group C changed centre. A and B did not need to move in these particular witnesses.
That small difference is the central planning question. If C is genuinely movable after the scenario is known, the two maps may contribute to an adaptive plan. If C must have one permanent assignment, the maps have not supplied it. A report should identify the changed group explicitly rather than present both successful scenarios as though the same operational commitment passed twice.
CHAPTER 6 OF 34 · Define scenarios and assignments
6. Test the tempting fixed choice for C
Fix A at East and B at West. If C is permanently assigned to East, scenario One gives East nine plus two, or eleven units. Its capacity is ten, so the fixed assignment fails.
If C is permanently assigned to West, scenario Two gives West eleven units. That fixed assignment fails too. The spare capacity at the other centre does not repair the stated fixed assignment because moving C was the action we excluded.
This checks two natural candidates, but it is not yet a proof that no fixed assignment exists. Perhaps moving A or B permanently would work. A careful impossibility argument must cover every permitted assignment, not just the two first choices that happen to be convenient. We next examine the complete small assignment space.
CHAPTER 7 OF 34 · Define scenarios and assignments
7. Cover every fixed assignment without missing a case
Three groups and two centres give eight labelled assignments. Because both centre capacities are the same, we can group complementary assignments together when proving infeasibility.
Putting all three groups together loads one centre with thirteen units in either scenario. Otherwise one group is alone and the other two share a centre. There are three possible pairings: A with B, A with C, or B with C.
A with B requires eleven units in both scenarios. A with C requires eleven in scenario One. B with C requires eleven in scenario Two. Every pairing violates a ten-unit capacity somewhere. This covers all assignments and proves that no fixed whole-group assignment serves both scenarios. The proof uses the complete set of possible pairings, not an assumption that the first failed map was representative.
CHAPTER 8 OF 34 · Compare commitment and adaptive information
8. Read the order of the decisions in ordinary language
The separate scenario tests establish this statement: for every scenario, there exists a feasible assignment. The fixed-plan question asks a different statement: there exists one assignment that is feasible for every scenario.
The order of those phrases matters. In the first statement, the assignment can depend on the scenario. In the second, it must be chosen before the scenario is resolved and retained across the set.
Our counterexample proves that the first statement does not imply the second. Both scenario-specific witnesses are correct, and the fixed-plan impossibility is also correct. There is no contradiction to resolve by changing a capacity figure. The statements answer different commitment questions. Writing the words before introducing optimisation symbols makes the reasoning easier to inspect in a planning meeting.
CHAPTER 9 OF 34 · Compare commitment and adaptive information
9. Separate an average-demand plan from a robust one
If the two scenarios receive equal probability for a separate calculation, the expected demand vector is A = 5.5, B = 5.5 and C = 2. Assign A alone to East and B with C to West. The average loads are 5.5 and 7.5, both below ten.
This plan is feasible for the expected-demand vector. It still overloads West in scenario Two, where B and C require eleven units. Averaging has hidden the peak local combination.
A mean-demand calculation can be useful when its objective and interpretation fit. It is not the same test as capacity feasibility in every supplied scenario. State whether the plan is being assessed against a mean, a probability of overload, an expected shortfall or a deterministic scenario requirement. One favourable summary cannot silently stand in for all four questions.
CHAPTER 10 OF 34 · Compare commitment and adaptive information
10. Make an adaptive rule explicit
Keep A at East and B at West. In scenario One, send C to West. In scenario Two, send C to East. This rule uses the scenario identity before C’s assignment is made.
The resulting loads are nine and four in the first scenario, and four and nine in the second. The rule therefore provides a feasible adaptive policy for the supplied two-scenario model.
It is stronger evidence than two unrelated successful maps because it states what changes, when it changes and which information selects the action. However, it remains conditional on the permission and practical ability to reassign C. A real plan also needs communication, staffing, accessible travel and any relevant administrative arrangements. The mathematical witness does not create those capabilities merely by naming an adaptive action.
CHAPTER 11 OF 34 · Compare commitment and adaptive information
11. Show that one movable group is enough here
Our rule leaves A and B permanently assigned and moves only C when needed. We already proved that moving no group cannot give one fixed feasible plan. Allowing one named group to adapt is sufficient through the constructed policy.
Thus one movable group is the minimum number needed under this particular definition of movement and the supplied permissions. The result concerns a count of groups, not the number of people affected, travel burden or implementation cost.
