A decision support system for configuring spare parts supply chains considering different manufacturing technologies

Figures & data

Figure 1. Control volume considered to develop this study (within the dashed rectangle).

The figure depicts the control volume considered to develop the mathematical model and achieve the decision support system.

Figure 2. Schematic representation of the five SC configurations considered. $\mathit{Deg}$ equal to 0 corresponds to a decentralised SC configuration, $\mathit{Deg}$ equal to 1 is a centralised configuration, and the values in between are hybrid SC configurations. The picture considers an example of a two-echelon SC serving six customers.

The figure shows a schematic representation of the five supply chain configurations examined to develop the decision support system. The five configurations vary based on the degree of centralization of the supply chain, which can assume value zero (that is full decentralisation), value one (that is full centralisation), three values (that are 0.25, 0.50, or 0.75), that correspond to an hybrid supply chain configuration.

Figure 3. Matrix of the spare parts SC designs considered in the DSS.

The figure depicts a mtrix which summarises all the the supply chain design cosidered to perform the analysis and develop the decision support system. The ten supply chain design can assume all the integer numbers between 1 and 10. Odd numbers refer to supply chains delivering AM spare parts, while even numbers refer to CM supply chains. Moreover, numbers 1 and 2 refer to decentralised supply chains, numbers 9 and 10 consider centralised supply chains, while numbers 3 to 8 imply hybrid supply chains (with a degree of centralisation equal to 0.25, 0.50, or 0.75).

Table 1. Input parameters for the mathematical model.

Input parameter	Description	Unit measure
$i$	Considered SC design. $i$ can assume integer values between 1 and 10 according to Figure 3	[–]
$j$	Manufacturing technology of the purchased spare parts. $j$ can be AM or CM	[–]
$\mathrm{\#customers}$	Number of customers served by the company	[–]
$\mathrm{ELTSL}$	Desired expected lead time service level$\mathrm{ELTSL}$	[–]
${\overline{D}}_{1\mathrm{customer}}$	Average annual demand for SKU emitted by one customer	[units/time]
$\mathrm{De}{g}_i$	Degree of centralisation in SC configuration $i$. It assumes a specific value according to Figure 3^a	[–]
$\mathrm{etcentra}{l}_i$	Unitary external transportation cost from the central DC to customers. It only refers to centralised SC configurations ($i=9$ or$i=10$)	[€/transportation]
$\mathrm{uback}$	Unitary cost of one backorder of SKU	[€/backorder]
$L_j$	Lead time needed by the supplier to deliver the j-th SKU to DCs	[time]
$u{c}_j$	Unitary cost of purchasing the j-th SKU from the supplier	[€/unit]
$\mathrm{mh}$	Hourly labour cost	[€/time]
$\mathrm{ot}$	Average time needed to send one replenishment order	[time]
$h_{\mathrm{\%}}$	Holding cost rate for keeping inventory of SKU	[€/time*unit]

^a $\mathrm{De}{g}_i$ is 0 if $i$ is equal to 1 or 2, is 0.25 if $i$ is equal to 3 or 4, is 0.5 if $i$ is equal to 5 or 6, is 0.75 if $i$ is equal to 7 or 8, while is 1 if $i$ is equal to 9 or 10.

Table 2. Parameters and values of discretised parametric analysis.

Input parameter	Admissible values	Unit measure	Source used to define the admissible values
$\mathrm{\#customers}$	5; 53; 100	[–]	Authors’ experience^a
$\mathrm{ELTSL}$	0.85; 0.92; 0.99	[–]	Authors’ experience
${\overline{D}}_{1\mathrm{customer}}$	1; 4; 7	[units/year]	(Knofius et al. 2021)
$\mathrm{etcentra}{l}_i$	100; 1,050; 2,000	[€/transportation]	Authors’ experience
$\mathrm{uback}$	1,000; 50,500; 100,000	[€/backorder]	(Peron et al. 2021)
$L_{\mathrm{AM}}$	1; 2.5; 4	[weeks]	(Knofius et al. 2021)
$L_{\mathrm{CM}}$	4; 15; 26	[weeks]	(Knofius et al. 2021)
$u{c}_{\mathrm{AM}}$	100; 1,300; 2’500	[€/unit]	(Knofius et al. 2021)^b
$u{c}_{\mathrm{CM}}$	10; 1,255; 2,500	[€/unit]	(Knofius et al. 2021)^c

^a The over twenty years' experience of some of the authors in the field of logistics and spare parts management combined with the consultation of expert staff from spare parts distribution companies make these assumptions reliable.

