Plumline

Model library

A library of ready-to-solve models.

Browse worked optimisation models by the decision they answer. Each one opens in the solver already configured — objective, variable types and limits set — so you can solve it, then change the numbers to fit your own problem.

36 models

Model library

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Model type
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36 models shown

Ready to solve

01 Production & operations

Production plan

How many units of each product should we make to maximise profit within our hours?

Model type
continuous
Goal
Maximise
Difficulty
beginner
3 decisions 2 limits 5 min
Open in solver
02 Production & operations

Workshop chart

With two products and two resources, what mix maximises profit — and what does the feasible region look like?

Model type
continuous
Goal
Maximise
Difficulty
beginner
2 decisions 2 limits 6 min
Open in solver
03 Blending & formulation

Cheapest feed blend

What is the cheapest blend of feeds that still meets every nutritional requirement?

Model type
continuous
Goal
Minimise
Difficulty
intermediate
3 decisions 3 limits 8 min
Open in solver
04 Marketing & finance

Marketing budget

How should a fixed budget be split across channels to maximise total return within per-channel limits?

Model type
continuous
Goal
Maximise
Difficulty
intermediate
3 decisions 1 limit 7 min
Open in solver
05 Workforce & scheduling

Workforce scheduling

How few staff can we schedule and still cover every day's demand?

Model type
integer
Goal
Minimise
Difficulty
advanced
7 decisions 7 limits 10 min
Open in solver
06 Logistics & transport

Shipping plan

How should whole units be shipped across routes to meet demand at least total cost?

Model type
integer
Goal
Minimise
Difficulty
advanced
6 decisions 5 limits 10 min
Open in solver
07 Marketing & finance

Project selection

Which projects should we pick to maximise value without exceeding the budget?

Model type
binary
Goal
Maximise
Difficulty
intermediate
4 decisions 2 limits 7 min
Open in solver
08 Logistics & transport

Delivery load

Which items should go on the vehicle to maximise value without exceeding its capacity?

Model type
binary
Goal
Maximise
Difficulty
intermediate
5 decisions 2 limits 7 min
Open in solver
09 Purchasing & suppliers

Supplier activation

Which suppliers should we activate, and how much to buy from each, to meet demand at least cost?

Model type
mixed
Goal
Minimise
Difficulty
advanced
6 decisions 4 limits 12 min
Open in solver
10 Production & operations

Bakery production mix

How many loaves, rolls and pastries should the bakery make today to maximise contribution?

Model type
continuous
Goal
Maximise
Difficulty
beginner
3 decisions 4 limits 4 min
Open in solver
11 Production & operations

Factory batch plan

How many whole batches of each product should the factory schedule to maximise margin?

Model type
integer
Goal
Maximise
Difficulty
intermediate
3 decisions 4 limits 6 min
Open in solver
12 Workforce & scheduling

Clinic staffing plan

How many staff should the clinic assign to overlapping shifts to cover every block at least cost?

Model type
integer
Goal
Minimise
Difficulty
intermediate
3 decisions 4 limits 6 min
Open in solver
13 Workforce & scheduling

Call centre shift plan

How many agents should start each staggered shift so every service period is covered at least cost?

Model type
integer
Goal
Minimise
Difficulty
intermediate
4 decisions 5 limits 7 min
Open in solver
14 Purchasing & suppliers

Purchase order split

How should the order be split across three suppliers to meet demand at least cost within their capacities?

Model type
continuous
Goal
Minimise
Difficulty
beginner
3 decisions 4 limits 4 min
Open in solver
15 Purchasing & suppliers

Ingredient sourcing plan

Which suppliers should be activated, and how much bought from each, to meet both composition needs at least total cost?

Model type
mixed
Goal
Minimise
Difficulty
advanced
6 decisions 5 limits 11 min
Open in solver
16 Logistics & transport

Fleet assignment plan

Which vehicles should be assigned to today's workload to meet the capacity requirement at least operating cost?

Model type
binary
Goal
Minimise
Difficulty
advanced
5 decisions 1 limit 9 min
Open in solver
17 Marketing & finance

Media channel mix

How should the budget be allocated across channels to maximise reach within budget and channel limits?

Model type
continuous
Goal
Maximise
Difficulty
intermediate
4 decisions 5 limits 5 min
Open in solver
18 Blending & formulation

Fertiliser blend plan

What is the lowest-cost blend of three fertilisers that meets the minimum N, P and K requirements?

