Mountain Shed – Candidate WBS Paths Generated from a Petri Net

1) Petri-net “logic skeleton” for the mountain shed

place = condition / deliverable “is ready” transition = task (work package) highlight = tasks used by selected option

This Petri net is deliberately “elementary”: it encodes *physical* precedence and key design choices (foundation type, wall method, interior scope), leaving durations/resources as a second layer. In Petri-net terms, a schedule option is a firing sequence from the initial marking to a completed marking; reachability is exactly “can we get from one marking to another by firing tasks?”. fileciteturn1file14

Places (conditions/deliverables) in plain language

p0_start — project kickoff
p1_perm_ready, p1_proc_ready — design complete, allowing permit + procurement branches to proceed (in parallel)
p2_permits_done — permits/approvals obtained
p3_materials_site_ready — materials/logistics ready for mobilization
p16_panel_option — decision token: prefab panel path vs stick-built path
p4_mobilized — crew/tools/materials staged on the mountain site
p5_site_ready — site prepped + layout complete
p6_foundation_ready — chosen foundation complete
p7_floor_ready — floor framing + deck complete
p15_panels_fabbed — prefab wall panels fabricated (only for the prefab option)
p8_walls_ready — walls erected + braced
p9_roof_dry_in — roof on / underlayment installed
p10i_shell_int_ready, p10e_shell_ext_ready — shell weatherproof enough for interior vs exterior work to proceed independently
p12_interior_done, p10b_exterior_done — interior and exterior completed
p13_ready_closeout — ready for closeout/inspection
p14_complete — finished

Transitions (tasks) in plain language

tA Design & scope (snow load, access/logistics, materials list)
tB Permits/approvals
tC Procurement & logistics
tH0 Offsite prefab wall fabrication or skip prefab (commit to stick framing)
tD Mobilize to mountain site
tE Site prep & layout
tF* Foundation choice: concrete piers vs skid/gravel vs helical piers
tG Floor system
tH* Wall choice: stick framing vs install prefab panels
tI Roof framing + roofing (dry-in)
tJ1 Wrap shell + temporary close openings
tK* Interior choice: standard vs minimal
tJ2 Final exterior (doors/windows/siding/flashing)
tJoin Integrate/punch-list → ready for inspection
tM Final inspection & cleanup

Background: Petri nets can be treated compositionally and are closely tied to (strict) symmetric/commutative monoidal categories; places/transitions present generators and morphisms, and reachability is about morphisms between markings. fileciteturn1file14 fileciteturn1file10

2) How we turn firing sequences into WBS paths

Map each transition → one leaf-level activity (an “elementary” work package).
Group leaf activities into a WBS tree (Preconstruction, Site, Foundation, Structure, Envelope, Interior, Closeout).
Pick a valid firing sequence (each next task must be enabled by the current marking).
Read off the WBS codes in that order → that ordered list is the “WBS path” for that schedule option.

This matches the idea that the same atomic activities participate in both the WBS tree and the schedule network; keeping them coherent is a core modeling goal. fileciteturn1file15

If you later want start times/durations, you can treat the dependency graph (or the Petri net’s reachability constraints) like a PERT chart and solve for a schedule that respects all constraints. fileciteturn1file1

Transition → WBS code mapping used below

Transition	WBS leaf
tA_design	1.1 Design & scope
tB_permit	1.2 Permits/approvals
tC_procure	1.3 Procurement & logistics
tH0_panel_fab	1.4 Prefab wall panels (offsite)
tH0_skip_panels	1.4 Construction method selection (stick-built)
tD_mobilize	2.1 Mobilize to site
tE_siteprep	2.2 Site prep & layout
tF1_concrete	3.1 Foundation – concrete piers
tF2_skid	3.2 Foundation – skid/gravel pad
tF3_helical	3.3 Foundation – helical piers
tG_floor	4.1 Floor system
tH1_stick_frame	4.2 Walls – stick framing
tH2_install_panels	4.2 Walls – install prefab panels
tI_roof	4.3 Roof dry-in
tJ1_shell	5.1 Wrap shell & temp close
tJ2_exterior	5.2 Final exterior
tK1_interior_std	6.1 Interior – standard
tK2_interior_min	6.2 Interior – minimal
tJoin_ready	7.1 Integrate & ready for closeout
tM_close	7.2 Final inspection & cleanup

3) Three distinct candidate WBS paths (schedule options)

Click a schedule option to (a) highlight the chosen branches in the Petri net, (b) see the firing sequence and markings, and (c) see the derived elementary WBS path. The three options differ by foundation type, wall method, and/or interior scope + ordering.

