A case study on sample average approximation method for stochastic supply chain network design problem

doi:10.15302/J-FEM-2017032

Front. Eng

2017, Vol. 4

Issue (3) : 338-347 https://doi.org/10.15302/J-FEM-2017032

RESEARCH ARTICLE

A case study on sample average approximation method for stochastic supply chain network design problem

Yuan WANG(

), Ruyan SHOU, Loo Hay LEE, Ek Peng CHEW

Department of Industrial Systems Engineering & Management, National University of Singapore, Singapore 117576, Singapore

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Abstract

This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies. Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation (SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.

Keywords supply chain network stochastic demand sampling average approximation Bayesian bootstrap Latin hypercube sampling

Corresponding Author(s): Yuan WANG

Just Accepted Date: 29 August 2017 Online First Date: 28 September 2017 Issue Date: 30 October 2017

Cite this article:

Yuan WANG,Ruyan SHOU,Loo Hay LEE, et al. A case study on sample average approximation method for stochastic supply chain network design problem[J]. Front. Eng, 2017, 4(3): 338-347.

URL:

https://academic.hep.com.cn/fem/EN/10.15302/J-FEM-2017032
https://academic.hep.com.cn/fem/EN/Y2017/V4/I3/338

Fig.1 Company SCN design

Fig.2 Supply chain strategies of the company

Decision variables	Description
$X ijcs$	No. of type c products shipped from FE i to DB j by shipment level s
$Y jkcs$	No. of type c products shipped from DB j to BE k by shipment level s
$α ijcs$	1 if type c products are shipped from FE i to DB j by shipment level s, 0 otherwise
$β jkcs$	1 if type c products are shipped from DB j to BE k by shipment level s, 0 otherwise
$γ j$	1 if DB j is selected, 0 otherwise
$δ$	1 if the route between Batam and U is selected (as it is a monthly fixed cost), 0 otherwise
$ζ i k c L s$	1 if demand $d i k c$ is larger than or equal to the lower bound of shipment level s, 0 otherwise
$ζ i k c U s$	1 if demand $d i k c$ is smaller than the upper bound of shipment level s, 0 otherwise
$η ikcs$	1 if shipment level s is used for demand $d i k c$ , 0 otherwise
$θ c$	1 if demand of type c products is nonzero, 0 otherwise.

Tab.1 Decision variables

Parameters	Description
$d i k c$	Demand of type c products from BE k, which is supposed to be produced at designated FE i
$L s$	Lower bound of shipment level s
$U s$	Upper bound of shipment level s
$c i j s α$	Transportation cost from FE i to DB j per carton by shipment level s in EURO
$c j k s β$	Transportation cost from DB j to BE k per carton by shipment level s in EURO
$c γ$	Transportation cost between B and U per trip in SGD
$f j$	Storage cost of DB j per month in EURO
$r E u r o S G D$	Exchange rate from EURO to SGD (based on the exchange rate on 27/10/16) ( $r E u r o S G D$ = 1.52)
$M$	No. of months per year (M= 12)
$W$	No. of weeks per year (W= 52)
$T$	No. of trips between B and U per week (t = 7)
$K$	A large integer (K= 100000)

Tab.2 Parameters used in the model

Fig.3 BFC on DB decision variables

Tab.3 DB decisions obtained based on 12-month demands

Tab.4 Objectives obtained based on 12-month demands for four cases defined by BFC

Tab.5 Top 3 SAA Solution values and Gaps

Tab.6 Comparative results between stochastic and deterministic demand

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