Modelling dynamics of a supply chain under uncertainty: a case from the automotive industry

354 Int. J. Automotive Technology and Management, Vol. 3, Nos. 3/4, 2003

Copyright © 2003 Inderscience Enterprises Ltd.

Modelling dynamics of a supply chain under uncertainty: a case from the automotive industry

Maria Grazia Gnoni* Department of Engineering for Innovation, University of Lecce, Italy E-mail: [email protected] *Corresponding author

Raffaello Iavagnilio, Giorgio Mossa and Giovanni Mummolo Department of Mechanical and Management Engineering, Polytechnic of Bari, Italy

Abstract: The authors investigate a three-stage supply chain of a multinational firm in the automotive components industry. Factories, located in Italy, carryout the manufacturing process of components for braking equipment. The first two manufacturing sites provide the final assembly site with components for original equipment (OEC); they also produce components for the aftermarket (AMCs).

The demand for OECs is dynamic and is deterministically known on a one-year horizon. On the other hand, the demand for AMCs is uncertain and is distributed according to probability density functions. To face such complexity in evaluating the supply chain performance, a dynamic and stochastic simulation model is proposed. Two different scenarios are investigated according to whether the manufacturing sites are considered as independent business units or as units that obey strict production requirements of the supply chain.

The results obtained confirm the effectiveness of the model, which reveals a suitable tool for tactical/strategic decision making.

Keywords: system dynamics; supply chain management; demand uncertainty; scenario analysis.

Reference to this paper should be made as follows: Gnoni, M.G., Iavagnilio, R., Mossa, G. and Mummolo, G. (2003) ‘Modelling dynamics of a supply chain under uncertainty: a case from the automotive industry’, International Journal of Automotive Technology and Management, Vol. 3, Nos. 3/4, pp.354–367.

Biographical notes: Maria Grazia Gnoni is a researcher in industrial engineering and teaches industrial plants at University of Lecce, Faculty of Engineering. Her research activity is focused on the management of production systems, logistics design, and simulation techniques.

Raffaello Iavagnilio has a PhD in advanced production systems. He is a senior researcher in the engineering of industrial plants at the Politecnico di Bari, where he teaches both engineering and safety of industrial plants. He is involved in research projects with academic and industrial partners in the field of project management, production planning and control, logistic and supply chain management as well as safety of industrial plants.

Modelling dynamics of a supply chain under uncertainty 355

Giorgio Mossa has a PhD in advanced production systems engineering and is Assistant Professor of Industrial Engineering at the Politecnico di Bari, where he teaches industrial plants. He also gives lectures on safety engineering for post-graduate courses. His research interests are in the fields of simulation modelling and environmental management systems in manufacturing. He is involved in research projects with academic and industrial partners in the area of simulation modelling in production planning and control, logistic and supply chain management.

Giovanni Mummolo is Professor of Industrial Engineering, graduate and postgraduate courses, offered by the Politecnico di Bari (Italy). He coordinates the industrial plants research group of the Politecnico di Bari and is responsible for research projects on design and management of production systems.

Mummolo is referee of the International Journal of Project Management, International Journal of Production Economics as well as of books edited by John Wiley & Sons.

1 Introduction

Synchronism of information and material flows between manufacturing sites belonging to a supply chain (SC) are features strongly required by modern industrial organisations. Automotive industrial groups are introducing structural changes in their manufacturing systems in order to guarantee optimal trade-off between customer satisfaction and production costs [1,2]. Automotive manufacturers are becoming more and more dependent on suppliers. An analysis of vulnerability of a supply chain of a mid-size European car manufacturer [3] revealed that disturbances appearing at the subcontractors’ level propagate downstream and upstream in the supply chain. As a consequence, more in depth levels of integration and cooperation among car manufacturers and subcontractors are recommended to avoid or reduce supply chain vulnerability. Several manufacturers integrated successfully their internal process to external suppliers and customers in a single SC [4].

