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

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## Abstract

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.

## Keywords

Multi-echelon supply chain Agility Hybrid taguchi-particle swarm optimization## Notations

## Indices

*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

## Notations

*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

## Decision Variables

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

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