Option A – Firing sequence → schedule

tA_design → tB_permit → tC_procure → tH0_skip_panels → tD_mobilize → tE_siteprep → tF1_concrete → tG_floor → tH1_stick_frame → tI_roof → tJ1_shell → tJ2_exterior → tK1_interior_std → tJoin_ready → tM_close

Option A – Elementary WBS path (tasks + subtasks)

Ordered WBS leaf codes: 1.1 → 1.2 → 1.3 → 1.4 → 2.1 → 2.2 → 3.1 → 4.1 → 4.2 → 4.3 → 5.1 → 5.2 → 6.1 → 7.1 → 7.2

WBS tree for Option A

1.0 Preconstruction
- 1.1 Design & scope
  - Confirm shed size, location, and snow/wind design assumptions (mountain conditions).
  - Define loads, anchoring approach, and moisture management strategy.
  - Create materials takeoff + cut list.
- 1.2 Permits/approvals
  - Submit drawings/site plan; address setbacks/frost depth requirements.
  - Coordinate inspections (foundation/framing if applicable).
- 1.3 Procurement & logistics
  - Order lumber, sheathing, roofing, fasteners, hardware.
  - Plan mountain delivery: staging, vehicle access, weather window.
- 1.4 Construction method selection (stick-built)
  - Commit to on-site wall framing (no prefab panel fabrication).
2.0 Mobilization & siteworks
- 2.1 Mobilize to site
  - Transport tools, hardware, and materials; set up safe staging area.
  - Establish power plan (generator/batteries) if off-grid.
- 2.2 Site prep & layout
  - Clear/grade pad, manage drainage, stake corners, verify square.
  - Erosion control / spoil management (mountain soil constraints).
3.0 Foundation
- 3.1 Concrete pier foundation
  - Dig below frost depth; form and pour piers; set anchors/hardware.
  - Cure time / strength check before framing load.
4.0 Structure
- 4.1 Floor system
  - Install beams/joists, rim board, blocking; lay and fasten subfloor.
- 4.2 Walls – stick framing
  - Frame wall sections; stand, plumb, and brace; install sheathing.
  - Frame rough openings (door/window) sized for mountain weather seals.
- 4.3 Roof dry-in
  - Install rafters/trusses, roof sheathing, underlayment, roofing.
  - Add snow-load details (e.g., ice/water barrier, snow guards if metal).
5.0 Shell & exterior
- 5.1 Wrap shell & temporary close openings
  - Housewrap, tape seams, flashing prep; temporary door/opening protection.
- 5.2 Final exterior
  - Install permanent door/windows, flashing, siding, trim.
  - Seal penetrations; add gutters/drip edge as needed.
6.0 Interior fit-out
- 6.1 Standard interior
  - Insulation/vapor control (if required), wall protection/lining.
  - Shelving/workbench; basic electrical/lighting if in scope.
  - Floor seal/finish for wet boots/snowmelt.
7.0 Closeout
- 7.1 Integrate & ready for closeout
  - Punch list; verify door/window operation; weather sealing check.
- 7.2 Final inspection & cleanup
  - Inspection sign-off; site cleanup; spare materials inventory.

Option A – Markings (state) after each firing step

Step	Firing event (transition = task)	Resulting marking (tokens = state)
0	Initial marking M0	Start
1	Fire tA_design: Design & scope	Design complete → permit package ready Design complete → procurement package ready
2	Fire tB_permit: Permits/approvals	Design complete → procurement package ready Permits/approvals complete
3	Fire tC_procure: Procure & logistics	Permits/approvals complete Materials/logistics ready to mobilize Prefabrication option token
4	Fire tH0_skip_panels: Skip prefab option	Permits/approvals complete Materials/logistics ready to mobilize
5	Fire tD_mobilize: Mobilize to site	Permits/approvals complete Crew/tools/materials mobilized to mountain site
6	Fire tE_siteprep: Site prep & layout	Site prepped & layout staked
7	Fire tF1_concrete: Foundation: concrete piers	Foundation complete
8	Fire tG_floor: Build floor system	Floor system/deck complete
9	Fire tH1_stick_frame: Frame walls (stick-built)	Walls erected & braced
10	Fire tI_roof: Frame & install roof (dry-in)	Roof dried-in (weather-tight roof)
11	Fire tJ1_shell: Wrap shell & temp close	Shell weatherproof → interior can start Shell weatherproof → exterior finish can start
12	Fire tJ2_exterior: Final exterior (windows/doors/siding)	Shell weatherproof → interior can start Exterior complete (windows/doors/siding)
13	Fire tK1_interior_std: Interior fit-out (standard)	Exterior complete (windows/doors/siding) Interior fit-out complete
14	Fire tJoin_ready: Integrate & ready for closeout	Ready for closeout/inspection
15	Fire tM_close: Final inspection & cleanup	Project complete