Problem complexity arises when suppliers are involved in different SCs or when suppliers are jointly faced with both their own demand and with SC demand. According to such a point of view, an integrated approach to supply-chain management requires a cooperative, rather than competitive, behaviour of legally independent but economically and strategically dependent subjects involved in a SC [5]. The main goal of supply-chain management consists of establishing an optimal combination of competition and cooperation considered as a basic feature of interfirm networks [6].

Problem complexity increases when production demand changes randomly and dynamically over the planning horizon. Stochastic variability in product demand as well as in manufacturing and transportation times are being increasingly considered as a major source of uncertainty [7].

In this paper the authors investigate a three sites SC of a multinational firm operating in the automotive industry (Section 2). The SC produces two original equipment components (OECs) for automotive braking systems. OECs’ demand is deterministically known and changes dynamically over a one-year production planning horizon. Moreover,

356 M.G. Gnoni, R. Iavagnilio, G. Mossa and G. Mummolo

each of the first two sites of the SC also provides the aftermarket with one component (AMC). Uncertainty affects the aftermarket demand.

Two scenarios are investigated. The first refers to the strategic policy adopted to manage the first two sites aiming at satisfying the deterministic demand of the SC with higher priority, and the external random demand, with lower priority. In such a scenario the manufacturing sites are considered to belong to a unique industrial firm and to pursue a common technical-economic goal characterising the SC.

The opposite condition occurs in the second scenario where the manufacturing sites of a SC are considered as independent business units; accordingly, in such a case, the first two sites are considered as basically interested in satisfying the aftermarket demand with a higher priority.

The effect of random variability of AMCs demand – characterising the first two sites – on the performance of the whole SC, subject to dynamic variability in OECs’ demand, is investigated by a simulation model which is described at Section 3. Finally, Section 4 illustrates results obtained.

2 The supply chain

The industrial case investigated refers to a SC consisting of three sites (Figure 1). The SC produces original equipment components (OECs) of braking systems for the automotive industry. Site 1 and Site 2 also provide the aftermarket with AMCs. Let OECij and AMCij be the jth component of original and aftermarket components, respectively, at the ith stage in the SC.

Figure 1 The supply chain of original equipment and aftermarket component of braking system

Site 1 transforms raw foundry blocks in different types of servo cylinders for hydraulic braking actuators, OEC11, OEC12 and AMC11. Site 2 performs intermediate assembly operations of semi-finished cylinder body OEC21, and OEC22. Moreover, Site 2 supplies the aftermarket with the cylinder body, AMC22. Finally, at Site 3, the manufacturing process of OECs is completed (products OEC31 and OEC32).

Demands of OEC1 and OEC2 change dynamically over a one-year horizon according to a monthly defined demand (Table 1). Demand is deterministically known.


Table 1 Monthly demand of OECs

Month OEC1 [Unit] OEC2 [Unit] 1 822 147 2 736 242 3 614 209 4 465 253 5 332 183 6 663 155 7 29 296 8 524 269 9 774 131 10 312 127 11 1020 190 12 217 168

Demand of AMC1 and AMC2, respectively for Site 1 and Site 2, is uncertain. Probability density functions (pdfs) of AMC1 and AMC2 monthly demand are in Table 2; pdfs are estimated by historical data of two years monthly demand.

Table 2 Pdfs of AMCs monthly demand

Pdf Shape Scale

[Unit/month] Expected value [Unit/month]

Standard deviation [Unit/month]

AMC1 Weibull 1.572 1016 913 593 AMC2 Weibull 2.251 796 705 331

Setup times as well as operation times considered for each product at each site are in Table 3.

Table 3 Operation times and setup times for each product and each site

OEC1 OEC2 AMC1 OEC1 OEC2 AMC2 OEC1 OEC2 Operation time [hour/unit] 0.0525 0.0520 0.0544 0.060 0.060 0.063 0.1 0.11 Setup [hour] 18 3 3

Site 1 and Site 3 are located in northern Italy; Site 2 is in the south. A daily shipment service operates between the sites. Transport times are deterministically known; they do not affect SC performance since shipping service capacity is available to satisfy any request for transportation.


