1 Introduction
2 Literature review
Number of echelons | Uncertainty | Capacity constraints | Facilities | Service level | Risk | Salvage value | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Paper | E | R | M | RL | O | C | RO | Objective | |||||
Aghezzaf (2005) | 3 | \(\bullet\) | \(\bullet\) | Min disc. costs | |||||||||
Allman and Zhang (2020) | 2 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min costs | ||||
Akbari et al. (2018) | 2 | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min weight. sum of primary & backup coverage, mean access time dev. from goal | ||||||||
Antunes and Peeters (2001) | 2 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min disc. costs | ||||||
Becker et al. (2019) | 2 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min costs | ||||
Behmardi and Lee (2008) | 2 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Max NPV | ||||||
Hammami and Frein (2014) | \(\geq\)3 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Max profit | |||||
2 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min costs | |||||
Lee (1991) | 2 | \(\bullet\) | \(\bullet\) | Min costs | |||||||||
Lee and Luss (1987) | 2 | \(\bullet\) | \(\bullet\) | Min costs | |||||||||
Martel (2005) | 3 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Max after tax net revenues | ||||||
Melachrinoudis and Min (2000) | 3 | (\(\bullet\)) | (\(\bullet\)) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Max disc. profit, Min access time, Max local incentives | ||||||
\(\geq\)3 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min discounted costs | ||||||
Paquet et al. (2004) | 3 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min costs | ||||||
Shulman (1991) | 2 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min disc. costs | |||||||
Thanh et al. (2008) | 3 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min costs | |||||||
Troncoso and Garrido (2005) | 2 | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min disc. costs | ||||||||
Vila et al. (2006) | 3 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Max profit | ||||||
Wilhelm et al. (2013) | \(\geq\)3 | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | \(\bullet\) | Min disc. costs | ||||||
Our model | 3 | \(\bf\bullet\) | \(\bf\bullet\) | \(\bf\bullet\) | \(\bf\bullet\) | \(\bf\bullet\) | \(\bf\bullet\) | \(\bf\bullet\) | \(\bf\bullet\) | \(\bf\bullet\) | \(\bf\bullet\) | \(\bf\bullet\) | Max weighted sum of NPV and CVaR |
3 A stochastic supply network design problem with relocatable modular capacities
3.1 Model Assumptions
3.1.1 Objective and risk awareness
3.1.2 Selection of production facilities
3.1.3 Installation of modular capacities at production facilities
3.1.4 Production process
3.1.5 Vendor selection to procure components
3.1.6 Consideration of stochastic demand
3.2 Approximation via piecewise linear functions
4 A programming approach for the RSNDPMC
4.1 A linear model formulation of the RSNDPMC
4.1.1 Objective function
4.1.2 NPV-related constraints
4.1.3 CVaR-related constraints
4.1.4 Demand fulfillment
4.1.5 Vendor-related constraints
4.1.6 Constraints regarding modular capacities
4.1.7 Selection of production facilities
4.2 A two-stage stochastic programming approach
5 Numerical results
5.1 Description of the test design
\(C\) | \(V\) | \(P\) | \(F\) | \(M\) | \(R\) | \(T\) | #TI | |
---|---|---|---|---|---|---|---|---|
PC 1 | 5 | 10 | 5 | 6 | 5 | 6 | 6 | 40 |
PC 2 | 5 | 10 | 10 | 10 | 10 | 6 | 12 | 40 |
TLim | TCPU | OptSol | ||
---|---|---|---|---|
[s] | [s] | [%] | ||
RSNDPMC-PLA | PC 1 | 21,600 | 6,311 | 80.0 |
PC 2 | 43,200 | 41,348 | 5.0 | |
RSNDPMC-PLA\({}_{s}\) | PC 1 | 3,600 | 68 | 98.8 |
PC 2 | 3,600 | 2,721 | 37.5 | |
RSNDPMC-NRL | PC 1 | 21,600 | 751 | 100.0 |
PC 2 | 43,200 | 38,580 | 17.5 |
5.2 Analysis of the relocatability of modules
-
the location of production facilities, i.e., establishing, running and closing,
-
and the assignment of modular capacities, i.e., the acquisition, holding, and selling of modules and, if applicable, their relocation
5.3 Simulation-based analysis of the robustness
SimFeas | \(P\times R\times T-\)Vio | ||
---|---|---|---|
[%] | [%] | ||
RSNDPMC-PLA | PC 1 | 90.0 | 0.14 |
PC 2 | 84.3 | 0.12 | |
RSNDPMC-PLA\({}_{s}\) | PC 1 | 92.0 | 0.09 |
PC 2 | 86.4 | 0.07 | |
RSNDPMC-NRL | PC 1 | 91.8 | 0.10 |
PC 2 | 84.2 | 0.12 |