Problem name and type, features		Difficulty
approx	Approximation: Piecewise linear approximation	**
	SOS-2, Special Ordered Sets, piecewise linear approximation of a nonlinear function, pwlin
burglar	MIP modeling: Knapsack problem: 'Burglar'	*
	simple MIP model with binary variables, data input from text data file, array initialization, numerical indices, string indices, record data structure
chess	LP modeling: Production planning: 'Chess' problem	*
	simple LP model, solution output, primal solution values, slack values, activity values, dual solution values
pricebrai	All item discount pricing: Piecewise linear function	***
	SOS-1, Special Ordered Sets, piecewise linear function, approximation of non-continuous function, step function, pwlin
pricebrinc	Incremental pricebreaks: Piecewise linear function	***
	SOS-2, Special Ordered Sets, piecewise linear function, step function

Problem name and type, features		Difficulty	Related examples
A‑1	Production of alloys: Blending problem formulation of blending constraints; data with numerical indices, solution printout, if-then, getsol	*	blending_graph.mos
A‑2	Animal food production: Blending problem formulation of blending constraints; data with string indices, as, formatted solution printout, use of getsol with linear expressions, strfmt	*	a1alloy.mos
A‑3	Refinery : Blending problem formulation of blending constraints; sparse data with string indices, dynamic initialization, union of sets	**	a2food.mos
A‑4	Cane sugar production : Minimum cost flow (in a bipartite graph) mo ceil, is_binary, formattext	*	e2minflow.mos, mincostflow_graph.mos
A‑5	Opencast mining: Minimum cost flow encoding of arcs, solving LP-relaxation only, array of set	**	a4sugar.mos
A‑6	Production of electricity: Dispatch problem inline if, is_integer, looping over optimization problem solving	**

Problem name and type, features		Difficulty	Related examples
B‑1	Construction of a stadium: Project scheduling (Method of Potentials)	***	projplan_graph.mos
	2 problems; selection with `|', sparse/dense format, naming and redefining constraints, subroutine: procedure for solution printing, forward declaration, array of set
B‑2	Flow shop scheduling	****	flowshop_graph.mos
	alternative formulation using SOS1
B‑3	Job shop scheduling	***	jobshop_graph.mos
	formulating disjunctions (BigM); dynamic array, range, exists, forall-do,array of set, array of list
B‑4	Sequencing jobs on a bottleneck machine: Single machine scheduling	***	sequencing_graph.mos
	3 different objectives; subroutine: procedure for solution printing, localsetparam, if-then
B‑5	Paint production: Asymmetric Traveling Salesman Problem (TSP)	***
	solution printing, repeat-until, cast to integer, selection with `|', round
B‑6	Assembly line balancing	**	linebal_graph.mos
	encoding of arcs, range

Problem name and type, features		Difficulty	Related examples
C‑1	Planning the production of bicycles: Production planning (single product)	***
	modeling inventory balance; inline if, forall-do
C‑2	Production of drinking glasses: Multi-item production planning	**	prodplan_graph.mos
	modeling stock balance constraints; inline if, index value 0
C‑3	Material requirement planning: Material requirement planning (MRP)	**
	working with index (sub)sets, dynamic initialization, automatic finalization, as
C‑4	Planning the production of electronic components: Multi-item production planning	**	c2glass.mos
	modeling stock balance constraints; inline if
C‑5	Planning the production of fiberglass: Production planning with time-dependent production cost	***	transship_graph.mos
	representation of multi-period production as flow; encoding of arcs, exists, create, isodd, getlast, inline if
C‑6	Assignment of production batches to machines: Generalized assignment problem	*	assignment_graph.mos

Problem name and type, features		Difficulty	Related examples
D‑1	Wagon load balancing: Nonpreemptive scheduling on parallel machines	****
	heuristic solution requiring sorting algorithm, formulation of maximin objective; nested subroutines: function returning heuristic solution value and sorting procedure, ceil, getsize, if-then, break, exit, all loop types (forall-do, repeat-until, while-do), setparam, qsort, cutoff value, loading a MIP start solution
D‑2	Barge loading: Knapsack problem	**	burglar1.mos, knapsack_graph.mos
	incremental problem definition with 3 different objectives, procedure for solution printing
D‑3	Tank loading: Loading problem	***
	2 objectives; data preprocessing, as, dynamic creation of variables, procedure for solution printing, if-then-else
D‑4	Backing up files: Bin-packing problem	**	binpacking_graph.mos
	2 versions of mathematical model, symmetry breaking; data preprocessing, ceil, range
D‑5	Cutting sheet metal: Covering problem	*	g6transmit.mos, j2bigbro.mos
D‑6	Cutting steel bars for desk legs: Cutting-stock problem	**	cutstock_graph.mos
	set operation(s) on range sets, set of integer (data as set contents)

Problem name and type, features		Difficulty	Related examples
E‑1	Car rental: Transport problem	***	transport_graph.mos
	data preprocessing, set operations, sqrt and ^2, if-then-elif
E‑2	Choosing the mode of transport: Minimum cost flow	**	mincostflow_graph.mos
	formulation with extra nodes for modes of transport; encoding of arcs, finalize, union of sets, nodes labeled with strings
E‑3	Depot location: Facility location problem	***	facilityloc_graph.mos
	modeling flows as fractions, definition of model cuts
E‑4	Heating oil delivery: Vehicle routing problem (VRP)	****	vrp_graph.mos
	elimination of inadmissible subtours, cuts; selection with `|', definition of model cuts
E‑5	Combining different modes of transport	***
	modeling implications, weak and strong formulation of bounding constraints; triple indices
E‑6	Fleet planning for vans	***
	maxlist, minlist, max, min