3 The simulation model

The performance of the SC, described in the previous section, is evaluated by a simulation model. A system dynamics model according to the Forrester approach [8] is adopted; the Stella® formalism and notation [9] are considered to built up the flow diagram outlining relationships among SC sites. Recently, system dynamics approach has been efficiently applied to generate and evaluate alternative scenarios to improve systems performances [10–13]. The stock-flow diagram of material flow of the SC is shown in Figure 2.

Figure 2 The material flow simulation model

The input inventory of Site 1 has infinite capacity; such an assumption also occurs for the input inventories of AMC1 and AMC2. The hypothesis does not affect the behaviour of the SC since supply lead times of raw materials at each site are negligible. Inventories inside the SC have finite capacity. Shipping between contiguous sites in the SC occurs when the levels of finished products at the upstream site reach a target value equal to the daily production volume; otherwise, shipping service waits until the target value is met. Performance of each site is upper limited by its bottleneck manufacturing resource.

3.1 Scenario analysis

Two scenarios of supply chain management are investigated by the simulation model. In the first scenario (A) (Figure 3a), the production plan of each site is consistent with production plans of the other sites. Production plan of OECs at each site, i.e. batch sizes and lot sequences, are in Table 4 and in Table 5, respectively; the production plan for each site is evaluated by a mathematical programming model (mixed integer linear programming) aimed at minimising the sum of setup, holding, and fixed costs. Details on


the model are in [14]. At the first two sites, production plans depending on the expected values of AMCs demand pdfs are considered (Table 2).

Figure 3a Scenario A information flows for production planning at each site

Table 4 Lot sizes of OECs at each period

Site 1 Site 2 Site 3

Month OEC1 [Unit]

OEC2 [Unit]

OEC1 [Unit]

OEC2 [Unit]

OEC1 [Unit]

OEC2 [Unit]

1 908 389 822 389 822 184

2 1729 0 1350 0 736 205

3 0 879 0 209 614 209

4 0 0 465 670 465 548

5 1548 0 1548 0 332 0

6 0 617 0 0 816 122

7 0 0 0 486 0 486

8 0 0 0 0 400 0

9 826 0 777 131 777 131

10 1497 485 492 485 492 485

11 0 0 837 0 837 0

12 0 0 217 0 217 0

Total 6508 2370 6508 2370 6508 2370


Table 5 Sequences for each site in scenario A

Month Site 1 Site 2 Site 3

1 O1-O2-A1 O1-O2-A2 O1-O2

2 A1-O2-O1 A2-O2-O1- O2-O1

3 O1-O2-A1 O1-A2-O2- O2-O1

4 A1-O1-O2 O2-O1-A2 O1-O2

5 O1-O2-A1 A2-O2-O1- O2-O1

6 A1-O1-O2 O1-A2-O2- O1-O2

7 O2-A1-O1 O2-O1-A2 O2-O1

8 O1-O2-A1 A2-O1-O2 O1-O2

9 A1-O1-O2 O2-O1-A2 O2-O1

10 O2-O1-A1 A2-O2-O1 O1-O2

11 A1-O1-O2 A2-O1-O2 O2-O1

12 O2-O1-A1 O2-O1-A2 O1-O2

Note: O1 = OEC1; O2 = OEC2; A1 = AMC1; A2 = AMC2

In the second scenario (B) (Figure 3b), each site is considered as an autonomous business unit. Site 1 and Site 2 are focused on meeting the production requirements of the aftermarket products, AMC1 and AMC2.

Figure 3b Scenario B information flows for production planning at each site

Lot sizes are the same as those considered in scenario A; on the other hand, the lot sequences considered in scenario A are modified by giving higher priority to AMC1 (Site 1) and AMC2 (Site 2) than to OEC1 and OEC2: as soon as a product demand from the aftermarket occurs, Site 1 or Site 2 starts working on it immediately after the previous batch is completed.


4 Results

SC performance is evaluated by the simulation model under scenarios A and B defined in Section 3. The performance measure considered is the completion time (CTj) of the annual production of the jth product (j = OEC1, OEC2, AMC1, AMC2). No due dates constraints are considered as the main goal pursued consists of identifying the stochastic dependency of such a performance measure from stochastic variability of the aftermarket demand. Two series of experiments are developed.

