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Optimizing capacity, pricing and location decisions on a congested network with balking

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Abstract

In this paper, we consider the problem of making simultaneous decisions on the location, service rate (capacity) and the price of providing service for facilities on a network. We assume that the demand for service from each node of the network follows a Poisson process. The demand is assumed to depend on both price and distance. All facilities are assumed to charge the same price and customers wishing to obtain service choose a facility according to a Multinomial Logit function. Upon arrival to a facility, customers may join the system after observing the number of people in the queue. Service time at each facility is assumed to be exponentially distributed. We first present several structural results. Then, we propose an algorithm to obtain the optimal service rate and an approximate optimal price at each facility. We also develop a heuristic algorithm to find the locations of the facilities based on the tabu search method. We demonstrate the efficiency of the algorithms numerically.

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Abbreviations

N :

A discrete set of demand nodes, N = {1, 2, . . . , n}

m :

Predefined number of facilities to be located on the network

w i :

Potential demand rate of node i

c :

Unit cost of service at facilities

d ij :

Distance between nodes \({i,j\in N}\)

α i :

The price sensitivity at node i, α i  > 0

l :

Queue length threshold

β :

Fraction of demand that abandon the facility when the queue length exceeds the threshold l

λ j :

Demand rate of facility j

\({p_{j}^{s}}\) :

Probability that a customer joins the queue at facility j

pr ij :

Fraction of demand of node i that arrives at facility j

\({c_{\mu}^{j}}\) :

Variable cost per unit of service rate at node j

\({c_{0}^{j}}\) :

Fixed cost of locating a facility at node j

Y j :

If a facility is located at node j, 0 otherwise

P :

Price of the service

μ j :

Service rate at facility j

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Authors and Affiliations

  1. Department of Management Sciences, University of Waterloo, Waterloo, N2L 3G1, Canada

    Hossein Abouee-Mehrizi

  2. Joseph L. Rotman School of Management, University of Toronto, Toronto, M5S 3E6, Canada

    Oded Berman

  3. Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

    Sahar Babri & Hassan Shavandi

Authors
  1. Hossein Abouee-Mehrizi
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  2. Sahar Babri
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  3. Oded Berman
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  4. Hassan Shavandi
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Corresponding author

Correspondence to Hossein Abouee-Mehrizi.

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Abouee-Mehrizi, H., Babri, S., Berman, O. et al. Optimizing capacity, pricing and location decisions on a congested network with balking. Math Meth Oper Res 74, 233–255 (2011). https://doi.org/10.1007/s00186-011-0361-6

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  • DOI: https://doi.org/10.1007/s00186-011-0361-6

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