School timetabling, starting with Israel

What the problem is, which solver to build on, how the Israeli market actually works, and where the product opportunity is.

Dotted-underlined terms show a short explanation when you hover or tab to them. Click one to jump to its full glossary entry.

Overview

This document answers three questions before any code is written: what problem a school-timetabling product is solving, in the exact terms computer science uses for it; which solver technology to build the first engine on; and how the market works, first in Israel and then globally. It is written for the person deciding the product's architecture and business direction, and it assumes no prior knowledge of optimisation. Every technical term is underlined and explained on hover, and defined again in the glossary at the end.

It is organised in four layers, and every major section repeats the same pattern: an overview of what the section covers, a summary of the findings, a bottom line you can act on, and then the detailed explanation with sources.

Summary

School timetabling is a proven NP-complete problem. That is not a blocker: schools of Israeli size are solved routinely today by treating the task as "satisfy every hard constraint, then keep reducing soft-constraint penalties for as long as the user is willing to wait". Nobody ships "the optimum".

Bottom line

Detailed explanation

1. The computer-science problem

What this problem is called

Overview

Is this a timetable problem, an allocation problem, or a constraint satisfaction problem? It is all three, but at different levels: one is the problem's proper name, one names a component inside it, and one names the language it is written in for a solver. This part gives the exact terms the literature uses, so the project can be described, searched for and discussed precisely.

The three labels, and what each one is

Summary

• Proper name. The High School Timetabling Problem, abbreviated HSTP or HSTT. It belongs to the educational timetabling family alongside university course timetabling and examination timetabling, a classification set by Schaerf's 1999 survey. Its historical core is the class-teacher timetabling problem, named by Gotlieb in 1963. Its modern canonical statement is the generalized high school timetabling problem defined by the XHSTT format in 2012.
• Field. Automated timetabling, a sub-area of operations research and artificial intelligence, with its own conference series, PATAT, running since 1995, and a EURO working group.
• Complexity classification. The decision version is NP-complete and the optimisation version is NP-hard. It is catalogued in Garey and Johnson's 1979 reference list of NP-complete problems under sequencing and scheduling as "Timetable design".
• Mathematical classification. A combinatorial optimisation problem of assignment type: discrete events are assigned to discrete time slots and resources subject to clash constraints. It is not "the assignment problem" of operations research, which is solvable in polynomial time, although room assignment inside it is exactly that.
• Modelling framework. It is usually written as a constraint satisfaction problem when only hard constraints matter and as a constraint optimisation problem, also called a weighted CSP, when soft constraints are scored. Operations research writes the same problem as an integer linear program; graph theory writes its core as edge colouring. These are notations for the problem, not its name.
• Neighbouring terms that are not this problem. Scheduling in the narrow sense means sequencing jobs with durations and precedence on machines. Rostering means assigning people to shifts. Resource allocation is an umbrella. Wren's 1996 taxonomy separates scheduling, timetabling, rostering and sequencing precisely so these are not confused.

Bottom line

Detailed explanation

Genealogy of the name. Gotlieb's 1963 paper "The construction of class-teacher time-tables" defined the problem through a requirements matrix stating how many times each teacher must meet each class, and gave the first algorithm, later refined with Csima. De Werra showed in 1970 that this pure form is bipartite edge colouring: by König's theorem a timetable exists whenever the number of periods is at least the busiest teacher's or class's load, and it can be built in polynomial time. Even, Itai and Shamir proved in 1976 that as soon as teachers have unavailable periods the problem becomes NP-complete. Cooper and Kingston showed in 1996 that NP-completeness arises in practice in several independent ways: wide subject choice, meetings of different durations, double periods, and even spread across the week. De Werra returned to the borderline cases in 2002. The name "high school timetabling" became standard through Kingston's work and the 2011 competition, and the generalized form is the one defined by XHSTT.

Where it sits in the taxonomy.

Your six items in the problem's own vocabulary. The schedule is the solution: an assignment of every event to a time. Classes and logical groups are resources of type Class and Student group, or in the 2024 extension, groups the solver forms itself. Teachers and physical rooms are resources of type Teacher and Room. The program of learning is the curriculum: it is the input that generates the event list, stating which class meets which subject for how many periods, and it is decided before timetabling begins. Decomposed by the literature, the whole task has four named sub-problems: the teacher assignment problem, which decides who teaches which class; the timetabling problem proper, which places events in time; the room assignment problem, a bipartite matching solved per slot; and student sectioning or group formation, which places pupils into hakbatsot and tracks.

