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Location and design decisions of facilities in a distribution system with elastic customer demand

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Abstract

This paper describes a bi-level programming model that seeks to simultaneously optimize location and design decisions of facilities in a distribution system in order to realize company’s maximal total profit subject to the constraints on the facility capacity and the investment budget. In the upper-level problem, two-echelon integrated competitive/uncompetitive capacitated facility location model, which involves facility location and design, is presented. In the lower-level problem, customer is assumed to patronize store based on facility utility which is expressed by service time cost in the store and its travel cost to customer. Customer’s facility choice behavior is presented by a stochastic user equilibrium assignment model with elastic demand. Since such a distribution system design problem belongs to a class of NP-hard problem, a genetic algorithm (GA)-based heuristic procedure is presented. Finally, a numerical example is used to illustrate the application of the proposed model and some parameter sensitivity analyses are presented.

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Abbreviations

B :

Total available budget

c ij :

Actual total generalized cost for customer i visiting store j

C :

Total profit of the distribution system

C i (c i ):

The minimum perceived generalized cost by customer i

C ij :

Perceived cost for customer i visiting store j

C kj :

Transportation cost per unit of commodity from DC k to store j

C x j :

Setup cost for installing store j

C x k :

Setup cost for installing DC k

C z j :

Fixed closing cost for store j

C z k :

Fixed closing cost for DC k

d ij :

Distant cost between customer i and store j

D i :

Total demand of customer i

D ij :

Demand from customer i to store j

D j :

Total demand in store j

D k :

Total demand in DC k

F k :

Facility operating cost for DC k

F j :

Facility operating cost for store j

I :

Set of customers, indexed by i ∈ I

J :

Set of potential sites for stores owned by the company, indexed by j ∈ I, J = Q − L

J c :

Set of existing stores owned by the company, J c ⊂ J

J 0 :

Set of sites available for new stores owned by the company, J 0 ⊂ J

J*:

The optimal set of locations for stores owned by the company, J* ⊂ J

K :

Set of existing and potential sites for DCs of the company, indexed by k ∈ K

K c :

Set of existing DCs owned by the company, K c ⊂ K

K 0 :

Set of potential sites for DCs owned by the company, K 0 ⊂ K

L :

Subset of existing stores owned by the competitors, L ⊂ Q

N k :

Set of possible number of servers in DCs

N j :

Set of possible number of servers in stores

p c :

The obtained profits of unit demand

P ij :

The probability of choosing store j for customer i

q :

The average queue length in steady state

Q :

Set of potential sites for stores including some of existing stores

s j :

The size of store j, j ∈ J 0

s k :

The size of DC k, k ∈ K 0

S 1 :

Set of possible sizes of the potential DCs

S 2 :

Set of possible sizes of the potential stores

tj :

The minimum service time for customer to visit store j

t q :

The average time of customer in queue

X j :

The state decision variable for store j

Y k :

The state decision variable for DC k

Z jk :

The decision variable for whether store j is serviced by DC k

α :

Positive dispersion parameter

β :

Demand elasticity parameter

γ :

Coefficient of service time cost

δ j (·):

Cost function determining the operating cost associated with opening an store

δ k (·):

Cost function determining the operating cost associated with opening a DC

λ :

Customer intensity

μ :

Service rate

ξ ij :

Random component of customer perceived cost C ij

χ j (·):

Cost function determining the setup cost associated with opening a new store

χ k (·):

Cost function determining the setup cost associated with opening a new DC te]Ψ i (·)-Customer function of the minimum generalized cost C i (c i )

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Authors and Affiliations

  1. Research Center of Cluster and Enterprise Development, School of Business and Management, Jiangxi University of Finance and Economics, Nanchang, 330013, China

    Xue-feng Wang  (王雪峰)

  2. Department of Industrial Engineering and Logistics Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

    Xue-feng Wang  (王雪峰)

Authors
  1. Xue-feng Wang  (王雪峰)
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Correspondence to Xue-feng Wang  (王雪峰).

Additional information

Foundation item: the 2009 Science Foundation for Youths of the Department of Education of Jiangxi Province (No. GJJ09558), and the 2009 Humanities and Social Science found of College of Jiangxi Province (No. GL0911)

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Wang, Xf. Location and design decisions of facilities in a distribution system with elastic customer demand. J. Shanghai Jiaotong Univ. (Sci.) 14, 606–612 (2009). https://doi.org/10.1007/s12204-009-0606-1

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