Model type
continuous
Goal
Minimise
Difficulty
intermediate
3 decisions 3 limits 7 min
Open in solver
19 Education & social sector

Scholarship allocation

How many scholarships of each type should be funded to support the most students within budget and balance rules?

Model type
integer
Goal
Maximise
Difficulty
intermediate
3 decisions 6 limits 7 min
Open in solver
20 Education & social sector

Food bank allocation

How should limited food be distributed across three centres to serve the most households within stock and volunteer limits?

Model type
integer
Goal
Maximise
Difficulty
intermediate
3 decisions 5 limits 6 min
Open in solver
21 Energy & sustainability

Renewable energy mix

What mix of solar, wind and grid meets demand at least cost while reaching the renewable target?

Model type
continuous
Goal
Minimise
Difficulty
intermediate
3 decisions 4 limits 6 min
Open in solver
22 Energy & sustainability

Microgrid capacity plan

How much solar, battery and backup capacity should be installed to meet firm capacity at least annualised cost?

Model type
continuous
Goal
Minimise
Difficulty
advanced
3 decisions 4 limits 10 min
Open in solver
23 Hospitality & retail

Hotel room allocation

How many rooms should go to each booking channel to maximise revenue within inventory and channel rules?

Model type
integer
Goal
Maximise
Difficulty
intermediate
3 decisions 4 limits 6 min
Open in solver
24 Learning & engine demonstrations

Linear optimisation basics

How many tables and chairs should the maker produce to maximise profit within wood and workshop hours?

Model type
continuous
Goal
Maximise
Difficulty
beginner
2 decisions 2 limits 3 min
Open in solver
25 Production & operations

Assembly line mix

How many standard and premium units should the line make to maximise profit within machine and assembly hours?

Model type
continuous
Goal
Maximise
Difficulty
beginner
2 decisions 2 limits 4 min
Open in solver
26 Production & operations

Machine shop job plan

How many whole runs of each job should the shop schedule to maximise contribution within lathe and mill hours?

Model type
integer
Goal
Maximise
Difficulty
intermediate
3 decisions 3 limits 6 min
Open in solver
27 Logistics & transport

Warehouse dispatch plan

How many loads should each depot dispatch to cover demand at least cost within capacity?

Model type
continuous
Goal
Minimise
Difficulty
intermediate
2 decisions 3 limits 5 min
Open in solver
28 Logistics & transport

Container loading plan

How many light and heavy pallets should be loaded to maximise value within weight and floor limits?

Model type
integer
Goal
Maximise
Difficulty
intermediate
2 decisions 2 limits 6 min
Open in solver
29 Marketing & finance

Budget allocation plan

How should the budget be split across search and social to maximise reach within limits?

Model type
continuous
Goal
Maximise
Difficulty
beginner
2 decisions 3 limits 4 min
Open in solver
30 Purchasing & suppliers

Raw material purchase plan

How much should be bought from each supplier to meet the requirement at least cost?

Model type
continuous
Goal
Minimise
Difficulty
intermediate
2 decisions 3 limits 5 min
Open in solver
31 Workforce & scheduling

Shift coverage plan

How many staff should each shift get to cover demand at least wage cost?

Model type
integer
Goal
Minimise
Difficulty
intermediate
2 decisions 3 limits 6 min
Open in solver
32 Blending & formulation

Animal feed blend

How much grain and soy should be blended to meet mass and protein needs at least cost?

Model type
continuous
Goal
Minimise
Difficulty
intermediate
2 decisions 3 limits 5 min
Open in solver
33 Education & social sector

Tutoring hours plan

How should tutoring hours be split to help the most students within tutor and room limits?

Model type
continuous
Goal
Maximise
Difficulty
beginner
2 decisions 3 limits 4 min
Open in solver
34 Energy & sustainability

Battery dispatch plan

How much solar and battery energy should be dispatched to maximise revenue within limits?

Model type
continuous
Goal
Maximise
Difficulty
intermediate
2 decisions 3 limits 5 min
Open in solver
35 Hospitality & retail

Menu planning mix

How many portions of each dish maximise margin within prep time and fresh stock?

Model type
continuous
Goal
Maximise
Difficulty
beginner
2 decisions 2 limits 4 min
Open in solver
36 Hospitality & retail

Retail shelf space plan

How many facings should each product line get to maximise weekly profit within limits?

Model type
integer
Goal
Maximise
Difficulty
intermediate
2 decisions 3 limits 6 min
Open in solver

How an example works

Open

The model opens in the solver, already configured.

Solve

Run it to see the verified optimal answer.

Change

Edit the numbers to fit your own problem.