Why the American version has a different name. In the United States each pupil has an individual course list, so the central problem is student sectioning and master scheduling rather than class-based timetabling. It is the same family but a different member, and the research community treats it under university course timetabling, post-enrolment variant.

Current status of the definition. The canonical statement is XHSTT from 2012, with 15 constraint types. It was extended in 2024 to include individual student course choice and dynamic group formation, which brings the Israeli hakbatsot case fully inside the standard. The most recent surveys of the field are Tan et al. 2021 and Ceschia, Di Gaspero and Schaerf 2022. The state of solving is in section 2.

Sources for this part

1. Gotlieb 1963, The construction of class-teacher time-tables, IFIP Congress. semanticscholar.org
2. Even, Itai, Shamir 1976, SIAM Journal on Computing. epubs.siam.org
3. Garey, Johnson 1979, Computers and Intractability. wikipedia.org
4. Cooper, Kingston 1996, The complexity of timetable construction problems, PATAT 1995, LNCS 1153. springer.com
5. Wren 1996, Scheduling, timetabling and rostering: a special relationship?, PATAT 1995, LNCS 1153. springer.com
6. Schaerf 1999, A survey of automated timetabling, Artificial Intelligence Review. springer.com
7. de Werra 2002, Complexity of some special types of timetabling problems, Journal of Scheduling. wiley.com
8. Marte 2002, Models and algorithms for school timetabling, doctoral thesis, LMU Munich. A thorough constraint-programming formulation. PDF
9. Kingston, Timetabling papers. jeffreykingston.id.au
10. PATAT conference series. patatconference.org

Background: what kind of problem this is

Computer science sorts problems by how the effort to solve them grows with their size. Problems in the class P can be solved in time that grows polynomially, so doubling the input roughly multiplies the work by a constant. Problems in the class NP are those where a proposed answer can be checked quickly, even if finding one is hard. NP-complete problems are the hardest in NP: a fast algorithm for any one of them would give a fast algorithm for all of them, and after fifty years of trying nobody has found one. Whether one exists is the P versus NP question, one of the seven Millennium Prize problems.

Timetabling sits squarely in this class. Checking a finished timetable is trivial: scan every slot for a teacher, class or room that appears twice. Building one is not. Even, Itai and Shamir showed in 1976 that a satisfiability problem, the canonical NP-complete problem, can be disguised as a timetable with teacher availability restrictions, so any fast timetabling algorithm would also crack satisfiability.

The search space makes the point concrete. A school with 40 classes and 35 weekly lessons each has about 1,400 lessons to place into 35 or 40 weekly slots. Ignoring every constraint, the number of ways to do that is 40 to the power 1,400, a number with more than 2,200 digits. The observable universe holds about 10 to the power 80 atoms. No computer will ever enumerate the options, so every practical method is a search that prunes almost all of them without looking.

Four things make the problem tractable in practice despite this.

• Constraint propagation. Each decision eliminates whole regions of the search space at once. Placing a teacher's lesson on Monday first period immediately removes all of that teacher's other lessons, and all of that class's other lessons, from that slot.
• Learning from dead ends. Modern SAT and CP solvers record why a branch failed and never revisit the same combination. This is the single biggest reason solvers today beat solvers of the 1990s.
• Slack in real schools. A teacher typically uses 70 to 85 percent of the available slots, rooms are rarely all full, and most lessons involve one class and one teacher. The instances that take minutes rather than seconds are the tight ones: part-time teachers with narrow availability, many hakbatsot blocks linking classes together, and scarce rooms such as labs and gyms.
• Accepting good enough. The school does not need a proof that no better timetable exists. It needs zero hard violations and a low soft penalty, and it needs to see progress while it waits. That reframes an intractable optimisation problem as a tractable anytime search.

Timetabling belongs to a family of related problems that share techniques: graph colouring, exam timetabling, university course timetabling, nurse rostering and sports scheduling. Progress in any of them tends to transfer.

Complexity

Even, Itai and Shamir proved in 1976 that even a primitive version of the class-teacher timetable problem is NP-complete. The only tractable case they found is when every teacher is available for at most two periods. The intuition: when everyone is fully available, the problem is bipartite edge colouring, which is easy. Add teacher availability and it becomes a graph-colouring problem. Add rooms, split lessons and spread rules and it is NP-complete.

In practice you never search for a provably optimal timetable. You search for one that satisfies all hard constraints and minimises a weighted sum of soft-constraint violations, delivered by an anytime algorithm that keeps improving until the user stops it.

