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System reliability for a multi-state distribution network with multiple terminals under stocks

  • S.I. : Reliability Modeling with Applications Based on Big Data
  • Published:
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Abstract

To achieve the most efficiency in supply chain management, the capability of distribution networks is a key point for the entire supply chain. Stocks are critical for enhancing the efficiency of satisfying the demand of retailers in the distribution network. A configuration of a distribution network is consisted of routes and nodes. Each route connects a pair of nodes and each node is denoted as a supplier, a distribution center, or a retailer. For each route, it has a carrier whose available capacity for demand transmission is multi state. Hence, a distribution network is also regarded as a multi state network and such a network is named as a multi state distribution network (MDN) in here. The propose of this paper is to evaluate the system reliability which is defined as the probability that the MDN can meet all retailers’ demand under stocks. In practical, all retailers’ demand should be satisfied by stocks in the distribution centers (DCs) firstly. Therefore flow assignment in MDN model is mainly clarified by the relationship between the demand of retailers, stocks on DCs, and suppliers. The concept of minimal capacity vectors (MCVs) is then proposed and an algorithm is developed to obtaining MCVs for evaluating system reliability.

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Abbreviations

N :

Set of nodes including suppliers, DCs and retailers

A :

Set of routes connecting nodes

G :

A multi-state distribution network (MDN)

n :

Number of routes

a i :

The ith route in G, i = 1, 2, …, n

r :

Number of suppliers

v e :

The eth supplier in G, e = 1, 2, …, r

o :

Number of DCs

c g :

The gth transfer center in G, g = 1, 2, …, o

q :

Number of retailers

T h :

The hth retailer in G, h = 1, 2, …, q

π i :

Number of states that route ai posses

b ir :

Capacity of route ai, r = 1, 2, …, πi where bi1 = 0

w :

The consumed capacity by per unit of commodity

d h :

The demand for the hth retailer, h = 1, 2, …, q

Z :

(z1, z2, …, zo)

z g :

The amount of stocks in the distribution center, g = 1, 2, …, o

D :

(d1, d2, …, dq)

(s, t):

(Source node, target node): a node pair

E(s, t):

Set of MP from s to t

m :

Total number of MPs in all E(s, t)

P k :

The kth path in in all E(s, t), k = 1, 2, …, m

f k :

Flow through Pk

F :

(f1, f2, …, fm)

x i :

The current capacity of route ai

X :

A capacity vector (x1, x2, …, xn)

R D :

System reliability for G

MP:

Minimal path

MDN:

Multi-state distribution network

D-MCV:

Minimal capacity vector for demand D under Z

RSDP:

Recursive sum of disjoint products

References

  • Chen, S. G., & Lin, Y. K. (2016). Searching for d-MPs with fast enumeration. Journal of Computational Science, 17, 139–147.

    Article  Google Scholar 

  • Chopra, S. (2003). Designing the distribution network in a supply chain. Transportation Research Part E: Logistics and Transportation Review, 39, 123–140.

    Article  Google Scholar 

  • Costa, A., Celano, G., Fichera, S., & Trovato, E. (2010). A new efficient encoding/decoding procedure for the design of a supply chain network with genetic algorithms. Computers and Industrial Engineering, 59, 986–999.

    Article  Google Scholar 

  • Ford, L. R., & Fulkerson, D. R. (1962). Flows in networks. New Jersey: Princeton University.

    Google Scholar 

  • Ho, W., & Emrouznejad, A. (2009). Multi-criteria logistics distribution network design using SAS/OR. Expert Systems with Applications, 36, 7288–7298.

    Article  Google Scholar 

  • Huang, C. F. (2019). Evaluation of system reliability for a stochastic delivery-flow distribution network with inventory. Annals of Operations Research, 277(1), 33–45.

    Article  Google Scholar 

  • Lin, Y. K. (2001). A simple algorithm for reliability evaluation of a stochastic-flow network with node failure. Computers and Operations Research, 28, 1277–1285.

    Article  Google Scholar 

  • Lin, Y. K., Huang, C. F., & Liao, Y. C. (2019). Reliability of a stochastic intermodal logistics network under spoilage and time considerations. Annals of Operations Research, 277(1), 95–118.

