Identifying, analyzing, and assessing risk in the strategic planning of a production network: the practical view of a German car manufacturer

Abstract

This paper addresses the issue of identifying and assessing risk relevant to production networks. The objective is to create a systematic, comprehensive record of the risks relevant to the planning of car manufacturer’s production networks and to analyze these risks. The paper also discusses the methodology for assessing relevant risk in terms of the probability that the risk will materialize and the scale of the potential loss. A further objective is to assess the options for mitigating the risk through the use of a flexibly structured production network and to evaluate the associated options for responding to a change in market conditions. A case study demonstrates the possible impact of the main risk factors on performance if the organization concerned does not build flexibility into the network.

Appendix A

Following optimization model is used for calculate the monetary impact of the risks on the production network.

The following indexes are defined for the optimization model:

$$\begin{aligned} \begin{array}{llll} \hbox {i}&{} \in &{} {\{}1, 2, {\ldots }, \hbox {I}{\}}&{} \hbox {products}\\ \hbox {i}2 &{}\in &{} {\{}1, 2, {\ldots }, \hbox {I}2{\}}&{} \hbox {supplied parts}\\ \hbox {f}&{} \in &{} {\{}1, 2, {\ldots }, \hbox {F}{\}}&{} \hbox {facilities}\\ \hbox {f}2&{} \in &{} {\{}1, 2, {\ldots }, \hbox {F}2{\}}&{} \hbox {supplier}\\ \hbox {t}&{} \in &{} {\{}1, 2, {\ldots }, \hbox {T}{\}}&{} \hbox {period}\\ \hbox {n}&{}\in &{} {\{}1, 2, {\ldots }, \hbox {N}{\}}&{} \hbox {scenarios}\\ \hbox {c}&{} \in &{}{\{}1, 2, {\ldots }, \hbox {C}{\}}&{} \hbox {configurations}\\ \hbox {m} &{}\in &{} {\{}1, 2, {\ldots }, \hbox {M}{\}}&{} \hbox {markets}\\ \end{array} \end{aligned}$$

The following variables are defined:

$DCF_{t,n,c}$ :

$=$ operating profit per period $t$ per scenario $n$ per configuration $c$

$P_{i,f,t,n,c}$ :

$=$ production volume of product typ $i$ in facility $f$ per period $t$ per scenario $n$ per configuration $c$

$\textit{MaxProd}_{i,f,t,c}$ :

$=$ maximum production volume of product typ $i$ in facility $f$ per period $t$ per configuration $c$

$\textit{MinProd}_{i,f,t,c}$ :

$=$ minimum production volume of product typ $i$ in facility $f$ per period $t$ per configuration $c$

$pf_{i,f,t,c}^{capa}$ :

$=$ capacity consumption per product typ $i$ in facility $f$ per period $t$ per configuration $c$

$C_{f,t,c}$ :

$=$ capacity of facility $f$ per period $t$ per configuration $c$

$\textit{BOM}_{i,i2}$ :

$=$ bill of material of product $i$ and supplied parts $i2$

$TV_{i,i2,f,f2,t,n,c}^f$ :

$=$ transport volume of supplied parts $i2$ for product $i$from supplier $f2$ to facility $f$ per period $t$ per scenario $n$ per configuration $c$

$TV_{i,f,t,n,c,m}^m$ :

$=$ transport volume of product $i$from facility $f$ for market $m$ per period $t$ per scenario $n$ per configuration $c$

$Costs_{t,n,c}$ :

$=$ costs per period $t$ per scenario $n$ per configuration $c$

$Revenue_{t,n,c}$ :

$=$ revenues per period $t$ per scenario $n$ per configuration $c$

$WACC$ :

$=$ discount factor

The objective function is:

$$\begin{aligned} \max \left\{ {DCF_{n,c} } \right\} \qquad \qquad \qquad \qquad \qquad \forall n,c \end{aligned}$$

where:

$$\begin{aligned} DC\!F_{n,c} =\mathop \sum \limits _{t=1}^T \frac{(Revenue_{t,n,c} -Costs_{t,n,c} )}{(1+WACC)^t} \qquad \qquad \qquad \qquad \qquad \forall n,c \end{aligned}$$

subject to:

$$\begin{aligned} \begin{array}{l@{\quad }l} P_{i,f,t,n,c} \le \textit{MaxProd}_{i,f,t,c} &{} \forall i,f,t,n,c \\ P_{i,f,t,n,c} \ge \textit{MinProd}_{i,f,t,c} &{} \forall i,f,t,n,c \\ \sum \limits _i P_{i,f,t,n,c} *pf_{i,f,t,c}^{capa} \le C_{f,t,c} &{} \forall f,t,n,c \\ \textit{BOM}_{i,i2} *P_{i,f,t,n,c} =\mathop \sum \limits _f TV_{i,i2,f,f2,t,n,c}^f &{} \forall i,i2,f2,t,n,c \\ P_{i,f,t,n,c} =\left( {\mathop \sum \limits _m TV_{i,f,t,n,c,m}^m +\mathop \sum \limits _{f2,i2} TV_{i,i2,f,f2,t,n,c}^f }\right) &{} \forall i,f,t,n,c \end{array} \end{aligned}$$