Benchmarks and standards

• XHSTT is the XML format the research community uses to describe a high-school timetable: times, typed resources, events with durations and resource slots, and 15 constraint types, each hard or soft with an integer weight. An archive of 25 real instances from 12 countries and a reference scorer, HSEval, are hosted by the University of Twente. No Israeli instance exists.
• The International Timetabling Competition of 2011 was on high schools; the winner, GOAL, combined simulated annealing and iterated local search on top of KHE. The 2019 competition was on universities and was won by a MIP-based matheuristic. Lesson: exact methods driving local search now beat pure heuristics.
• Since 2011 the strongest published approaches are two-step MIP, fix-and-optimize, MaxSAT with large neighbourhood search, and constraint programming with hot starts. A 2024 paper extends XHSTT with individual student course choice and dynamic group formation, which is exactly the hakbatsot shape.

Embeddable solvers

Expected performance for an Israeli-sized school of 40 to 80 teachers, 30 to 40 classes and 30 to 45 weekly slots: a feasible timetable within seconds to a few minutes on CP-SAT with eight or more workers, with soft-constraint improvement continuing for tens of minutes. This is an estimate; no rigorous benchmark of CP-SAT against XHSTT exists.

Modeling patterns that matter

• Hakbatsot and grade-wide blocks. One event that consumes several class resources and several teachers at the same time. XHSTT allows any number of pre-assigned resources per event.
• Free day and part-time teachers. Unavailable-times constraints plus a limit on the number of working days plus a workload limit.
• Double periods and split subjects. One event with the total weekly duration, split by rule, for example six hours as 2+2+1+1.
• Labs and room types. A preferred room group per event. Assign rooms last.
• Spread, idle time, daily maximum. Dedicated constraint types exist for each in XHSTT.
• Decomposition. Teacher-to-class first, which is a staffing decision made by people, then times, then rooms. Both KHE and the Danish two-stage method assign times before resources.
• Warm start and repair. Feed last year's or the current timetable as a hint. Fix-and-optimize, which frees one day or one teacher and re-solves, is the academic name for interactive repair.

Key readings

Ordered from foundations to current work. Peer-reviewed unless marked otherwise.

1. Clay Mathematics Institute, the P versus NP problem. A plain-language statement of the question. claymath.org
2. Even, Itai, Shamir 1976, On the complexity of timetable and multi-commodity flow problems. The NP-completeness proof. cris.technion.ac.il
3. de Werra 1985, An introduction to timetabling. The classic tutorial on the graph models behind class-teacher timetabling. sciencedirect.com
4. Schaerf 1999, A survey of automated timetabling. The most-cited overview of the field's first forty years. springer.com
5. Post et al. 2012, XHSTT: an XML archive for high school timetabling. Defines the data format this brief recommends mirroring. springer.com
6. Post et al., the ITC 2011 report. What the competition instances look like and how the winning solvers worked. PDF
7. Kingston, the KHE guide. The reference implementation, and the clearest description of decomposing time and resource assignment. PDF
8. Dorneles, de Araújo, Buriol 2014, A fix-and-optimize heuristic for high school timetabling. The technique behind interactive repair. sciencedirect.com
9. Kristiansen, Sørensen, Stidsen 2015, Integer programming for the generalized high school timetabling problem. First exact method for arbitrary XHSTT. PDF
10. Demirović, Musliu 2017, MaxSAT-based large neighborhood search for high school timetabling. sciencedirect.com
11. Demirović, Stuckey 2018, Constraint programming for high school timetabling: a scheduling-based model with hot starts. Closest published relative of the CP-SAT approach recommended here. monash.edu
12. Fonseca, Santos, Carrano, Stidsen 2018, parallel local search for XHSTT. sciencedirect.com
13. Tan et al. 2021, A survey of the state-of-the-art of optimisation methodologies in school timetabling problems. sciencedirect.com
14. Ceschia, Di Gaspero, Schaerf 2022, Educational timetabling: problems, benchmarks, and state-of-the-art results. Preprint. The best single map of the current field. arxiv.org
15. Krystallidis, Ruiz-Torrubiano 2024, extending XHSTT with student course choice and group formation. Preprint, also at PATAT 2024. arxiv.org
16. Krupke, The CP-SAT Primer. Not peer-reviewed. The practical guide to modeling with the recommended solver. github.com
17. Timefold, school timetabling quickstart. Not peer-reviewed. A working reference implementation of the alternative engine. github.com