Experiment 1

A sensitivity analysis concerning the effect of uncertainty of demand for AMCs on SC performance is developed in this experiment referring to both the considered scenarios. Demand uncertainty level is expressed by the coefficient of variation (CV) of annual demand (CV = standard deviation/expected value). Three uncertainty levels are considered assuming the same expected value and different standard deviations of AMC1 and AMC2 annual demand: the first one (low uncertainty level, case #1) refers to both CV values of the actual annual demand observed for AMC1 and AMC2. Higher levels of uncertainty are considered in case #2 and case #3, according to the CV values shown in Table 6.

Table 6 Coefficient of variation of demand for AMCs in case of low (case #1), medium (case #2), and high (case #3) uncertainty level

Case # CVAMC1 CVAMC2

1 0.192 0.143

2 0.252 0.224

3 0.730 0.508

Each case is investigated by 100 simulation runs generated in order to estimate stochastic variability of the SC performance measure. With reference to case #1, completion time of OEC1, OEC2, AMC1, and AMC2 annual production demand under both scenarios are estimated (Table 7). It should be noted that scenario A allows a reduction in the expected CT of OEC1 (16%) and OEC2 (18%) annual production while causing an increase of AMC1 (9%) and AMC2 (20%) completion time. Such a behaviour stresses out how a strong policy of the SC focal company (scenario A) can significantly affect performance of suppliers (Site 1 and Site 2) in meeting their own production requirements. On the other hand, the expected CTs of AMC1 and AMC2 are lower in scenario B than in scenario A.


Table 7 Pdf, expected value and coefficient of variation of the completion time for each product in case #1 and scenarios A and B

OEC1 OEC2 AMC1 AMC2

pdf

E(CT) [hour]

CV (CT)

pdf E(CT) [hour]

CV (CT)

pdf E(CT) [hour]

CV (CT)

pdf E(CT) [hour]

CV (CT)

Scenario A LogN 1573 0.062 LogN 1409 0.068 Loglogistic 1327 0.096 Loglogistic 1489 0.073

Scenario B LogN 1832 0.094 LogN 1668 0.104 Loglogistic 1199 0.041 Loglogistic 1185 0.038

∆E(CT) (%) -16.4 -18.3 9.64 20.41

Scenario A also allows a lower stochastic variability in the CT of OEC1 and OEC2 annual production if compared with scenario B (see CV values in Table 7). The opposite situation occurs under scenario B where the CT of AMC1 and AMC2 are characterised by a lower uncertainty, i.e. a better service level for customers of the aftermarket. The more uncertain the aftermarket demand is, the higher expected values, E(CT), and standard deviations, σ(CT), of OEC1 and OEC2 completion times are, as shown in Figure 4 with reference to scenario A: by comparing case #1 and case #3 for OEC2 an increase of about 5% in E(CT) and 150 % in σ(CT) occurs. The increase in the OEC1 and OEC2 completion time causes a reduction (∼2%) of the expected SC resource utilisation, U, estimated as average of sites’ expected utilisation (see Figure 4). Once more, the raising of demand variability from case #1 to case #3 causes an increase (∼60%) in the U standard deviation, σ(U).

Figure 4 Expected value and ±σ range of CT(OEC1) and CT(OEC2) and average SC utilisation at different level of AMCs demand uncertainty, as per case #1, #2, and #3 in scenario A


Experiment 2

A sensitivity analysis is also performed to assess the influence of demand uncertainty location on SC performance. For a given product, the sensitivity parameter considered is defined as:

CV(CTj)Sj=CVS(AMC)

where:

CVS(AMC) = CV(AMC1) + CV(AMC2) and j = OEC1, OEC2, AMC1, AMC2.

Three situations are considered under scenario A:

I. Uncertainty in the aftermarket demand occurs only in AMC1 demand (Site 1) while AMC2 demand is deterministically known (CV(AMC2) = 0) and equal to the monthly expected value.

