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A location-inventory-distribution model under gradual injection of pre-disaster budgets with application in disaster relief logistics: a case study

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Abstract

Natural disasters lead to massive human and financial losses yearly; thus, disaster planning is of critical importance. One of the most crucial measures for disaster planning is developing an efficient disaster relief supply chain (DRSC) network. Thus, many researchers have focused on this field while overlooking some crucial actual conditions as a result of the complexity of the problem. Consequently, this study develops a DRSC network considering the perishability of relief commodities (RCs), the gradual injection of the limited pre-disaster budgets, pre-disaster lateral transportation, and the time value of money. In this respect, a novel multi-period multi-commodity mixed-integer non-linear programming model is presented, which optimizes pre-disaster warehouse location and inventory management and the post-disaster re-procurement and distribution of RCs in each period. Utilizing a new service utility index, the proposed model strives to minimize deprivation cost while maximizing demand coverage and fair service. To provide the required RCs in the pre-disaster phase, a bidirectional quantity flexibility contract (BQFC) is proposed, which is integrated with multi-sourcing and allows for two-part buybacks, installment and delayed payments, and quantity-based discounts on its terms. The applicability and performance of the model are validated via a real case study in Mashhad, Iran. Various sensitivity analyses are provided to highlight the desirable performance of the model and achieve helpful managerial insights.

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Data availability

The datasets generated during and, or analyzed during the current study and the model's codes in IBM ILOG CPLEX 12.10 software are available in the Github repository, https://github.com/leylafazli/ DRSC.

Notes

  1. It is a special case of the supplier selection problem, which determines which suppliers should be selected and how much should be purchased from each selected supplier.

  2. Lateral transportation refers to horizontal transportation within the same echelon.

  3. In an OC, a specific quantity of the suppliers' inventory can be reserved.

  4. A BC allows the buyer to return commodities up to the quantity of the initial purchase at an identical price for each unit.

  5. A QFC supplies the commodity up to a certain pre-agreed amount in excess of the initial order quantity.

  6. The concept of equity and how to measure it have been widely investigated in the literature. Braveman and Gruskin (2003) defined equity as the lack of systematic disparities among groups of people. The consideration of the equity concept in allocation/distribution decisions represents supplying demand points in a fair manner, as well as the best efforts to ensure that the required relief commodities are equally distributed among all demand points. Fair relief distribution among demand points is also an important point in HRSC (Beamon and Balcik 2008). The three main approaches frequently used to achieve equity as an objective in relief distribution include: 1. Minimax approach, 2. Maximin approach, and 3. Maxisum approach (Ransikarbum and Mason 2016).

  7. Social cost includes both logistics costs and deprivation costs. Deprivation costs include the costs imposed on casualties due to lack of access to required items or services (Holguín-Veras et al. 2013); consequently, these costs represent human suffering. Given the importance of deprivation costs in HRSC, certain researchers including Holguín-Veras have focused on how to estimate deprivation cost for each person affected by a disaster and have presented different deprivation cost functions.

  8. The possibility of returning commodities such that the supplier purchases a part of the total returned commodities at a specific unit price and the rest at another unit price.

  9. The duration an affected person is deprived of relief commodities.

  10. We conducted oral interviews with three experts from Mashhad's Red Crescent Society, one expert from the Department of Passive Defense of Mashhad's Governorate, and one expert from the Department of Passive Defense of Astan Quds Razavi, who specialize in crisis management and have complete information on the performance and situation of Iran's relief systems. We also conducted oral interviews with three professors of Ferdowsi University of Mashhad, who specialize in earthquakes.

  11. \(\sum_{w,g,a<{\acute{a}}_{g},t}{in}_{wgat}\)

  12. \(\sum_{s,d,g,t}{u}_{sdgt}\)

  13. \(\sum_{w,d,g,t}{z}_{wdgt}+\sum_{s,d,g,t}{u}_{sdgt}\)

  14. \(\sum_{w,d,g,t}F\left({\overline{t} }_{wd}\right){z}_{wdgt}+\sum_{s,d,g,t}F\left({\overline{\overline{t}}}_{sdg}\right){u}_{sdgt}\)(Cotes and Cantillo 2019)

  15. \(\sum_{t}{\delta }_{t}\)

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Authors and Affiliations

  1. Department of Industrial Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Leyla Fazli, Majid Salari & Hossein Neghabi

Authors
  1. Leyla Fazli
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  2. Majid Salari
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  3. Hossein Neghabi
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Contributions

LF: conceptualization, methodology, software, writing—original draft, review & editing. MS: conceptualization, methodology, and writing—review & editing. HN: conceptualization, methodology, and writing—review & editing.

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Correspondence to Majid Salari.

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Appendix 1: Data of the case study

Appendix 1: Data of the case study

Tables 5, 6, 7, 8, 9, 10, 11, 12 and Figs. 7, 8, 9, 10 present the data and information of the case study conducted in the present research.

Fig. 7
figure 7

Seismicity map of Iran from 1900 to 2020 (IIEES, www.iiees.ac.ir)

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Fig. 8
figure 8

Seismic hazard level map of different areas of Mashhad (Hafezi-Moghaddas 2007)

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Fig. 9
figure 9

Locations of affected areas, candidate warehouses, and suppliers

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Fig. 10
figure 10

Vulnerability rating of Mashhad's network of passages

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Table 5 Budgets for the establishment and procurement of relief supplies) million tomans(
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Table 6 Predicted damage percentage (%), population size, number of affected people, and demand (unit)
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Table 7 Storage capacity (unit), establishment cost (million tomans), and percentage of unusable inventory (%)
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Table 8 Contract parameters for every supplier-provided quantity interval
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Table 9 Coefficient of disruption in transport route, and normal and post-earthquake travel time (in minutes) between the warehouses and the centers of the affected areas
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Table 10 Coefficient of disruption in transport route, and normal and post-earthquake travel time (in minutes) between the suppliers of drinking water and the centers of the affected areas
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Table 11 Coefficient of disruption in transport route, and normal and post-earthquake travel time (in minutes) between suppliers of conserves and centers of affected areas
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Table 12 Sensitivity analysis on \({\beta }_{1}\) and \({\beta }_{2}\)
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As can be seen in Table 12, by increasing \({\beta }_{1}\) or decreasing \({\beta }_{2}\), the optimal values of TSU and TES follow an incremental trend and a decremental trend, respectively. Notably, TSU has slightly increased, and TES has been realized very little by raising \({\beta }_{1}>\) 0.5 or decreasing \({\beta }_{2}<\) 0.5. Moreover, by decreasing \({\beta }_{1}<\) 0.5 or increasing \({\beta }_{2}>\) 0.5, TSU has considerably reduced, while TES has significantly increased. Therefore, considering the higher priority of the efficacy-distress measure than the balance measure and the obtained results, \({\beta }_{1}\) and \({\beta }_{2}\) are set to 0.5 in this case study.

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Fazli, L., Salari, M. & Neghabi, H. A location-inventory-distribution model under gradual injection of pre-disaster budgets with application in disaster relief logistics: a case study. Soft Comput 28, 2125–2159 (2024). https://doi.org/10.1007/s00500-023-09184-8

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