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Design and Optimization of Multi Echelon Green Distribution Network

Abrar Ahmad, Riaz Ahmad, Mujtaba Agha School of Mechanical and Manufacturing Engineering (SMME)

National University of Sciences and Technology (NUST), H 12- Islamabad, Pakistan.

Abstract-According to World Bank report, in Pakistan about 360 Billion rupees are being wasted annually due to poor logistic operation. [1] This paper is a small effort for increasing the awareness of making the Green Distribution Network a competitive advantage in Small and medium Enterprises in Pakistan. Building efficiency in supply chain is combination of art and science. So, in this paper, quantitative and qualitative factors have been catered for designing a Green Distribution Network. This research work studies the impact of different factors on designing of Green Distribution Network and then formulates the mathematical model for determining the transportation schedule and number of distribution channels in a Green Distribution Network. we formulated our model in MS Excel 2007 using Optimization tool box. Since this research work deals with a practical problem, we have taken case of a FMCG company operating in Pakistan. Lastly, I suggested some areas for focus of research in this specific area. Keywords- Green Distribution Network, Supply Chain, Optimization, MILP, cost minimization, First Marketing warehouse

1. INTRODUCTION Supply Chain management means ordering and

sequencing of activities like Plan, Source, Make, Deliver and Return while coordinating and integrating Supplier’s Supplier to customer’s Customer.

In this paper we have analyzed Multistage Distribution network of a Fast Moving Consumer Goods (FMCG) company, having multiple plants, multiple First Marketing Warehouses, a large number of distributors and complex network of retailers.

To address the problem, a Mixed Integer linear program for solving the problem has been developed.

2. LITERATURE REVIEW Distribution and Logistics has become very vital

component in the supply chain. One of the very open and hot issue is the accurately determining the appropriate number of Distribution Channels, determined transshipment schedule, and transshipment cycle time, while keeping the inventory

holding cost, transportation cost and warehousing cost minimum.

A. Cost benefit analysis based approach for design of Distribution Network

Sunil Chopra [4] presented different configurations of distribution network for variety of customers and product characteristics. This paper highlighted factors influencing decision of configuration of distribution channels and at last presents a cost based model for determining number of distribution channels required for the optimum operation of company.

B. Mathematical Programming Based approach for design of Distribution Network

The alternative to the Cost benefit analysis is the mathematical modeling of distribution network. These mathematical models began to emerge in 1970s with limited computational capabilities.

Geoffrion and Graves’s Model 1974 [6] presented one of the earliest works on distribution problem. The problem was quite basic. It optimally determined the location of distribution centers between plants and customers. The problem is formulated as a single-period, multiproduct, mixed integer linear program. The model is successfully solved by Benders decomposition technique and implemented in a major food company.

C. H. Aikens [7] studied lots of mathematical models on facility location with or without capacity constraints, with single or multiple echelons, etc. It suggested that it is very essential to make multistage and multicommodity model.

V. Verter and C. Dincer [8] reviewed global supply chain problems, in which majority of the models were dedicated to the design of distribution system.

Geoffrion and Powers [9] reviewed the development of distribution network design over the 20 years before 1995. They highlighted a number of factors which contributed to towards the evolution of distribution networks, including the logistics system, optimization algorithms, and information technology etc.

I would like to thank Shell Pakistan Ltd. For Sponsoring my MSc at NUST Abrar.amad@gmai.com Ph: +92 03215475747

___________________________________ 978-1-4244-9698-3/11/$26.00 ©2011 IEEE

Vidal and Goetschalckx [10] reviewed about mathematical models on distribution network. Different Problem formulations, solution approaches, and computational results were compared. The authors concluded that very few models include stochastic parameters like customer service in their mathematical model.

Wesolowsky and Truscott [11] presented mathematical equations for the multi-period allocation and location problem with reconfiguration of facilities. He modeled a distribution system containing a group of facilities objecting to serve the demand at prescribed locations.

Williams [12] developed a dynamic programming model for simultaneously determining the production and distribution batches at each echelon within a supply chain system. The total cost was minimized over an infinite time period.