Group C consumes two demand units in each scenario, but those units might represent different real activities in another model. Do not describe the mathematical minimum as automatically the least disruptive social arrangement. The useful conclusion is narrower: the example identifies exactly which flexibility makes its capacity account feasible, allowing the practical consequences of that flexibility to be discussed openly.
CHAPTER 12 OF 34 · Compare commitment and adaptive information
12. Ask whether the information arrives in time
An adaptive rule cannot depend on information revealed after the decision has become irreversible. If C’s centre must be chosen before anyone knows which group has nine units of demand, the scenario-dependent rule is not executable under that timing.
Conversely, if a relevant demand record is available before appointments are assigned, a later decision may be possible. The model should specify the observation, decision time and action that remains open.
This is often called a non-anticipation requirement: choices made before distinguishing information arrives must be the same in states that still look identical. The phrase is less important than the practical test. Ask the planner to describe what the decision maker actually knows at the moment of assignment. A policy requiring knowledge of the future has not supplied a usable repair.
CHAPTER 13 OF 34 · Compare commitment and adaptive information
13. Notice when the available observation cannot distinguish scenarios
Suppose the only early observation is total demand. Both scenarios have thirteen units. That observation does not tell the decision maker whether A or B is the larger group.
Any rule that uses only that total must choose the same action for C in both scenarios. Sending C permanently to either centre creates one of the eleven-unit overloads already shown. The adaptive policy therefore needs more informative evidence than the total.
This makes data requirements concrete. More timely data can be valuable when it distinguishes states requiring different actions. A dashboard that reports the same aggregate in both states does not supply that distinction, even if it updates frequently. The useful question is which observation changes the permitted decision, not simply how many indicators the dashboard displays.
CHAPTER 14 OF 34 · Compare commitment and adaptive information
14. Test a bounded observation of one group's demand
In a separate fictional observation model, A’s true demand is either two or nine and its early reading differs from truth by at most δ. The possible reading intervals are [2 − δ, 2 + δ] and [9 − δ, 9 + δ].
They are disjoint when δ < 3.5. Under that supplied bound, the reading can distinguish the two scenarios before C is assigned. At δ = 3.5, both intervals include 5.5, so that reading can be compatible with either state.
This is a deterministic identification check, not a statistical confidence statement or a recommended data threshold for a real service. It illustrates why an adaptive plan must preserve the quality and timing of the evidence it uses. An observation can be available early yet still leave the relevant action unresolved.
CHAPTER 15 OF 34 · Test capacity repairs and changed actions
15. Repair the fixed plan by adding capacity deliberately
Return to the fixed-assignment requirement. Increase West’s capacity from ten to eleven, keep East at ten, and permanently assign A to East and B together with C to West.
Scenario One gives loads nine and four. Scenario Two gives loads two and eleven. Both fit the revised capacities. We have constructed a fixed feasible repair with one additional capacity unit at a specified centre.
This does not establish that such an expansion is physically, financially or administratively available. It identifies a conditional mathematical option for evaluation. A real planning record must say who can provide the capacity, when it becomes operational and what it actually measures. Capacity that exists only in an unfunded future proposal should not be counted as present service.
CHAPTER 16 OF 34 · Test capacity repairs and changed actions
16. Prove the smallest total capacity addition in this example
Every fixed assignment places either all three groups together or some pair together. The earlier case analysis showed a scenario load of at least eleven at a centre for any paired assignment, while the all-together option requires thirteen.
Starting from ten at each centre, less than one total added unit cannot raise any centre to eleven. No fixed plan can then meet the required load in every scenario. Our one-unit repair reaches that lower bound, so one is the minimum total added capacity in this particular model.
The proof concerns the sum of capacity increments, not money or overall welfare. One unit at one site might cost much more than another arrangement. Keep the mathematical objective explicit before calling the repair optimal. A matching lower bound and construction complete the stated capacity question, not every planning decision.
CHAPTER 17 OF 34 · Test capacity repairs and changed actions
17. Consider a third centre without claiming it is cheaper
Another fictional repair provides a third centre with capacity two and permanently assigns C there. A stays at East and B at West. The largest load at either original centre is nine, and the new centre serves two in both scenarios.