Problem name and type, features		Difficulty	Related examples
F‑1	Flight connections at a hub: Assignment problem	*	assignment_graph.mos, i1assign.mos, c6assign.mos
F‑2	Composing flight crews: Bipartite matching	****	matching_graph.mos
	2 problems, data preprocessing, incremental definition of data array, encoding of arcs, logical or (cumulative version) and and, procedure for printing solution, forall-do, max, finalize
F‑3	Scheduling flight landings: Scheduling problem with time windows	***
	generalization of model to arbitrary time windows; calculation of specific BigM, forall-do
F‑4	Airline hub location: Hub location problem	***
	quadruple indices; improved (re)formulation (first model not usable with student version), union of index (range) sets
F‑5	Planning a flight tour: Symmetric traveling salesman problem	*****	tsp_graph.mos
	loop over problem solving, TSP subtour elimination algorithm; procedure for generating additional constraints, recursive subroutine calls, working with sets, forall-do, repeat-until, getsize, not

Problem name and type, features		Difficulty	Related examples
G‑1	Network reliability: Maximum flow with unitary capacities	***	maxflow_graph.mos, j1water.mos
	encoding of arcs, range, exists, create, algorithm for printing paths, forall-do, while-do, round, list handling
G‑2	Dimensioning of a mobile phone network	**
	if-then, exit
G‑3	Routing telephone calls: Multi-commodity network flow problem	***	multicomflow_graph.mos
	encoding of paths, finalize, getsize
G‑4	Construction of a cabled network: Minimum weight spanning tree problem	***	spanningtree_graph.mos
	formulation of constraints to exclude subcycles
G‑5	Scheduling of telecommunications via satellite: Preemptive open shop scheduling	*****	openshop_graph.mos
	data preprocessing, algorithm for preemptive scheduling that involves looping over optimization, ``Gantt chart'' printing
G‑6	Location of GSM transmitters: Covering problem	*	covering_graph.mos, d5cutsh.mos, j2bigbro.mos
	modeling an equivalence; sparse data format

Problem name and type, features		Difficulty	Related examples
H‑1	Choice of loans	*
	calculation of net present value
H‑2	Publicity campaign	*
	forall-do
H‑3	Portfolio selection	**	h7qportf.mos
	sets of integers, second formulation with semi-continuous, parameters
H‑4	Financing an early retirement scheme	**
	inline if, selection with `|'
H‑5	Family budget	**
	formulation of monthly balance constraints including different payment frequencies; as, mod, inline if, selection with `|'
H‑6	Choice of expansion projects	**	capbgt_graph.mos
	experiment with solutions: solve LP problem explicitly, ``round'' some almost integer variable and re-solve
H‑7	Mean variance portfolio selection: Quadratic Programming problem	***	folioqp_graph.mos
	parameters, forall-do, min, max, loop over problem solving

Problem name and type, features		Difficulty	Related examples
I‑1	Assigning personnel to machines: Assignment problem	****	assignment_graph.mos, c6assign.mos
	formulation of maximin objective; heuristic solution + 2 different problems (incremental definition) solved, working with sets, while-do, forall-do
I‑2	Scheduling nurses	***
	2 problems, using mod to formulate cyclic schedules; forall-do, set of integer, getact
I‑3	Establishing a college timetable	***	timetable_graph.mos
	many specific constraints, tricky (pseudo) objective function
I‑4	Exam schedule	**
	symmetry breaking, no objective
I‑5	Production planning with personnel assignment	***
	2 problems, defined incrementally with partial re-definition of constraints (named constraints), exists, create, dynamic array
I‑6	Planning the personnel at a construction site	**	persplan_graph.mos
	formulation of balance constraints using inline if

Problem name and type, features		Difficulty	Related examples
J‑1	Water conveyance / water supply management: Maximum flow problem	**	j1water_graph.mos, g1rely.mos
	encoding of arcs, selection with `|', record data structure
J‑2	CCTV surveillance: Maximum vertex cover problem	**	j2bigbro_graph.mos, g6transmit.mos, d5cutsh.mos
	encoding of network, exists
J‑3	Rigging elections: Partitioning problem	****	j3elect_graph.mos, partitioning_graph.mos
	algorithm for data preprocessing; file inclusion, 3 nested/recursive procedures, working with sets, if-then, forall-do, exists, finalize
J‑4	Gritting roads: Directed Chinese postman problem	****	j4grit_graph.mos
	algorithm for finding Eulerian path/graph for printing; encoding of arcs, dynamic array, exists, 2 functions implementing Eulerian circuit algorithm, round, getsize, break, while-do, if-then-else, list handling
J‑5	Location of income tax offices: p-median problem	****
	modeling an implication, all-pairs shortest path algorithm (Floyd-Warshall); dynamic array, exists, procedure for shortest path algorithm, forall-do, if-then, selection with `|'
J‑6	Efficiency of hospitals: Data Envelopment Analysis (DEA)	***
	description of DEA method; loop over problem solving with complete re-definition of problem every time, naming and declaring constraints

Problem name		Difficulty
K‑1	Playing Mastermind	**
K‑2	Marathon puzzle	*
K‑3	Congress puzzle	*
K‑4	Placing chips	*
K‑5	Nephew puzzle	**
K‑6	N-queens problem	*