II. Uncertainty occurs only in AMC2 demand (Site 2) while AMC1 demand is deterministically known (CV(AMC1) = 0) and equal to monthly expected value.

III. Uncertainty occurs both in AMC1 and in AMC2 demand ((CV(AMC1) ≠ 0) and (CV(AMC2) ≠ 0)).

With reference to situation I., in Figures 5a, Sj parameter as well as CV(CTj) of annual production completion time of OEC1, and OEC2 are plotted against CVS(AMC) = CV(AMC1). The values of Sj parameter are constantly lower than 1; this is a measure of reduction in uncertainty transferred to CT from AMC1 demand uncertainty. Moreover, for CV(AMC1) = 0.252 (see case #2 in Table 6), Si assumes the highest value, i.e. the manufacturing system shows its best attitude in transferring uncertainty from demand to product completion time. Finally, a decreasing trend of Si occurs for CVS(AMC) > 0.252. It reveals an increasing attitude of the SC in filtering and absorbing part of uncertainty introduced as demand variability at Site 1. However, for increasing CVS(AMC) values, CV(CT) of OEC1 and OEC2 increase as well, even if Si decreases. For example in Figure 5a, for CVS(AMC) ranging from 0.252 to 0.730, CV[CT(OEC1)] increases from 0.087 to 0.128 even if Si decreases from 0.347 to 0.175.

A lower effect on OEC1 and OEC2 completion time is due to demand variability of AMC2 at site 2 than to demand variability of AMC1 at site 1, as shown in Figure 5b (situation II, scenario A).


Figure 5a CVS(AMC) and CV(CTj) for each original equipment product in situation I under scenario Ad)

Figure 5b CVS(AMC) and CV(CTj) for each original equipment product in situation II under scenario A

The combined effect of both AMC1 and AMC2 demand variability on OEC1 and OEC2 completion time variability (situation III, scenario A) is shown in Figure 5c. The values of Sj and CT are lower than the corresponding values calculated under scenario B (Figure 5d). This is a tangible effect of the production policy adopted under the scenario A aiming at giving preference in meeting SC production requirements (OCE1 and OEC2). On the contrary, the higher Sj and CT values of OEC1 and OEC2 under scenario B are caused by local production policies of Site 1 and Site 2 which assign priority in meeting production requirements from the aftermarket.


Figure 5c CVS(AMC) and CV(CTj) for each original equipment product in situation III under scenario A

Figure 5d CVS(AMC) and CV(CTj) for each original equipment product in situation III under scenario B

5 Conclusions

Demand uncertainty affects SC performance. This paper investigates the effects of stochastic variability of demand level and location in a three stage SC of a multinational firm producing components for automotive braking equipments.

A SC dynamic demand of original equipment components is deterministically defined; a stochastically variable demand from the aftermarket at the first two stages of SC also occurs.

Sensitivity analyses of demand stochastic variability are performed under different scenarios. Scenarios differ in scheduling priorities of original vs. aftermarket equipment


components. A simulation model based on the Forrester approach is proposed to investigate completion times of both original and aftermarket components production.

Results obtained outline how level and location of demand uncertainty affect SC performance. A strategic planning of SC aimed at satisfying SC production requirements causes lower performance in those sites of the SC also involved in their aftermarket productions. On the other hand, in the case of production plans independently formulated by site, higher priorities are assigned to local rather than to SC productions. Results obtained in such a scenario show a decrease in SC performance in terms of increasing of both expected SC production completion time and in the standard deviation of such a performance.

In such a context, the simulation model reveals a suitable tool to negotiate contractual agreements between the focal company and the suppliers of a SC, as it represents a rationale basis for strategic and tactical decision making.

Acknowledgement

The research proposed in this paper was partially supported by the Italian Ministero della Ricerca Scientifica e Tecnologica (MURST) by funding a scientific project involving a research group of seven Italian universities on the topic of supply chain management by a federation of interacting simulators.

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Modelling dynamics of a supply chain under uncertainty: a case from the automotive industry