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Locating and capacity planning for retailers of a new supply chain to compete on the plane

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Journal of the Operational Research Society

Abstract

This paper investigates the network design problem of a two-level supply chain (SC), which is applicable for industries such as automotive, fuel and tyre manufacturing. Models presented in this paper aim at locating retail facilities of an SC and identifying their required capacities in the presence of existing competing retailers of a rival SC. We consider feasible locating space of the retail facilities on the continuous plane with bounded constraints and static competition among the rivals of the markets with deterministic demands. The problem is used for both essential and luxury product cases; hence, we consider elastic and inelastic demands, both. The models discussed in this paper are non-linear and non-convex which are difficult to solve. We use interval branch-and-bound as optimization algorithm for small size single-retailer problems, but for large-scale, multi-retailer problems we need to have more efficient methods. Therefore, we apply a heuristic algorithm (H1), a simulated annealing (SA) algorithm, an interior point (IP) algorithm, a genetic algorithm (GA) and a pattern search algorithm for solving multi-retailer problem with elastic and inelastic demands. Computational results obtained from performing different solution approaches for both elastic and inelastic show that mostly IP, PS, and H1 methods outperform the other approaches. The computational results on a real-life case are also promising. Several extended mathematical models and an example of a typical case with details are presented in the appendices of the paper.

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Authors and Affiliations

  1. Kingston University, Surrey, UK

    Reza Zanjirani Farahani

  2. The University of Oklahoma, Norman, OK, USA

    Shabnam Rezapour

  3. California State University, Fullerton, Fullerton, CA, USA

    Tammy Drezner

  4. Amirkabir University of Technology, Tehran, Iran

    Ameneh Moharerhaye Esfahani

  5. KEDGE Business School, Bordeaux, France

    Mehdi Amiri-Aref

Authors
  1. Reza Zanjirani Farahani
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  2. Shabnam Rezapour
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  3. Tammy Drezner
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  4. Ameneh Moharerhaye Esfahani
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Appendices

Appendix A

A.1. Model extension

All models presented in this section are non-linear and non-convex with an objective function that is neither convex nor concave.

A.1.1. Extended competitive SC model with inelastic demand

Subject to:

A.1.2. Extended competitive SC model with elastic demand

Subject to:

Appendix B

B.1. Nature of the model

This is a typical example of a consumer product with three demand points between two competing SCs with only one wholesaler and one retailer for each. The locations of the wholesaler and the retailers for the existing SC are known but the new SC has identified the location of its wholesaler and is trying to determine the location and the capacity of the retailer in the new SC. The input data and parameters are shown in Table B1.

Table B1 Parameters for the example
Full size table

Regarding these parameters, we formulated the extended mathematical model as follows:

Subject to:

For this typical example in small scale, a sensitivity analysis on its parameters is graphically presented that shows the complexity of the problem. Figure B1(a) and (b) depict the objective function surface and constraints contours in two different views. Figure B2 represents objective function contours based on vertical and horizontal variables for a given number of facility capacity setting S (1)=5. Figure B3(a) depicts objective function surface and constraints contours in terms of variables X and S (1) (fixing Y=5) and Figure B3(b) illustrates objective function contours in the same situation.

Figure B1
figure 4

Objective function surface and constraints contours in terms of vertical and horizontal variables in two different views (a) and (b).

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Figure B2
figure 5

Objective function contours in terms of vertical and horizontal variables setting S (1)=5.

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Figure B3
figure 6

The objective function and constraints in terms of variables X and S (1): (a) the objective function surface and constraints contours; (b) objective function contours.

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Appendix C

C.1. A real-life case

The initial motivation of this research was from an oil products SC in the Middle East. Figure C1 illustrates this SC comprises four levels: (a) origins including refineries, coastal origins and ports, which are used for liquid fuel importation, (b) main national depots, (c) secondary domestic depots, and (d) customers or retailers such as fuel stations and large industries.

Figure C1
figure 7

The oil products SC network in the real-life case study.

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Based on districting pattern in the company, the country has been divided into a number of zones from the perspective of oil products supplying operations. Each zone itself has at least one depot in order to meet its demands. Tanker trucks are the modes used for oil products transportation in order to carry products from one depot to another or retailers. There are different road conditions in terms of surface, geographical condition and traffic affect transportation costs.

By the effect of the government devolution strategies, two levels of the SC will remain governmental and the other two will be privatized. Moreover, the government still keeps its previous distributers and retailers while inviting the other investors to enter to the market for competing to offer better service level to the end-consumers. Therefore, from now onwards, there will be competition in the retailers’ level for the new investor.

As explained, the oil product SC consists of four levels. The products do not necessarily get involved in all levels and it is even possible that they move between fixed entities within a level. Figure C1 illustrates the flow of the oil products between and within the levels. It is worthwhile to mention that procurement and secondary depots are almost similar and the only difference between them is in their capacity and level of equipment.

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Farahani, R., Rezapour, S., Drezner, T. et al. Locating and capacity planning for retailers of a new supply chain to compete on the plane. J Oper Res Soc 66, 1182–1205 (2015). https://doi.org/10.1057/jors.2014.84

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