Designing an integrated multi-echelon agile supply chain network: a hybrid taguchi-particle swarm optimization approach

The present paper attempts to explore the integration of production, distribution and logistics activities at the strategic decision making level where, the objective is to design a multi-echelon supply chain network considering agility as a key design criterion. The design network conceived here addresses a class of five echelons of supply chains including suppliers, plants, distribution centers, cross-docks and customer zones. The problem has been mathematically formulated as a multi-objective optimization model that aims to minimize the cost (fixed and variable) and maximizes the plant flexibility and volume flexibility. The notion of cross-dock has been introduced as an intermediate level between distribution centers and customer zones to increase the profitability of manufacturing and service industries. In order to solve the underlying problem, a novel algorithm entitled hybrid taguchi-particle swarm optimization (HTPSO) has been proposed that incorporates the characteristics of statistical design of experiments and random search techniques. The main idea is to integrate the fundamentals of taguchi method i.e. orthogonal array and signal to noise ratio (SNR) in the PSO meta-heuristic to minimize the effect of the causes of variations. The proposed model has been authenticated by undertaking problem instances of varying size. Extensive computational experiments are conducted to validate the same and also the efficacy of the proposed HTPSO algorithm. The results obtained reveal that proposed solution methodology is an effective approach to solve the underlying problem.

s = 1, 2,..., S :

Set of suppliers

p = 1, 2,..., P :

Set of plants

k = 1, 2,..., K :

Set of possible distribution centers

j = 1, 2,..., J :

Set of possible cross-docks

m = 1, 2,..., M :

Set of customer zones

i = 1, 2,..., I :

Product type

r = 1, 2,..., R :

Raw material type

λ _ip :

Quantity of product i produced at plant p

ν _ipk :

Quantity of product i transported from plant p to distribution center k

φ _rsp :

Quantity of raw material r transported from supplier s to plant p

AGCD _j :

Agility level of cross-dock j

AGDC _k :

Agility level of distribution center k

AGP _p :

Agility level of plant p

AGS _s :

Agility level of supplier s

CCD _j :

Capacity of cross-dock j to handle product families

CDC _k :

Capacity of distribution center k to handle product families

CDF :

Cross-dock flexibility

CSC _mj :

Cost to supply product i from cross-dock j which would be used by the customer zone m

DCF :

Distribution center flexibility

D _mi :

Demand from customer zone m for product i

DVF _m :

Distribution volume flexibility of customer zone m

FCD _j :

Fixed operating cost to open cross- dock j

FCP _p :

Fixed cost for plant p

FDC _k :

Fixed cost for distribution center k

HAG _l :

Lower bound of high agility performance index (0.8)

HAG _u :

Upper bound of high agility performance index (1.0)

I :

Total number of products to be manufactured

J :

Total number of cross-docks

K :

Total number of distribution centers

LAG _l :

Lower bound of low agility performance index (0.4)

LAG _u :

Upper bound of low agility performance index (0.6)

M :

Total number of customer zones

MAG _l :

Lower bound of medium agility performance index (0.6)

MAG _u :

Upper bound of medium agility performance index (0.8)

MNPV _ip :

Minimum production volume for product i at plant p

MNTH _k :

Minimum throughput at distribution center k

MXC :

Maximum number of cross-docks to be opened

MXD :

Maximum number of distribution centers to be opened

MXPV _ip :

Maximum production volume for product i at plant p

MXTH _k :

Maximum throughput at distribution center k

norm(.) :

Represents normalized objective (.)

Obj :

Final integrated objective function

P :

Total number of plants

PCP _p :

Production capacity for each plant p

PCV _rs :

Production capacity of supplier s for raw material r

PF :

Plant flexibility

PVF _m :

Plant volume flexibility

SUP _ip :

Standard units at plant p per unit of product i

R :

Total number of raw material to be supplied

S :

Total number of suppliers

SF :

Supplier flexibility

SUDC _ik :

Standard units at distribution center k per unit of product i

TC _m :

Total cost of m customer zone

UCR _rs :

Unit cost of raw material r for supplier s

UCT _ik :

Unit cost of throughput (handling and inventory) for product i at distribution center k

UPCP _ip :

Unit production cost for product i at plant p

UR _ri :

Utilization rate for each raw material r per unit of product i

UTCD _ikj :

Unit transportation cost from distribution center k to cross-dock j for product i

UTCP _ipk :

Unit transportation cost from plant p to distribution center k for product i

UTCR _rsp :

Unit transportation cost from supplier s to plant p for raw material r

w _1m :

Weight assigned by manufacturer to cost objective

w _2m :

Weight assigned by manufacturer to distribution volume flexibility

w _2m :

Weight assigned by manufacturer to distribution volume flexibility

w _3m :

Weight assigned by manufacturer to plant flexibility

X _p :

$$ =\left\{ \begin{array}{ll} 1, & {\rm if\, plant}\, p\,{\rm is\, open}\\ 0, & {\rm otherwise} \end{array} \right. $$

Y _k :

$$=\left\{\begin{array} {ll} 1, & {\rm if\, distribution\, center}\, k\,{\rm is\, open}\\ 0, & {\rm otherwise} \end{array}\right.$$

Z _j :

$$=\left\{ {\begin{array}{ll} 1, & {\rm if\, cross\, dock}\, j\,{\rm is\, open}\\ 0, & {\rm otherwise} \end{array}} \right.$$

R _jki :

$$=\left\{ {\begin{array}{lll} 1, & {if\, cross\, dock}\, j\,{\rm is\, assigned\, to}\\ & {\rm distribution\, center\, k\, for\, product\, i} \\ 0, & {\rm otherwise}\\ \end{array}} \right.$$

A _mji :

$$=\left\{ {\begin{array}{lll} 1, & {\rm if\, customer\, zone}\, m\,{\rm is assigned}\\ &{\rm to\, cross\, dock\, j\, for\, product\, i}\\ 0, & {\rm otherwise} \end{array}} \right.$$

N _s :

$$ =\left\{ {\begin{array} {ll} 1, & {\rm if\, supplier}\, s\,{\rm is\, selected}\\ 0, & {\rm otherwise} \end{array}} \right.$$

Authors and Affiliations

1. Department of Manufacturing Engineering, NIFFT, Ranchi, India

   Manish Bachlaus & Mayank Kumar Pandey

2. Software Engineer, Hewlett Packard Global Soft Limited, Chennai, India

   Chetan Mahajan

3. Department of Management Studies, IIT, Delhi, India

   Ravi Shankar

4. Department of Industrial Engineering and Management, IIT, Kharagpur, India

   M. K. Tiwari

Corresponding author

Correspondence to M. K. Tiwari.

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