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European J. Industrial Engineering, Vol. 7, No. 1, 2013

The application of linear programming by the General Electric Company to efficiently allocate routes to trucking companies Xu Yang Center for Transportation and Logistics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, E40-276 Cambridge, MA 02139, USA E-mail: [email protected]

Sunderesh S. Heragu* and Gerald W. Evans Department of Industrial Engineering, University of Louisville, Louisville, KY 40292, USA E-mail: [email protected] E-mail: [email protected] *Corresponding author

Mark D. Shirkness and Anna Coats General Electric Appliance and Lighting, GE Appliance Park, AP3-232, Louisville, KY 40225, USA E-mail: [email protected] E-mail: [email protected] Abstract: The appliance and lighting group of the General Electric (GE) Company allocates its shipping truckload to 17 different trucking companies over 701 different routes from one of its nine terminals. A sequence of several linear programming models was developed to help the management of the appliance and lighting division develop an optimal allocation. Two user-friendly interfaces were also developed to aid GE management in the use of one of the models. The tool is being used at GE and significant savings (approximately 15.5% of shipping costs) are possible with the optimal truckload allocation solution provided by the model. [Received 8 May 2010; Revised 2 June 2011; Accepted 15 June 2011] Keywords: truckload allocation; linear programming; LP; distribution; third party logistics; 3PLs. Reference to this paper should be made as follows: Yang, X., Heragu, S.S., Evans, G.W., Shirkness, M.D. and Coats, A. (2013) ‘The application of linear programming by the General Electric Company to efficiently allocate routes to trucking companies’, European J. Industrial Engineering, Vol. 7, No. 1, pp.38–54.

Copyright © 2013 Inderscience Enterprises Ltd.

The application of linear programming by the GE Company Biographical notes: Xu Yang is a Postdoctoral Research Associate at the MIT Center for Transportation and Logistics. Her research interests include distribution network design, optimisation and simulation, logistics, supply chain management, and operations management. Currently, she is also studying sustainability issues in supply chains, climate change policies and their impact on supply chain decision-making. She received her PhD and MS from the Department of Industrial Engineering at the University of Louisville. Sunderesh S. Heragu is a Professor and the Mary Lee and George F. Duthie Chair in Engineering Logistics in the Industrial Engineering department at the University of Louisville. He is also the Director of the Logistics and Distribution Institute (LoDI). Previously, he was a Professor of Decision Sciences and Engineering Systems at Rensselaer Polytechnic Institute. He has taught at State University of New York, Plattsburgh and held visiting appointments at State University of New York, Buffalo, Technical University of Eindhoven and University of Twente, in the Netherlands and IBM’s Thomas J. Watson Research Center in Yorktown Heights, NY. Gerald W. Evans is a Professor in the Department of Industrial Engineering at the University of Louisville. He has served as a NASA/ASEE Faculty Fellow at Langley Research Center and Kennedy Space Center. In addition, he has served as a Senior Research Engineer for General Motors Research Laboratories and as an Industrial Engineer for Rock Island Arsenal, Department of the Army. His teaching and research interests include multi-objective decision analysis, simulation modelling and analysis, optimisation, and project management. Mark D. Shirkness joined GE in 1986 and has held a variety of positions all in the appliances division. With experience in service, sales, marketing, and Six Sigma, he brings a very broad background to his current position as the General Manager – Distribution Services. Most notable of his assignments include running the aftermarket services group that handles post customer and consumer sales activities, leading the Home Depot account during the initial launch of appliances in the stores, and overseeing the home builder sales channel during the historic housing run-up. In his current role, he is responsible for all warehousing, transportation, logistics, and fulfilment for North American operations. Most recently, he assumed additional responsibilities for leading the company’s initiative to implement a new enterprise resource planning (ERP) system that will upgrade all of appliances major IT systems over the next five years. Anna Coats is currently the Sourcing/Compliance Manager for GE Appliances Local Delivery Network. During the development of this model, she was the Transportation Productivity Manager. She came to GE from the Ford Motor Company in 1998 and began her career at GE Appliances in refrigeration technology, including refrigeration product safety manager. She then was certified as a DMAIC Black Belt, and moved to the distribution function. She holds BS and MS degrees in Mechanical Engineering from the Missouri University of Science and Technology and the University of Michigan, respectively.

