diff --git a/doc/groups.dox b/doc/groups.dox
--- a/doc/groups.dox
+++ b/doc/groups.dox
@@ -317,15 +317,15 @@
 
 The \e maximum \e flow \e problem is to find a flow of maximum value between
 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
-digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and
+digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
 \f$s, t \in V\f$ source and target nodes.
-A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the
+A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
 following optimization problem.
 
-\f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f]
-\f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a)
-    \qquad \forall v\in V\setminus\{s,t\} \f]
-\f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f]
+\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
+\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
+    \quad \forall u\in V\setminus\{s,t\} \f]
+\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
 
 LEMON contains several algorithms for solving maximum flow problems:
 - \ref EdmondsKarp Edmonds-Karp algorithm.
@@ -350,30 +350,98 @@
 
 The \e minimum \e cost \e flow \e problem is to find a feasible flow of
 minimum total cost from a set of supply nodes to a set of demand nodes
-in a network with capacity constraints and arc costs.
+in a network with capacity constraints (lower and upper bounds)
+and arc costs.
 Formally, let \f$G=(V,A)\f$ be a digraph,
 \f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and
-upper bounds for the flow values on the arcs,
+upper bounds for the flow values on the arcs, for which
+\f$0 \leq lower(uv) \leq upper(uv)\f$ holds for all \f$uv\in A\f$.
 \f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow
-on the arcs, and
-\f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values
-of the nodes.
-A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of
-the following optimization problem.
+on the arcs, and \f$sup: V\rightarrow\mathbf{Z}\f$ denotes the
+signed supply values of the nodes.
+If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
+supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
+\f$-sup(u)\f$ demand.
+A minimum cost flow is an \f$f: A\rightarrow\mathbf{Z}^+_0\f$ solution
+of the following optimization problem.
 
-\f[ \min\sum_{a\in A} f(a) cost(a) \f]
-\f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) =
-    supply(v) \qquad \forall v\in V \f]
-\f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f]
+\f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
+\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
+    sup(u) \quad \forall u\in V \f]
+\f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
 
-LEMON contains several algorithms for solving minimum cost flow problems:
- - \ref CycleCanceling Cycle-canceling algorithms.
- - \ref CapacityScaling Successive shortest path algorithm with optional
+The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
+zero or negative in order to have a feasible solution (since the sum
+of the expressions on the left-hand side of the inequalities is zero).
+It means that the total demand must be greater or equal to the total
+supply and all the supplies have to be carried out from the supply nodes,
+but there could be demands that are not satisfied.
+If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
+constraints have to be satisfied with equality, i.e. all demands
+have to be satisfied and all supplies have to be used.
+
+If you need the opposite inequalities in the supply/demand constraints
+(i.e. the total demand is less than the total supply and all the demands
+have to be satisfied while there could be supplies that are not used),
+then you could easily transform the problem to the above form by reversing
+the direction of the arcs and taking the negative of the supply values
+(e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
+However \ref NetworkSimplex algorithm also supports this form directly
+for the sake of convenience.
+
+A feasible solution for this problem can be found using \ref Circulation.
+
+Note that the above formulation is actually more general than the usual
+definition of the minimum cost flow problem, in which strict equalities
+are required in the supply/demand contraints, i.e.
+
+\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) =
+    sup(u) \quad \forall u\in V. \f]
+
+However if the sum of the supply values is zero, then these two problems
+are equivalent. So if you need the equality form, you have to ensure this
+additional contraint for the algorithms.
+
+The dual solution of the minimum cost flow problem is represented by node 
+potentials \f$\pi: V\rightarrow\mathbf{Z}\f$.
+An \f$f: A\rightarrow\mathbf{Z}^+_0\f$ feasible solution of the problem
+is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$
+node potentials the following \e complementary \e slackness optimality
+conditions hold.
+
+ - For all \f$uv\in A\f$ arcs:
+   - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$;
+   - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
+   - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
+ - For all \f$u\in V\f$:
+   - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
+     then \f$\pi(u)=0\f$.
+ 
+Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc
+\f$uv\in A\f$ with respect to the node potentials \f$\pi\f$, i.e.
+\f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]
+
+All algorithms provide dual solution (node potentials) as well
+if an optimal flow is found.
+
+LEMON contains several algorithms for solving minimum cost flow problems.
+ - \ref NetworkSimplex Primal Network Simplex algorithm with various
+   pivot strategies.
+ - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
+   cost scaling.
+ - \ref CapacityScaling Successive Shortest %Path algorithm with optional
    capacity scaling.
- - \ref CostScaling Push-relabel and augment-relabel algorithms based on
-   cost scaling.
- - \ref NetworkSimplex Primal network simplex algorithm with various
-   pivot strategies.
+ - \ref CancelAndTighten The Cancel and Tighten algorithm.
+ - \ref CycleCanceling Cycle-Canceling algorithms.
+
+Most of these implementations support the general inequality form of the
+minimum cost flow problem, but CancelAndTighten and CycleCanceling
+only support the equality form due to the primal method they use.
+
+In general NetworkSimplex is the most efficient implementation,
+but in special cases other algorithms could be faster.
+For example, if the total supply and/or capacities are rather small,
+CapacityScaling is usually the fastest algorithm (without effective scaling).
 */
 
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