2. The research frontier, and what AI changes

Where the classical frontier stands

• Benchmarks are quiet. The last posted improvements to the XHSTT best-known solutions date from January 2023. The reference methods are still MaxSAT with large neighbourhood search and the two-step MIP that proved several instances optimal. The current open reference solver is KHE24, released March 2024.
• Competitions are won by hybrids. ITC 2019 on university timetabling was won by a parallel fix-and-optimize matheuristic over a MIP, which held every best solution but one. ITC 2021 on sports scheduling was won by Southampton, with a multi-neighbourhood simulated annealing from Udine second, and post-competition improvements through 2025 came from the same families of method. There was no ITC 2023; the active competition was IHTC 2024 on hospital scheduling.
• The deployed version of the idea. CP-SAT's portfolio of LNS workers, each taking a different neighbourhood and sharing solutions, is the production form of the techniques that win these competitions.
• Quantum annealing is not competitive. A 2025 staff-scheduling study on D-Wave's hybrid solver only matched Gurobi's optimum up to 30 staff, reached it in a fifth of runs at 35, and found no feasible solution at 40. No timetabling instance of practical size has been solved competitively on quantum hardware.

Machine learning inside the solver

• Reinforcement learning for neighbourhood choice. Ceschia, Di Gaspero, Rosati and Schaerf (LION 2023) learn which local-search move to try next inside simulated annealing. It beats hand-tuned move probabilities within the same framework. It does not claim to beat a different state-of-the-art solver. This is the credible, modest version of the idea.
• Graph neural networks guiding search. A 2026 EvoApplications paper couples a GNN with a genetic algorithm for rostering and reports gains over the genetic algorithm alone. No comparison against CP, MIP or simulated annealing, and no standard benchmark. Several similar papers exist in minor venues with the same weakness.
• Learning to branch and neural LNS. General MIP research, not timetabling-specific. A December 2025 preprint documents the gap between wins measured in search-tree nodes and wins measured in wall-clock time; GPU dependence and poor generalisation to unseen instances remain the standing objections. The practical thread is bandit-based adaptive LNS, which needs no neural network; a 2025 preprint reports it competitive with Gurobi on hard MIP benchmarks.
• Learning from last year's timetable. No credible machine-learning paper exists. The established approach is classical minimal perturbation: re-solve while penalising every change from the previous timetable. Learning soft-constraint weights from history is studied under the name inverse optimisation, but has not yet been applied to timetabling.
• Bottom line. No paper from 2022 to 2026 applies reinforcement learning or neural networks to XHSTT or ITC 2019 instances with results that are competitive with the best-known solutions. The 2025 survey "Machine Learning for Scheduling" frames ML explicitly as a complement that guides search while the solver keeps responsibility for feasibility.

Large language models

• Natural language to constraint model. Systems such as OptiMUS, ORLM, Chain-of-Experts and CP-Agent take a problem described in prose and write the optimisation model. Reported accuracy on the standard NL4Opt benchmark is around 86 percent, falling to roughly 33 to 38 percent on the harder IndustryOR set, and the benchmark problems are textbook-sized descriptions of a few hundred characters. None of these evaluate on any timetabling benchmark. They address modelling productivity, not solver quality.
• LLM-designed heuristics. FunSearch (Nature 2024), EoH (ICML 2024), ReEvo (NeurIPS 2024) and EoH-S (AAAI 2026) use an LLM to evolve heuristic code. A controlled re-benchmark at EvoSTAR 2025 found that hand-designed heuristics still ranked best across the full bin-packing suite and that most LLM-evolved heuristics do not generalise beyond their training distribution. No LLM-evolved heuristic has published a best-known solution on any timetabling benchmark.
• Explanation and interaction. TRACE-cs (AAAI 2025 demo, KR 2025 full paper) answers "why is lesson X here and not there" questions about a timetable. The LLM only translates the question and the answer; correctness comes from a SAT solver computing the contrastive explanation. This solver-grounded pattern is the one worth copying.

Commercial "AI" claims

Every vendor claim examined follows the same pattern: the word AI refers to a chat front-end, or to a long-standing heuristic engine, and no benchmark results are published. aSc's AI panel lets a user type a change request that is applied to the data and re-run through its existing generator. Timely Schools says its optimiser "evaluates millions of combinations" and is "trained on the real logic of district master schedules" without disclosing a method. TimetableMaster claims machine learning with no technical evidence. Kindix describes its AI as pedagogical insight; the timetable module states no method. None of them claims, let alone shows, an improvement on the underlying computer-science problem.