This fixed arrangement works under the supplied eligibility and route assumptions. It adds two capacity units, compared with one in the earlier expansion. That comparison does not establish which option has the lower financial or social cost.
Land, staffing, travel, maintenance and the value of keeping a particular group together could differ. A responsible alternatives table records the objective and conditions of each option rather than declaring a winner from a capacity count alone. The model has helped generate a precise option; the wider planning assessment still has work to do.
CHAPTER 18 OF 34 · Test capacity repairs and changed actions
18. Change the rule to permit split demand
Now allow every group’s demand to be divided equally between East and West. Use the same one-half routing fraction for every group in both scenarios. Each centre receives half of thirteen, or 6.5 units.
This is a fixed fractional routing policy that works in both scenarios. It does not contradict the whole-group impossibility proof because the permitted action changed. Splitting may be appropriate for some service units and inappropriate for others.
For example, a model of interchangeable requests can differ from one requiring a group to attend the same place. The decision record should identify which unit is indivisible and why. Do not repair an infeasible whole-group plan by dividing its demand in a spreadsheet unless the actual service arrangement permits the resulting split.
CHAPTER 19 OF 34 · Test capacity repairs and changed actions
19. Keep fixed fractions separate from fixed amounts
The one-half policy sends a fraction of each group’s realised demand to each centre. The actual amount sent changes when that group’s demand changes. A fixed fraction is therefore not a promise to send an identical number of units in every scenario.
For A, the policy sends 4.5 units to each centre in scenario One and one unit to each in scenario Two. Both follow the same routing fraction. The fractional units are valid only because this revised mathematical model permits divisible demand.
If actual units must be integral, additional rounding or assignment conditions enter. Their effect must be checked rather than hidden in a decimal allocation. A seemingly small change from fixed group choices to fixed proportions can alter both feasibility and the operational meaning of the plan. Preserve those meanings in the comparison table.
CHAPTER 20 OF 34 · Test capacity repairs and changed actions
20. Do not replace the scenario set with unrelated combinations
Our original uncertainty set contains two vectors: (9, 2, 2) and (2, 9, 2). It does not include the simultaneous-heavy state (9, 9, 2).
If that additional state is admitted, its total is twenty, exactly equal to combined capacity. Nevertheless, whole-group allocation to two ten-unit centres fails: C must share with one of the nine-unit groups, producing eleven.
The earlier adaptive whole-group policy therefore does not establish feasibility for this enlarged set. Equal fractional splitting would give ten per centre in the new state, but that uses the different divisible-demand rule. Preserve the actual joint scenario description. Taking each group’s separate maximum can create a deliberately conservative test, but it is a new uncertainty set and should be labelled as such rather than presented as the original two-state account.
CHAPTER 21 OF 34 · Test capacity repairs and changed actions
21. Test all interpolated demand states carefully
Consider another explicitly supplied set: A = 2 + 7t, B = 9 − 7t and C = 2 for every t between zero and one. The endpoints reproduce the original scenarios in reverse order. Total demand remains thirteen.
Keep A at East and B at West, then assign C to the centre with the smaller A-or-B load. The larger base load is at most nine. The smaller base load is at most 5.5, so adding C gives at most 7.5. Both centres stay within ten.
This proves an adaptive policy for the whole stated interpolation set, not merely for its endpoints. It uses the observed relative base loads before C’s placement. If demand is restricted to integers, the set of allowed t values would need adjustment, but the same inequalities remain useful wherever the supplied demands and indivisible-group convention are meaningful.
CHAPTER 22 OF 34 · Preserve routes, evidence and objectives
22. Explain when endpoint checks suffice for a fixed assignment
For a fixed assignment and linearly interpolated demand, each centre’s load is a linear interpolation of its endpoint loads. If both endpoint loads are within capacity, every intermediate load is also within capacity.
That gives a valid endpoint test for a fixed assignment over the convex combinations of the supplied scenarios. It does not manufacture a fixed assignment when different endpoint witnesses use different maps.
The distinction matters because a report may show one successful map at each endpoint and then invoke linearity. Linearity applies to loads under a retained assignment. It does not join two incompatible commitments into one fixed map. In our original example, no fixed assignment passes both endpoint tests, so interpolation cannot repair the missing commitment. State what remains fixed when using an endpoint argument.