Option B – Firing sequence → schedule

tA_design → tC_procure → tH0_panel_fab → tB_permit → tD_mobilize → tE_siteprep → tF2_skid → tG_floor → tH2_install_panels → tI_roof → tJ1_shell → tK1_interior_std → tJ2_exterior → tJoin_ready → tM_close

Option B – Elementary WBS path (tasks + subtasks)

Ordered WBS leaf codes: 1.1 → 1.3 → 1.4 → 1.2 → 2.1 → 2.2 → 3.2 → 4.1 → 4.2 → 4.3 → 5.1 → 6.1 → 5.2 → 7.1 → 7.2

WBS tree for Option B

1.0 Preconstruction
- 1.1 Design & scope
  - Design wall panels with handling/transport constraints for mountain access.
  - Confirm foundation is compatible with skids and site drainage.
- 1.3 Procurement & logistics
  - Order all materials early (to support offsite fabrication).
  - Plan “two-stream” logistics: offsite panel shop + on-site delivery staging.
- 1.4 Prefab wall panels (offsite)
  - Cut/assemble/sheath panels; label; pre-install blocking where useful.
  - Bundle for transport; protect edges from moisture.
- 1.2 Permits/approvals
  - Run permits in parallel with prefab fabrication where allowed.
2.0 Mobilization & siteworks
- 2.1 Mobilize to site
  - Deliver skid materials + panel packages; set up lifting/handling plan.
- 2.2 Site prep & layout
  - Prepare level pad and drainage (gravel base is sensitive to water paths).
3.0 Foundation
- 3.2 Skid / gravel pad foundation
  - Place geotextile + gravel; level; set skids; anchor against uplift.
  - Faster build, often good for remote access, but check local code.
4.0 Structure
- 4.1 Floor system
  - Frame and sheath floor (square/level matters for prefab fit).
- 4.2 Walls – install prefab panels
  - Set corners first; plumb/brace; fasten panel joints and top plates.
  - Seal joints for wind-driven mountain rain/snow.
- 4.3 Roof dry-in
  - Install roof structure + sheathing + underlayment + roofing quickly.
5.0 Shell & exterior
- 5.1 Wrap shell & temporary close openings
  - Housewrap + tape; temporary closures to protect interior work window.
- 5.2 Final exterior
  - Install door/windows and siding after (or alongside) interior tasks.
6.0 Interior fit-out
- 6.1 Standard interior
  - Get interior work started as soon as the shell is weatherproof (mountain weather risk).
  - Shelving/workbench; insulation/vapor control if needed; basic lighting.
7.0 Closeout
- 7.1 Integrate & ready for closeout
  - Coordinate final exterior + interior completion for inspection readiness.
- 7.2 Final inspection & cleanup
  - Inspection sign-off; cleanup; demobilize.

Option B – Markings (state) after each firing step

Step	Firing event (transition = task)	Resulting marking (tokens = state)
0	Initial marking M0	Start
1	Fire tA_design: Design & scope	Design complete → permit package ready Design complete → procurement package ready
2	Fire tC_procure: Procure & logistics	Design complete → permit package ready Materials/logistics ready to mobilize Prefabrication option token
3	Fire tH0_panel_fab: Offsite fab wall panels	Design complete → permit package ready Materials/logistics ready to mobilize Prefab wall panels fabricated
4	Fire tB_permit: Permits/approvals	Materials/logistics ready to mobilize Prefab wall panels fabricated Permits/approvals complete
5	Fire tD_mobilize: Mobilize to site	Prefab wall panels fabricated Permits/approvals complete Crew/tools/materials mobilized to mountain site
6	Fire tE_siteprep: Site prep & layout	Prefab wall panels fabricated Site prepped & layout staked
7	Fire tF2_skid: Foundation: skid/gravel	Prefab wall panels fabricated Foundation complete
8	Fire tG_floor: Build floor system	Prefab wall panels fabricated Floor system/deck complete
9	Fire tH2_install_panels: Install prefab wall panels	Walls erected & braced
10	Fire tI_roof: Frame & install roof (dry-in)	Roof dried-in (weather-tight roof)
11	Fire tJ1_shell: Wrap shell & temp close	Shell weatherproof → interior can start Shell weatherproof → exterior finish can start
12	Fire tK1_interior_std: Interior fit-out (standard)	Shell weatherproof → exterior finish can start Interior fit-out complete
13	Fire tJ2_exterior: Final exterior (windows/doors/siding)	Interior fit-out complete Exterior complete (windows/doors/siding)
14	Fire tJoin_ready: Integrate & ready for closeout	Ready for closeout/inspection
15	Fire tM_close: Final inspection & cleanup	Project complete

Option C – Firing sequence → schedule

tA_design → tB_permit → tC_procure → tH0_skip_panels → tD_mobilize → tE_siteprep → tF3_helical → tG_floor → tH1_stick_frame → tI_roof → tJ1_shell → tK2_interior_min → tJ2_exterior → tJoin_ready → tM_close