Further reading on the frontier

1. Ceschia, Di Gaspero, Rosati, Schaerf 2023, Reinforcement learning for multi-neighborhood local search. LION 2023. springer.com
2. Rosati et al. 2022, multi-neighborhood simulated annealing for ITC 2021, Journal of Scheduling. springer.com
3. Holm et al. 2022, the ITC 2019 winner, Journal of Scheduling. springer.com
4. ITC 2021 sports scheduling competition site and results. robinxval.ugent.be
5. Machine Learning for Scheduling: A Paradigm Shift, 2025 survey preprint. arxiv.org
6. Branching strategies based on subgraph GNNs: theoretical promise versus practical reality, 2025 preprint. arxiv.org
7. ParBalans, bandit-based parallel adaptive LNS for MIP, 2025 preprint. arxiv.org
8. Perron, CP-SAT and its LNS worker portfolio, Scheduling Seminar slides. PDF
9. Minimal perturbation for university timetabling with MaxSAT, CPAIOR 2020. springer.com
10. OptiMUS-0.3, LLMs for optimisation modelling, preprint. arxiv.org
11. CP-Agent, LLM agent for constraint modelling, 2025 preprint. arxiv.org
12. Survey of LLMs for optimisation modelling, 2025 preprint. arxiv.org
13. Liu et al. 2024, Evolution of Heuristics, ICML 2024. arxiv.org
14. Beyond the Hype: benchmarking LLM-evolved heuristics, EvoSTAR 2025. arxiv.org
15. Vasileiou, Yeoh, TRACE-cs: contrastive explanations for course scheduling, AAAI 2025 and KR 2025. PDF
16. Quantum annealing for staff scheduling on D-Wave Advantage2, 2025 preprint. arxiv.org
17. IHTC 2024, the healthcare timetabling competition. ihtc2024.github.io

3. Israel: how the market works

Regulation and procurement

The Ministry of Education publishes an approved-vendor list with two mandated categories: pedagogical management, and timetable and teaching-staff management. Every school must pick one product in each. Schools on a PLG-only budget are exempt from the timetable requirement. Prices are capped per school per year, tiered by teacher count, and every vendor in each category sits within a few shekels of the cap.

Prices include VAT. The timetable category is approved through the 2027-28 school year. The Ministry's software standard mandates a Hebrew and Arabic interface and interfaces to MANBAS, the teacher-staff registry, Shiluvim and unified login, with data exchange for timetables, learning groups and attendance.

Schools with a GEFEN flexible budget pay the vendor directly; others are paid through the Ministry after a procurement committee. The selection deadline is around 10 to 15 September, and a school that switches mid-year still pays the old vendor in full. Education networks influence the choice, but the school is the legal chooser.

Incumbents

• Mashov: pedagogical management only, about 1,550 institutions, acquired by Priority Software in December 2021. Its timetable partner is Shahaf, close to 1,000 schools, Hebrew and Arabic, with an automatic solver plus a paid marketplace of human schedulers billed by hours placed.
• SmartSchool / Webtop: pedagogical management and a parent app; its timetable builder is Talmash.
• Schooly: approved in both categories.
• aSc Timetables / EduPage: a Slovak import with a full Hebrew interface, resold locally.
• Lantiv: an Israeli Windows desktop tool, also sold abroad.
• Smaller web tools: Cnafaim, Kindix Start, Maarechit and Maarechtit.

Structural facts the model must handle

• Scale. About 1,800 secondary institutions, many of them six-year schools. Roughly 334,000 pupils in junior high and 518,000 in upper secondary. 78 percent Hebrew education, 22 percent Arab.
• Classes. Administrative cap of 40 pupils; averages around 29 in grades 7 to 9 and 26 in grades 10 to 12. Typically 3 to 8 parallel classes per grade.
• Weekly hours. About 32 to 37 hours per class in junior high and at least 37.5 in secondary. The Director-General circular sets the day to start at 08:00, no dismissal before 11:50, Friday ending by 14:00, lessons of 45 to 50 minutes and at most 100 consecutive minutes.
• Five or six days. Since August 2021 any secondary school may drop Friday. Weekly hours stay constant, so weekdays get longer.
• Teacher contracts. Ofek Hadash in junior high: 36 hours as 23 frontal, 4 individual and 9 staying, with age reductions and a protected free day in six-day schools. Oz LaTmura in high school: from 2024-25, 38 hours as 25 frontal, 3 individual and 10 supporting, all on site. A six-year school runs both contracts at once. Role hours count as frontal and must sit in the grid.
• Bagrut. At least 21 study units, math and English at 3, 4 or 5 units, and at least one 5-unit elective from 43 subjects. This forces grade-wide blocks where all parallel classes split into tracks at the same time.
• Hakbatsot. Math and English in junior high are taught in ability groups across parallel classes, often regrouped after the first semester of grade 7.
• Sectors. State, state-religious, Haredi and Arab-Druze-Bedouin schools differ in core clusters and hours. PE is split by gender in religious schools.