CHAPTER 23 OF 34 · Preserve routes, evidence and objectives
23. Add route eligibility before trusting a capacity repair
Until now every group can use both centres. Suppose a new rule permits C to use East only, while A and B retain their earlier fixed destinations. Scenario One then puts A and C together at East, requiring eleven units.
The adaptive policy that previously moved C to West is no longer permitted. Spare capacity at West does not help without an eligible route or service arrangement. Capacity and eligibility are separate constraints.
The existing guide to service visits, timetables and opening hours examines another access condition. A centre’s nominal capacity is useful only when the relevant people can actually reach and use its service under the applicable arrangements. Add those conditions explicitly rather than treating a capacity allocation as a complete accessibility finding.
CHAPTER 24 OF 34 · Preserve routes, evidence and objectives
24. Keep demand groups separate from representative map points
Our groups have supplied demand totals and eligibility relationships. A dot on a diagram represents that record; it does not prove that every household within a geographical area has the same route or needs.
The existing article on household walking routes and neighbourhood centres develops the representative-point problem. Its route evidence should be resolved before treating all members of a group as interchangeable for access.
This article isolates a different question: even after suitable group demands and routes have been supplied, can one assignment survive the stated demand scenarios? Keeping the two layers distinct prevents a correct robust-capacity calculation from being credited with validating a spatial aggregation or route assumption that it never tested.
CHAPTER 25 OF 34 · Preserve routes, evidence and objectives
25. Record how much reassignment an adaptive plan actually needs
An adaptive map should identify the change relative to a chosen baseline. In our policy, only C changes destination, and its demand is two units in both scenarios. A and B keep their destinations.
Other feasible maps might swap A and B instead, affecting the larger group. Those maps can have different operational consequences even if both satisfy capacity. A feasible witness does not automatically minimise disruption.
If reassignment burden matters, define its unit: groups moved, demand units redirected, additional travel, changes per period or another relevant measure. Then optimise or bound that quantity under the capacity constraints. Do not treat the number of changed arrows as a complete social-impact measure. The model helps make the action explicit so affected users and responsible operators can evaluate what the mathematical flexibility would mean in practice.
CHAPTER 26 OF 34 · Preserve routes, evidence and objectives
26. Do not confuse a scenario with a forecast probability
The original robust test requires feasibility in both supplied states. It needs no probability for either state. Adding probabilities answers a different question, such as expected overload or expected travel.
Suppose scenario Two is assigned a small probability. The fixed map A to East, B and C to West still fails the deterministic every-scenario requirement. Its expected performance may be acceptable under some separately stated objective, but that would be a different decision rule.
Conversely, a robust plan for a small chosen scenario set does not guarantee performance outside that set. State how scenarios were constructed, which uncertainties they represent and which changes would trigger review. Robust is always relative to a specified uncertainty description and permitted actions, not a general promise that nothing can go wrong.
CHAPTER 27 OF 34 · Preserve routes, evidence and objectives
27. Build a compact assignment evidence record
A useful record contains the group definitions, demand units, period, capacity basis, route eligibility, whole-or-split rule, scenario set and decision timing. It identifies what is fixed and what can adapt, including the evidence available at each decision.
For every claimed feasible plan, include the assignment and centre loads. For an impossibility claim, show a complete argument covering the allowed alternatives or clearly state the limits of the search. A failed trial map is not enough by itself.
Where a policy adapts, record the observation that selects its action, when that observation becomes available and who can implement the change. Include unresolved permissions and service dependencies. This makes the plan reviewable by another person instead of requiring them to infer operational assumptions from an attractive map with apparently balanced totals.
CHAPTER 28 OF 34 · Preserve routes, evidence and objectives
28. Repair a misleading multi-scenario report
A fictional report says that the service arrangement is ready because every demand scenario has a map with loads below ten. Ask whether the maps keep the same group assignments and whether the actual service permits changes.
In our example, the first map places C at West and the second places C at East. If a fixed assignment is required, the report has not supplied one. The pairing proof establishes that none exists under the original capacities and whole-group rule.
Repair the conclusion without discarding the valid scenario calculations. State that both scenarios are individually feasible, a fixed whole-group plan is infeasible, and an explicit one-group adaptive policy or a specified capacity change would alter that result. This preserves useful work while making the commitment and missing capability visible.