Another mathematical model was presented by Ishii et al. [13]. That aimed to calculate the base stock level and lead time associated with the lowest cost for a coordinated supply chain system in a limited time period.

P. Tsiakis, N. Shah, and C. C. Pantelides [14] modeled a mathematical program for deciding the number, location, and capacity of warehouses and distribution centers to be set up in a three tire distribution network while minimizing the total distribution network cost.

Brown et al [15], described a mathematical model for a system that used to deal with intricate problems involving sites selection, equipment selection, manufacturing and distribution of products. He focused on operational and strategic issues.

Pooley [16] formulated an MILP used by the Ault Foods Company to reconfigure their supply chain network. The objective of the model is to minimize the cost of a distribution network. This model is used to know the answers of where should the plants and distribution channels are located, how products will be serve to the customers.

Arntzen et al. [17] formulated an MILP for global supply chain network for determining location and numbers of first marketing warehouses, which customer will be serviced by which FMW with the objective function to minimize a total cost (including production, inventory and transportation costs) and number of operating days.

3. DATA ANALYSIS & PROBLEM FORMULATION Analysis of Supply Chain Cost:

TABLE 1

Fig. 1 Comparison of Distribution Cost with Production, Marketing and Sales Cost.

Fig. 2 Distribution Cost and Production Volume:

4. PROBLEM STATEMENT There are two Plants, twelve First Marketing warehouses,

and 225 Distributors. Supply capacity of each Plant is given and demand of each Distributor is given. Cost for transporting goods from each Plant to each FMW is given; Cost of transporting goods from each FMW to Distributors is given.

Fig. 3 Multi Echelon Distribution Network

A. Assumptions in the Model: Warehouses have flexible capacities. Total volume of

01,000,0002,000,0003,000,000

Year 2004

Year 2005

Year 2006

Year 2007

Year 2008

Year 2009

Marketing & Sales Cost Production Overheads

Distribution Cost

27 31 35 37 41 41

01020304050

0200,000400,000600,000800,000

Year

200

4

Year

200

5

Year

200

6

Year

200

7

Year

200

8

Year

200

9

Prod

uctio

n Vo

lum

e in

Bi

llion

Stic

ks

Dist

ribut

ion

Cost

in (,

000

Rs)

Distribution Cost Sticks

Sr. # Year Marketing & Sales Cost

Production Overheads

Distribution Cost

4 2007 1,198,765 1,932,237 579,028

5 2008 1,249,080 2,314,499 684,284

6 2009 1,503,693 2,433,653 742,321

products shipped to Distributors does not exceed the throughput capacity of the serving warehouse. Goods carrier is always available of required size. Transportation Cost is independent of TL or LTL. Warehouse can be engaged when required. There is no Miss match between Supply & Demand. Distribution Network holds true for a fixed period of time. i.e Freight Cost is constant during the operation period.

B. Parameter Definitions:

I= denotes the number of plants (i= 1,2….n) J= denotes the number of FMW (j= 1, 2, ..m) Xi,j = Quantity supplied from Plant to FMW Ci,j = Transportation Cost per stick per round from Plant to FMW.

C. Decision variables: Xi,j = Quantity supplied from Plant to FMW Objective Function:

JjIijii j

ji XCZ ������� ,,,

(1)

D. Constraints: ∑ �1, � = 18,526,912,000

� =�

� =0 (2) ∑ �2, � = 22, 644, 000,000

� =�

� =0 (3) ∑ � �, ��=�

�=1,� =1 <= 4117091000 (4) ∑ � �, ��=�

�=1,� =2 <= 2,881,964,000 (5)

∑ � �, ��=��=1,� =3 ≤ 2,881,964,000 (6)

∑ � �, ��=��=1,� =4 ≤ 2,470,255,000 (7)

∑ � �, ��=��=1,� =5 ≤ 2,058,546,000 (8)

∑ � �, ��=��=1,� =6 ≤ 2,470,255,000 (9)

∑ � �, ��=��=1,� =7 ≤ 3,293,673,000 (10)