Who builds the timetable, and when

A timetable coordinator or a deputy principal. Staffing is reported in March to May, the timetable is built June to August, and re-cut in September and October when the final hour allocation lands. Expect several re-plans a year. Reported pain: juggling individual, supporting and role hours that all need grid placement, partial opt-in to the reforms, and keeping pupils at school for end-of-day individual hours. Avney Rosha, the principals' institute, calls timetabling one of a principal's biggest time thieves and notes that even the best software "does not plan 100 percent of hours". Daily substitution is a separate workflow with its own modules at Schooly and Shahaf.

Market size

About 1,800 institutions times a cap of 2 to 3 thousand shekels gives roughly 4 to 5 million shekels a year for the entire timetable category. Pricing is fixed by the list. Upside must come from the pedagogical-management tier at 2 to 3 times the price, from services along the lines of Shahaf's scheduler marketplace, or from export. Getting onto the next Ministry approval cycle is the gating event.

4. The global landscape

Two problem shapes

• Class-based (Europe, Israel, most of Asia and Africa): the class is the unit, electives are handled as option blocks, hard constraints dominate.
• Student-based master scheduling (US, some Nordic upper secondary): each student submits course requests, the system builds sections and then loads students into them. It is a two-stage problem inseparable from enrolment data in the SIS.

A data model with "class" as the atomic unit will not generalize to the US without a rewrite. Model lessons as sets of student groups from day one, so a class is just a special case.

Market observations

• Sales models: per-school perpetual license plus maintenance, per-school annual subscription tiered by size, or bundled into a SIS. Substitution and cover are monetised separately almost everywhere.
• SIS vendors are internalising timetabling: Compass built Griddle, Bromcom built wTimeTable, Key Group bought TimeTabler, Tes bought Edval. SIS export is the adoption gate.
• Reviews complain of dated interfaces at aSc and Untis, phantom conflicts at aSc, opaque solvers, and slow cloud tools at Bromcom.

Gaps

1. Cloud, multi-user collaboration. Most incumbents are Windows desktop.
2. Explainability: "why can't this fit" answered with an unsat core. Nobody does it.
3. One live model for timetable, absences, substitutes and room bookings, pushed to the SIS.
4. API-first and SIS-agnostic, which matters most in Israel's fragmented SIS market.
5. RTL Hebrew and Arabic done well. Global cloud tools do not.
6. A generalizable model covering both class-based and US sectioning.
7. Israeli price headroom is limited; revenue comes from bundling or export.

5. How to proceed

6. Vegman's inputs: Mevo Hagalil

The requirements of the pilot school, captured on 5 September 2026 from Vegman, deputy manager of Mevo Hagalil primary school. Every item has an ID: D source documents, R requirements stated by Vegman, S facts observed in the school's own timetable, Q open questions, N next steps. Click an ID to jump to it. A standalone copy of this section lives on its own page.

Captured 2026-09-05 from Vegman, deputy manager of Mevo Hagalil primary school (grades 1-6), Israel. This is the working input document for implementation. Every item has an ID: D = source document, R = requirement stated by Vegman, S = fact observed in the school's current timetable, Q = open question, N = next step. Refer to items by ID.

Overview

Vegman gave fourteen rules, in Hebrew, describing how Mevo Hagalil's weekly timetable must be built, plus two reference documents showing the timetable the school actually achieved for the 2026-27 school year: a Google Sheet exported from the Tik-Tak software, and a photo of the physical magnet board. This document records each rule verbatim, translates it, interprets it as a constraint a solver can use, checks it against the achieved timetable where possible, and lists what is still unknown. It is deliberately a working document: the R items are the input, the Q items are what must be answered before the rules are complete.

Summary

• The school has 18 classes, three per grade, a five-day week of 33 periods per class, and heavy co-teaching: 42 percent of class-slots have two named teachers, more once assistants are counted. This is a Ofek Hadash primary school, so the teacher-hours model is the primary-school one, not the high-school one described in the research brief.
• Of the fourteen rules, six are structural facts confirmed by the data (R-01, R-02, R-03, R-09, R-11 in its per-grade reading, R-12 in shape). Five are teacher-welfare rules that the achieved timetable only partly satisfies (R-05, R-06, R-07), which means they are probably soft or need a precise definition (Q-05 to Q-08). Three depend on subject information the data does not contain (R-08, R-13, R-14), because the sheet has only teacher names and the board's colour code has no legend.
• The achieved timetable contains structures Vegman did not list: staff-meeting slots that block teachers, grade-wide music, choir and orchestra blocks, cross-grade mentoring pairs, class splits with a national-service soldier, and a Tuesday block where all grade 5 classes meet ten staff at once. These must be modelled as fixed or pre-placed events (S-05 to S-08).