    Article  Google Scholar 

  • Lin, Y. K., Huang, C. F., Liao, Y. C., & Yeh, C. C. (2017). System reliability for a multistate intermodal logistics network with time windows. International Journal of Production Research, 55, 1957–1969.

    Article  Google Scholar 

  • Mishra, U., Cárdenas-Barrón, L. E., Tiwari, S., Shaikh, A. A., & Treviño-Garza, G. (2017). An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment. Annals of Operations Research, 254(1–2), 165–190.

    Article  Google Scholar 

  • Ni, D., & Li, K. W. (2012). A game-theoretic analysis of social responsibility conduct in two-echelon supply chains. International Journal of Production Economics, 138, 303–313.

    Article  Google Scholar 

  • Ozsen, L., Coullard, C. R., & Daskin, M. S. (2008). Capacitated warehouse location model with risk pooling. Naval Research Logistics, 55, 295–312.

    Article  Google Scholar 

  • Ramezani, M., Bashiri, M., & Tavakkoli-Moghaddam, R. (2013). A new multi-objective stochastic model for a forward/reverse logistic network design with responsiveness and quality level. Applied Mathematical Modelling, 37, 328–344.

    Article  Google Scholar 

  • Sarkar, B. (2013). A production-inventory model with probabilistic deterioration in two-echelon supply chain management. Applied Mathematical Modelling, 37, 3138–3151.

    Article  Google Scholar 

  • Sarkar, B., Mandal, B., & Sarkar, S. (2015). Quality improvement and backorder price discount under controllable lead time in an inventory model. Journal of Manufacturing Systems, 35, 26–36.

    Article  Google Scholar 

  • Shaikh, A. A., Bhunia, A. K., Cárdenas-Barrón, L. E., Sahoo, L., & Tiwari, S. (2018). A fuzzy inventory model for a deteriorating item with variable demand, permissible delay in payments and partial backlogging with shortage follows inventory (SFI) policy. International Journal of Fuzzy Systems, 20(5), 1606–1623.

    Article  Google Scholar 

  • Sicilia, J., González-De-la-Rosa, M., Febles-Acosta, J., & Alcaide-López-de-Pablo, D. (2014). An inventory model for deteriorating items with shortages and time-varying demand. International Journal of Production Economics, 155, 155–162.

    Article  Google Scholar 

  • Tiwari, S., Cárdenas-Barrón, L. E., Goh, M., & Shaikh, A. A. (2018). Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain. International Journal of Production Economics, 200, 16–36.

    Article  Google Scholar 

  • Whicker, L., Bernon, M., Templar, S., & Mena, C. (2009). Understanding the relationships between time and cost to improve supply chain performance. International Journal of Production Economics, 121, 641–650.

    Article  Google Scholar 

  • Yang, C. T. (2014). An inventory model with both stock-dependent demand rate and stock-dependent holding cost rate. International Journal of Production Economics, 155, 214–221.

    Article  Google Scholar 

  • Yeh, W. C. (2018). Fast algorithm for searching d-MPs for all possible d. IEEE Transactions on Reliability, 67(1), 308–315.

    Article  Google Scholar 

  • Yeh, W. C., Bae, C., & Huang, C. L. (2015). A new cut-based algorithm for the multi-state flow network reliability problem. Reliability Engineering and System Safety, 136, 1–7.

    Article  Google Scholar 

  • Yu, M., & Nagurney, A. (2013). Competitive food supply chain networks with application to fresh produce. European Journal of Operational Research, 224, 273–282.

    Article  Google Scholar 

  • Zuo, M. J., Tian, Z., & Huang, H. Z. (2007). An efficient method for reliability evaluation of multistate networks given all minimal path vectors. IIE Transactions, 39, 811–817.

    Article  Google Scholar 

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Acknowledgements

This research was supported in part by the Ministry of Science and Technology (MOST) of Taiwan, ROC under Grant MOST107-2218-E-035-011-MY2.

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  1. Department of Business Administration, Feng Chia University, Taichung, 40724, Taiwan, ROC

    Cheng-Fu Huang

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Huang, CF. System reliability for a multi-state distribution network with multiple terminals under stocks. Ann Oper Res 311, 117–130 (2022). https://doi.org/10.1007/s10479-020-03546-3

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  • DOI: https://doi.org/10.1007/s10479-020-03546-3

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