Option C – Elementary WBS path (tasks + subtasks)

Ordered WBS leaf codes: 1.1 → 1.2 → 1.3 → 1.4 → 2.1 → 2.2 → 3.3 → 4.1 → 4.2 → 4.3 → 5.1 → 6.2 → 5.2 → 7.1 → 7.2

WBS tree for Option C

1.0 Preconstruction
- 1.1 Design & scope
  - Prioritize fast “dry-in”: roof + wrap early; plan staged exterior finish.
  - Decide minimal interior scope to reduce weather exposure time.
- 1.2 Permits/approvals
- 1.3 Procurement & logistics
- 1.4 Construction method selection (stick-built)
2.0 Mobilization & siteworks
- 2.1 Mobilize to site
- 2.2 Site prep & layout
3.0 Foundation
- 3.3 Helical piers
  - Install helical piers and brackets (often fast, less excavation).
  - Check uplift/torque specs and inspection requirements.
4.0 Structure
- 4.1 Floor system
- 4.2 Walls – stick framing
- 4.3 Roof dry-in
  - Drive hard to reach “roof dry-in” milestone before forecasted storms.
5.0 Shell & exterior
- 5.1 Wrap shell & temporary close openings
  - Make it weatherproof enough to work inside, even if siding waits.
- 5.2 Final exterior
  - Finish windows/doors/siding later when weather improves.
6.0 Interior fit-out
- 6.2 Minimal interior
  - Shelving + tool hooks + minimal wall protection.
  - Basic floor seal; defer insulation/electrical if not required.
7.0 Closeout
- 7.1 Integrate & ready for closeout
- 7.2 Final inspection & cleanup

Option C – Markings (state) after each firing step

Step	Firing event (transition = task)	Resulting marking (tokens = state)
0	Initial marking M0	Start
1	Fire tA_design: Design & scope	Design complete → permit package ready Design complete → procurement package ready
2	Fire tB_permit: Permits/approvals	Design complete → procurement package ready Permits/approvals complete
3	Fire tC_procure: Procure & logistics	Permits/approvals complete Materials/logistics ready to mobilize Prefabrication option token
4	Fire tH0_skip_panels: Skip prefab option	Permits/approvals complete Materials/logistics ready to mobilize
5	Fire tD_mobilize: Mobilize to site	Permits/approvals complete Crew/tools/materials mobilized to mountain site
6	Fire tE_siteprep: Site prep & layout	Site prepped & layout staked
7	Fire tF3_helical: Foundation: helical piers	Foundation complete
8	Fire tG_floor: Build floor system	Floor system/deck complete
9	Fire tH1_stick_frame: Frame walls (stick-built)	Walls erected & braced
10	Fire tI_roof: Frame & install roof (dry-in)	Roof dried-in (weather-tight roof)
11	Fire tJ1_shell: Wrap shell & temp close	Shell weatherproof → interior can start Shell weatherproof → exterior finish can start
12	Fire tK2_interior_min: Interior fit-out (minimal)	Shell weatherproof → exterior finish can start Interior fit-out complete
13	Fire tJ2_exterior: Final exterior (windows/doors/siding)	Interior fit-out complete Exterior complete (windows/doors/siding)
14	Fire tJoin_ready: Integrate & ready for closeout	Ready for closeout/inspection
15	Fire tM_close: Final inspection & cleanup	Project complete

Note: The Petri net defines the allowed task orderings (what can happen when). Start times/durations/resources can be added as a separate “timing” layer—e.g., PERT-style constraints. fileciteturn1file1

4) Why this matches the project instructions (Petri net → SMC → WBS)

Your project rationale is that a Petri net can be treated as a generative specification for (a strict/commutative) symmetric monoidal category, and that schedule/WBS variants come from different reachable markings and firing sequences.

In the attached “Open Petri nets” paper, a Petri net is treated as presenting a free commutative/symmetric monoidal category, and reachability is described as a relation between markings. fileciteturn1file10 fileciteturn1file19
In the attached operads/complex-systems design paper, Petri-net transitions are described as primitive tasks and as generators for monoidal-category structure. fileciteturn1file9
The “Project Scheduling and Copresheaves” note connects scheduling constraints (PERT-like) to categorical structure, and even discusses coherence between schedule networks and WBS trees. fileciteturn1file1 fileciteturn1file15

If you want to go further into executable/compositional tooling, wiring-diagram semantics and graph rewriting provide an operational way to “run” these structures. fileciteturn0file20 And if you need to transfer plans across domains, functorial data migration gives a principled way to map plans between ontologies. fileciteturn0file21

Related compositional “open systems” ideas also appear for stock–flow diagrams (useful when you later add resource/consumption dynamics). fileciteturn1file0 fileciteturn0file18