Bottom line

The rules are enough to start modelling the domain, and not yet enough to run a solver. Three inputs unlock everything: the colour legend or a Tik-Tak export with subjects (N-01), a teacher table with weekly hours, part-time days and late or early constraints (N-02), and a curriculum table of weekly periods per subject per grade with double-period rules (N-03). The five ambiguous rules need a one-line answer each (Q-05 to Q-09). With those, Mevo Hagalil becomes the first benchmark instance for the product.

Detailed explanation

D. Source documents

D-02 and D-03 are meant to be equivalent. A cell-by-cell comparison of the Sunday block confirms they match, with small later edits on the board (for example an added magnet "ליאת" in class ב' תאנה, Sunday period 5). The board is the more recent state.

R. Requirements as stated by Vegman

Each item: the Hebrew original, the English translation, the interpretation as a constraint, what the achieved timetable shows, and open questions. Hard means must never be violated; soft means minimised with a penalty.

"בוא נתחיל מזה" — Vegman: "let's start with this." The following three were added after.

S. Facts observed in the achieved timetable

Q. Open questions

• Q-01 What are the clock times of periods 1 to 7 and the breaks? Does period 7 differ in length? Needed for the printed timetable, not for solving.
• Q-02 What is the exact derivation of individual and staying hours from frontal hours for this school? Ofek Hadash sets 36 hours as 23 frontal, 4 individual and 9 staying for a full post; part-time posts scale, and age reductions apply. A per-teacher table (N-02) removes the need to encode the formula.
• Q-03 Must individual and staying hours be placed in specific grid slots by the solver, or only counted? If placed, do they have their own constraints, such as individual hours needing pupils present, therefore not after the class's last lesson?
• Q-04 Is the no-gaps rule (R-05) hard for every teacher, including part-time and specialist teachers?
• Q-05 For R-06, must the period-1 start be in the homeroom teacher's own class? Is 3 a hard minimum?
• Q-06 For R-07, is "twice" exactly 2, at least 2, or at most 2? Does it apply to part-time teachers, and to teachers whose contract excludes the long day?
• Q-07 For R-08, is it exactly one mathematics lesson per day or at least one? Does "language" mean Hebrew only? Does it apply to Tuesday?
• Q-08 For R-11, does "not the same day" mean different days per grade (as achieved) or per class? Is the grade 4 Tuesday block a fourth trip to model the same way?
• Q-09 Who are teachers x, y, z in R-12, and in which grades do they work?
• Q-10 For R-14, which subjects are core, and is "end of day" the last period of each day or specifically period 7? Hard or soft?
• Q-11 Are the staff-meeting slots (S-05) fixed inputs that the timetable must respect, or are they placed after the timetable?
• Q-12 Are the special programmes (S-06, S-07) fixed for the year, so they can be pre-placed, or should the solver be free to move them?
• Q-13 Rooms: does the school need room assignment at all, beyond the gym and any shared spaces? The data shows no rooms.
• Q-14 Which is the authoritative current state, the board (3 Sep) or Tik-Tak (30 Aug)? Are changes made on the board copied back into Tik-Tak?

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A. Vegman's answers, 6 September 2026

Answers to Q-01 to Q-19, received by message. Each answer is filed on its question in the table; the requirements affected (R-05, R-06, R-07, R-08, R-09, R-11, R-14) and the new facts (S-11 to S-17) were updated from them. Follow-up questions are Q-20 to Q-24.