^b Knofius et al. (2021) considered 1197 €/unit. We have assumed a wider range.

^c Knofius et al. (2021) reported that the cost of CM parts is typically lower than AM ones, but this does not always hold true (it depends on the part complexity). Hence, we assumed a minimum value lower than AM, but the same upper limit.

Table 3. Values considered in the Sobol-based parametric analysis. The range extreme values are based on Table 2.

Input parameter	Range of admissible values	Unit measure
$\mathrm{\#customers}$	integers between 5 and 100	[–]
$\mathrm{ELTSL}$	floats between 0.85 and 0.99	[–]
${\overline{D}}_{1\mathrm{customer}}$	integers between 1 and 7	[units/year]
$\mathrm{etcentra}{l}_i$	floats between 100 and 2,000	[€/transportation]
$\mathrm{uback}$	floats between 1,000 and 100,000	[€/backorder]
$L_{\mathrm{AM}}$	integers between 1 and 4	[weeks]
$L_{\mathrm{CM}}$	integers between 4 and 26	[weeks]
$u{c}_{\mathrm{AM}}$	floats between 100 and 2,500	[€/unit]
$u{c}_{\mathrm{CM}}$	floats between 10 and 2,500	[€/unit]

Figure 4. Results of the ANOVA (Main Effects Plots) for the optimal SC design.

The figure depicts the results of the ANOVA analysis conducted. Nine graphs are represented (one for each independent variable affecting the proposed mathematical model). The plots prove that the impact of three out of nine variables (lead time AM, lead time CM, and the expected service level) can be considered negligible in respect to the optimal supply chain design suggested by the mathematical model.

Figure 5. Sensitivity analysis on the accuracy ($\mathit{A}$) of the decision tree.

The figure depicts by means of a graph the sensitivity analysis conducted to study the trend of the decision tree accuracy (y-axes) when varying the maximum depth of the tree (x-axes).

Figure 6. Decision tree with a maximum depth of 4 levels ($\mathit{Dmax}=4$).

The figure depicts the 4-levels decision tree provided as a decision support system. Threshold values are reported for the independent variables, to guide managers and practitioners in choosing the optimal supply chain design.

Figure 7. Relative importance of the independent parameters on the decision of the optimal SC design.

The figure presents a histogram, showing the relative importance (y-axes) of the model independent variables (x-axes), where a higher relative importance means that such variable strongly affect the optimal SC design suggested by the decision support system.

Figure A1. Relationship between centralised and decentralised transportation costs.

The figure depicts the relationship between centralised and decentralised transportation costs. Specifically, an interpolating curve represents the increase in transportation cost achieved by moving from a decentralised configuration (where each DC is close to its specific customer) to a centralised one, passing through hybrid configurations.

Knofius, N., M. C. van der Heijden, A. Sleptchenko, and W. H. M. Zijm. 2021. “Improving Effectiveness of Spare Parts Supply by Additive Manufacturing as Dual Sourcing Option.” OR Spectrum 43: 189–221. doi:10.1007/s00291-020-00608-7.

 Web of Science ®Google Scholar

Peron, M., N. Knofius, R. Basten, and F. Sgarbossa. 2021. Impact of Failure Rate Uncertainties on the Implementation of Additive Manufacturing in Spare Parts Supply Chains, in: IFIP Advances in Information and Communication Technology. Presented at the IFIP WG 5.7 International Conference on Advances in Production Management Systems, APMS 2021, Nantes, pp. 291–299. doi:10.1007/978-3-030-85914-5_31.

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6. Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary material.