CHAPTER 29 OF 34 · Practise and continue
29. Try an independent changed-capacity example
Use two new centres, each with capacity twelve. Groups P, Q and R have demands (11, 2, 2) in state Red and (2, 11, 2) in state Blue. Each group must initially remain whole and every group can use either centre.
Before reading the answer, construct a feasible assignment for each state. Then determine whether one fixed assignment can serve both. A complete answer should cover every possible pairing, not merely test one preferred map.
Next ask which single group can be allowed to adapt while the other two keep their destinations. Finally propose a minimum total capacity addition that permits a fixed assignment. State why the addition is sufficient and why anything smaller cannot work under this model. These questions change the numbers while preserving the distinction between a scenario witness and a shared commitment.
CHAPTER 30 OF 34 · Practise and continue
30. Check the transfer from both directions
Place P at the first centre and Q at the second. In Red, send R to Q’s centre, giving loads eleven and four. In Blue, send R to P’s centre, giving four and eleven.
No fixed whole-group assignment works at capacity twelve. P with Q requires thirteen in both states. P with R requires thirteen in Red; Q with R requires thirteen in Blue. All three together require fifteen. This covers the pairings.
Adding one capacity unit to the centre permanently serving Q and R permits fixed loads of four in Red and thirteen in Blue, while P’s centre has at most eleven. Less than one total added unit cannot bring any original centre to thirteen. The one-unit construction therefore reaches the lower bound. The proof uses the stated capacity objective and does not establish an actual expansion’s cost or availability.
CHAPTER 31 OF 34 · Practise and continue
31. Compare a changed information rule independently
Return to the original two scenarios and suppose only the total thirteen is known when C must be assigned. Explain why the adaptive policy cannot use that observation to select a safe destination in both states.
Now supply an early exact reading of A’s demand. A reading of nine identifies scenario One; a reading of two identifies scenario Two. The policy can then send C to the other centre from the larger base load, provided the change is still operationally permitted.
For a further extension, use the bounded-reading intervals from the earlier chapter. Explain why a shared possible reading at the touching point must be treated as ambiguous. The learning check is about admissible information, not merely finding another feasible map after the answer is known. A policy should work with what the decision maker can actually distinguish.
CHAPTER 32 OF 34 · Practise and continue
32. Choose a learner route from loads to commitments
The repair route starts with one scenario, consistent units and a centre-load ledger. Establish why total spare capacity does not validate every local assignment.
The stabilisation route holds the assignment fixed while changing demand. Construct the two successful scenario maps, identify the changed group and prove the fixed-plan failure by covering the pairings. Ask the learner to repair the plan through one explicitly changed assumption.
The extension route adds information timing, adaptive actions, fractional demand and uncertainty sets. Independence appears when the learner can explain which proof still applies after a condition changes. The Education parent guide connects this with transfer: a method is useful when its decision boundary and assumptions remain understandable in a new setting.
CHAPTER 33 OF 34 · Practise and continue
33. Questions about feasible scenarios and fixed plans
Does enough total capacity guarantee a fixed assignment?
No. Local loads, indivisible groups and eligibility can prevent a fixed plan even when total demand is below total capacity. Our complete pairing proof supplies one example.
Is an adaptive plan automatically better?
It uses a different permitted action set. Its practical value depends on information, timing, user effects and the ability to implement changes. A mathematical policy does not grant those permissions.
Can I average the demand scenarios?
An average can support an explicitly average-based question. It does not establish feasibility in every scenario. The original average-demand plan conceals an eleven-unit overload in one state.
Does a successful solver output settle the planning decision?
It supports the model and inputs actually solved. The real objective, capacities, routes, operating arrangements and implementation responsibilities still need appropriate evidence.
CHAPTER 34 OF 34 · Practise and continue
34. Continue through access, allocation and source evidence
Return to Urban Planning for the wider task of connecting places, services and delivery. Use location–allocation for choosing sites and assigning demand, and the linked timing and household-route guides for their separate access questions.
Esri's official location–allocation documentation describes capacity constraints, whole-demand-point allocation in its capacitated-coverage model and cases where the nearest facility is not assigned. Those source-specific features provide context; no software result is claimed here. Every scenario, policy, proof and transfer task above is an original fictional construction.
Source checked on 24 October 2026. This lesson establishes conditional allocation results, not service readiness, a catchment decision or permission to change a real facility. Explore How X Works for wider first-principles reading routes.