• Q-01 Period clock times: Period 1 08:00-08:45; 2 08:45-09:25; breakfast 09:25-09:35; break 09:35-09:55; 3 09:55-10:40; 4 10:40-11:25; break 11:25-11:45; 5 11:45-12:30; 6 12:30-13:15; lunch 13:15-13:35; break 13:35-13:55; 7 13:55-14:45 (50 minutes).
• Q-02 Hour derivation formula: Confidential; the teacher table cannot be shared during the trial phase. Work with counts derived from the export.
• Q-03 Placing non-frontal hours: Count only; do not place individual and staying hours in the grid.
• Q-04 No-gaps rule scope: Applies to all teachers. Gap budget per teacher = individual + staying hours remaining after deductions: every teacher working on Tuesday spends 2 staying hours in the after-teaching staff meeting; almost every teacher has 2 lunch duties (not in the export), each consuming 1 individual hour. Example: 24 frontal, 5 individual, 4 staying becomes 24 frontal, 3 individual, 2 staying, so exactly 5 gaps. Day edges are not gaps: a gap has a lesson before and after it. If a teacher is placed on 25 frontal slots, one individual hour is already in the grid and 4 gaps remain.
• Q-05 Homeroom period-1 rule: Own class only. Soft rule; sometimes there is no choice.
• Q-06 Long-day rule semantics: Teachers working 4 or more days: exactly 2 long days, except ענת and עידית who asked for 3. Part-time: depends on the post.
• Q-07 Daily math and language semantics: Mathematics exactly 1 per day; language at least 1 per day, including Tuesday. In half-class lessons each half gets language with the homeroom teacher, which counts as one language hour per child.
• Q-08 Trip day semantics: Different day per grade, as achieved.
• Q-09 Identity of x, y, z: Vegman offers to list them; detail requested as Q-20.
• Q-10 Core subjects definition: Strong preference, not hard. 'End of day' means period 7 only.
• Q-11 Staff meetings as input: Fixed in advance; the timetable adapts to them.
• Q-12 Special programmes fixed?: Fixed for the year; the solver must not move them.
• Q-13 Rooms needed?: Yes, three shared rooms. Science room: קרן ס. and שירלי; when one teaches with a second teacher, the other must teach alone to a whole class. Gym: אתי ח. and רגב, as few simultaneous uses as possible. Music shelter: נגה and שני, as few simultaneous uses as possible.
• Q-14 Authoritative state: Board, sheet and Tik-Tak are all kept updated; the board of 3 Sep is the newest.
• Q-15 ליבנה double booking: No clash. On Tuesday period 2 ליבנה is in ד' כלנית; the 30 Aug export is stale for that cell.
• Q-16 Unscheduled day equals part-time day?: Always a fixed day off: part-time teachers are scheduled only on their working days. Absence in the export means a hard unavailable day.
• Q-17 Meeting attendees: Management: אורלי, קרן ס., יפעת. Mathematics: אורלי, רעות. Individual-hours: אורלי, שלי, לירן, יפעת. Deputies: אורלי, קרן.
• Q-18 Music programme staffing: Homeroom teacher versus an external teacher, each class separately. Monday: half the class with the homeroom, the other half with the external teacher; Wednesday the halves swap. So no clash with שני.
• Q-19 Soldiers as named people: Five soldiers. They are not yet assigned to slots.

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N. Next steps

• N-01 Obtain the colour legend for the board, or better, a Tik-Tak export that includes subjects. Without subjects R-08, R-13 and R-14 cannot be modelled or checked.
• N-02 Obtain a teacher table: name, subjects, frontal hours, individual hours, staying hours, working days, late-arrival and early-leave constraints, homeroom class if any, and which teachers always pair with the homeroom (R-12).
• N-03 Obtain the curriculum table: for each grade, weekly periods per subject, which subjects are taught as double periods, and which are co-taught.
• N-04 Get one-line answers to Q-05 to Q-10 to fix hard versus soft.
• N-05 Transcribe the full board (D-03) once the legend exists, and diff it against D-02 to learn what was changed by hand between 30 Aug and 3 Sep; those hand edits reveal the constraints Vegman applies without stating them.
• N-06 Encode Mevo Hagalil as the first instance in the product's domain model and as an XHSTT file, so the achieved timetable can be scored against the rules.

Glossary

Terms used above. On the web version each underlined term shows this on hover.

• Ofek Hadash: the 2008 reform governing teacher employment in Israeli primary and junior-high schools. A full post is 36 weekly hours split into frontal, individual and staying hours.
• Frontal, individual and staying hours: frontal hours are ordinary lessons with a class; individual hours are small groups of up to five pupils; staying hours are preparation, meetings and duties on site.
• Homeroom teacher (מחנכת): the teacher responsible for a class, who teaches it most of the week.
• Co-teaching: two adults in the classroom for the same lesson.
• Hard and soft constraints: a hard constraint must never be broken; a soft one is a preference with a penalty weight.
• Tik-Tak (תיק-תק): the Israeli school-management and timetabling software the school currently uses.
• XHSTT: the XML format used by researchers to describe a school timetabling problem and its solution; the product's domain model mirrors it.
• Pre-placed event: a lesson or activity whose time is fixed before solving.
• National-service soldier (חיילת): a young woman doing national service as a classroom assistant.

Glossary

Every abbreviation and technical term used above, in alphabetical order.

Sources