Fig 1.
Two examples of a three-tiered supply network.
The two supply networks follow different topologies in the wholesaler and retailer tier: (a) Homogeneous topology (regular degree distribution with ); (b) Heterogeneous topology (power law degree distribution with
).
Fig 2.
Representation of the supply chain random network.
The SC includes three tiers: Suppliers (Ts), Wholesalers (Tw) and Retailers (Tr). Ns,Nw and Nr represent the number of suppliers, wholesalers and retailers, respectively. Arrows indicate flow and direction of material between firms. The bidirectional arrow indicates horizontal relationships.
Fig 3.
It illustrates the order allocation rule in the SCRN at every time step.
Fig 4.
Empirical degree distributions of links in the SC of the Mercado del Mar, Guadalajara, Mexico.
The variables are: , out-degree distribution of suppliers;
, in-degree distribution of wholesalers;
, out-degree distribution of wholesalers;
, in-degree distribution of retailers. Three hypothetical degree distributions with the same mean than the empirical sample were added: Blue, uniform distribution; Red, zero-truncated Poisson distribution; Green, power law degree distribution.
Fig 5.
Order fulfillment rate (OFR) along 15 time steps for different wholesalers’ and retailers’ degree distributions.
The retailers’ demand follows Eq (1) and demand shock occurs at t* = 3. Four discrete distributions for the wholesalers’ (W) in- and out-degree ( and
) and the retailers’ (R) in-degree (
) are assumed (blue square–Uniforms (W and R); red triangle–Poisson (W and R); green star—Power law (W and R); black bullet–Poisson (W) and Power law (R)). The model is simulated combining four different conditions: Assortativiy (+), where the relationships among wholesalers and retailers are ordered according to their degrees; Assortativity (=), where the relationships among wholesalers and retailers are randomly assigned; Product sharing (+), where the production is shared among suppliers by following a zero-truncated power law probability function; Product sharing (=), where the production is evenly shared among suppliers. The graph is obtained by doing 1000 simulations of the SCRN and taking mean values, samples were taken with a gap between the simulated and theoretical mean degree lower than 5%. The 95% confidence interval for the OFR mean values from simulation 800 to 1000 is also included as error bar. Technical details: (i) The ratio of the number of firms between tiers is 3:1:6, the number of wholesalers is Nw = 100 and there is not horizontal relationships; (ii) The mean in-degree of retailers is
and, to assure consistency, the mean degree
and
; (iv) The sample of
and
is ordered, so the wholesaler with the highest in-degree has also the highest out-degree, and so on.
Table 1.
Agility results for different wholesalers’ and retailers’ degree distributions.
Immediate effect of the demand shock (ΔOFR(t*)) and recovery time (τ) for the simulations of cases a, b, c and d in Fig 5.
Fig 6.
Order fulfillment rate (OFR) along 15 times steps for different percentage of horizontal links and mean in-degree of retailers.
The baseline case corresponds to the conditions of Fig 5C: Wholesalers’ in- and out-degree ( and
) are zero-truncated Poisson and retailers in-degree (
) is zero-truncated power law: (a) Results for five different percentages of wholesalers with horizontal links (HL); (b) Results for four mean in-degrees of retailers. The observed OFR is obtained by doing 1000 simulations of the SCRN and taking mean values.
Table 2.
Agility results for different percentage of horizontal links and mean in-degree of retailers.
Immediate effect of the demand shock (ΔOFR(t*)) and recovery time (τ) for the simulations in Fig 6.