∑ , �=�= ,�=� <= 2,058,546,000 (11)

∑ , �=�= ,�=� <= 5,352,218,000 (12)

∑ , �=�= ,�= � <= 5,763,927,000 (13)

∑ , �=�= ,�= <= 2,058,546,000 (14)

∑ , �=�= ,�= � <= 5,763,927,000 (15)

E. Non Negativity Constraints:

Xi,j >= 0 for all I and j

F. Transportation cost per stick per round

G. Input Data

5. RESULTS

Savings due to model: Primary Logistics Cost before MILP Model = 145,084,692.00 Primary Logistics cost calculated by model = 165,878,482.00 Reduction in cost = 165,878,482 -145,084,692 = 20,793,790 Percentage Reduction in Cost = 12 %

6. CONCLUSION A comprehensive mathematical model has been presented in this paper that helps in determining the number of distribution channels a company should have while minimizing the total distribution cost.

7. DIRECTIONS FOR FUTURE WORK In this paper we studied the earliest and most recent papers on distribution network or facility location design within the supply chain. We have concluded that though immense work has been done in this area but still some areas require extensive research. Stochastic models of distribution network are one of them. Very few papers addresses stochastic in multichannel distribution network design.

LIST OF REFERENCES [1] Supply Chain Association of Pakistan (SCAP).

https://groups.google.com/group/supply-chain-association-of-

pakistan/files?hl=en

[2] David Blanchard “Supply Chain Management Best Practices, Chapter 8”

[3] David Blanchard “Supply Chain Management Best Practices, Chapter 8”

[4] Sunil Chopra “Designing the Distribution Network in a Supply Chain”

[5] Donald B. Rosenfield, “Design and control of Multi Echelon Distribution

System” Working paper Alfred P. Sloan School of Management, M.I.T, USA.

[6] Geoffrion, A. M.; Graves, G. W. “Multicommodity Distribution System

Design by Benders Decomposition”. Manage. Sci. 1974, 20, 822 844.

[7] C. H. Aikens, “Facility location models for distribution planning,” Eur.J.

Oper. Res., vol. 22, pp. 263–279, 1985.

[8] V. Verter and C. Dincer, “An integrated evaluation of location, capacity

acquisition, and technology selection for designing global manufacturing

strategies,” Eur. J. Oper. Res., vol. 60, pp. 1–18, 1992.

[9] A. M. Geoffrion and R. F. Powers, “Twenty years of strategic distribution

system design: An evolutionary perspective,” Interfaces, vol. 25,pp. 105–128,

1995.

[10] C. J. Vidal and M. Goetschalckx, “Strategic production-distribution

models: A critical review with emphasis on global supply chain models,” Eur.

J. Oper. Res., vol. 98, pp. 1-18, 1997.

[11] Wesolowsky, G. O.; Truscott, W. G. “The Multiperiod Location

Allocation Problem with Relocation of Facilities”. Sci. 1975, 22,57 65.

[12] Williams, J. F. “A Hybrid Algorithm for Simultaneous Scheduling of

Production and Distribution in Multi-Echelon Structures”. Manage. Sci. 1983,

29,77 92.

[13] Ishii, K. Takahashi, K.; Muramatsu, R. Integrated Production, Inventory

and Distribution Systems. Int. J. Prod. Res. 1998, 26, 473 482.

[14] P. Tsiakis, N. Shah, and C. C. Pantelides “Design of Multi-echelon

Supply Chain Networks under Demand Uncertainty” Ind. Eng. Chem. Res.

2001, 40, 3585 3604

[15] Brown, G. G.; Graves, G. W.; Honczarenko, M. D. Design and Operation

of a Multicommodity Production/Distribution System using Primal Goal

Decomposition. Manage. Sci. 1987, 33, 1469 1480.

[16] John Pooley “Integrated Production and Distribution Facility Planning at Ault Foods” Interfaces Vol. 24, No. 4, July-August 1994, pp. 113-121 [17] Arntzen et al. Global Supply Chain Management at Digital Equipment

Corporation Interfaces.1995; 25: 69-93