This supply chain simulation consists of two manufacturers, two retailers, and two demand markets. The equilibrium solution is computed using the Euler method, a discrete time algorithm. This is Example 5 in the paper, Dynamics of Supply Chains: A Multilevel (Logistical-Informational-Financial) Network Perspective, by Anna Nagurney, Ke Ke, Jose Cruz, Kitty Hancock, and Frank Southworth, Environment and Planning B (2002), 29, pp. 795-818. Click here for a pdf file of  the paper.
 
 

The production cost functions for the manufacturers are:

f₁(q) = 2.5q₁² + q₁q₂ + 10q₁

f₂(q) = 2.5q₂² + q₁q₂ + 2q_2.

The transaction cost functions faced by the manufacturers and associated with transacting with the retailers are:

c₁₁(q₁₁) = q²₁₁ + 3.5q₁₁

c₁₂(q₁₂) = 0.5q²₁₂ + 3.5q₁₂

c₂₁(q₂₁) = 0.5q²₂₁ + 3.5q₂₁

c₂₂(q₂₂) = 0.5q²₂₂ + 3q₂₂.

The handling costs of the retailers are:

c₁(Q¹) = 0.5 (Sq_i1)^{2
                             i}=1,2

c₂(Q¹) = 0.75 (Sq_i2)^{2.
                              i=1,2}

The demand functions at the demand markets are:

d₁(p₃) = -2p₃₁ – 1.5p₃₂ + 1200

d₂(p₃) = -2.5p₃₂ – 1p₃₁ + 1000.

The transaction costs between the retailers and the consumers at the demand markets are:

c₁₁(Q²) = q₁₁ + 5

c₁₂(Q²) = q₁₂ + 5

c₂₁(Q²) = 3q₂₁ + 5

c₂₂(Q²) = q₂₂ + 5.