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Introduction

The General Electric Company (GE) is one of the largest companies in the world. GE is composed of many divisions, including the GE appliance and lighting (GEAL) division which supplies lighting and appliance products. This paper focuses on the transportation of appliance products by GEAL. Annual costs for the transportation of these products are on the order of nine million dollars. GEAL uses a number of trucking companies to fulfill these transportation requirements, one of which is a subsidiary of GE, with the rest being contract carriers. Due to GEAL’s competitive business environment, its managers realised that they needed to ship products to its customers in a more effective and efficient way. They also realised that they were not allocating the shipping truckload in an optimal fashion to the various trucking companies in the existing distribution network. In order to stay competitive in a dynamic market, a well-designed distribution network and an optimal allocation of the truckloads are necessary and critical to achieve this goal. This paper describes a project which involved the development of a sequence of transportation models to address this problem. In the next section of this paper, a brief literature review is provided, followed by a problem statement in Section 3. Sections 4 and 5 describe the data collected and the models developed for optimal truckload allocation. Section 6 details the model evolution. Model results are detailed in Section 7 and a software tool developed to allow GE personnel to easily interact with the models is described in Section 8. Results of the model implementation and additional notes are provided in Sections 9 and 10.

2

Literature review

Physical distribution systems perform a number of important functions over a complex network including warehousing, transportation, and inventory control. Research on distribution problems includes the study of facility location, warehousing, transportation and inventory (Ambrosino and Scutella, 2005). Ahn and Kaminsky (2005) point out that in many companies, the costs of transportation and distribution, as well as inventory costs are a large portion of the total product costs. Parthanadee and Logendran (2006) mention that transportation cost is typically the highest single expense in a logistics system, which is usually greater than warehousing cost, inventory cost and order processing cost. A large number of researchers have studied different types of distribution problems. Sheu (2006) describes the design of a comprehensive distribution system framework, which includes order processing, customer order grouping and ranking, and container and vehicle assignment for dynamic logistics in a multiple-resource allocation environment. Another distribution model to minimise the total costs of manufacturing and transportation is developed by Wang et al. (2004) and they apply the just-in-time concept in the model to supply products in time and under limited supply capacity. Campbell (1993) considers distribution with transshipment, which causes inventory cost to increase, but reduces transportation cost due to the economies of scale. Ko et al. (2006) propose a hybrid optimisation approach to design a distribution network considering the dynamics of customers and service time at each warehouse. Van Roy (1989) applies mathematical

The application of linear programming by the GE Company

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programming to solve a complex multi-level production and distribution network optimisation problem. Third party logistics providers (3PLs) are external logistics service providers offering single or multiple logistics activities to their customers. From the provider’s point of view, their business covers a great number of relationships involving everything from simple logistical activities to advanced logistical solutions; from the customer’s point of view, the degree of outsourcing varies and the outsourced logistics activities differ greatly. Outsourcing business to 3PLs is becoming a widespread practice in industry, because more companies are focusing their efforts on their core competencies which are critical to survival (Skjoett-Larsen, 2000). 3PLs play an important role in the entire process of logistics, especially in providing services for warehousing and transportation, since their customers expect them to improve lead time, fill rate, inventory and other performance measures (Ko et al., 2006). Undoubtedly, 3PLs can manage warehouses, as well as pick-up and deliver customer orders; however, today the business of 3PLs is so much more than that. During the last 20 years, 3PLs have changed dramatically (Stefansson, 2006). In particular, in recent years, 3PLs have expanded their service content, which involves more complex activities and significantly more customer service than before. Companies large and small are turning to 3PLs. The research of Leahy et al. (1995) shows that the cooperation with 3PLs can help manufacturers reduce transportation and administrative costs, focus on core competencies, improve productivity and upgrade communication capabilities. Moreover, the benefits of building business collaboration relationships with 3PLs also result in an improvement in service levels and operation efficiencies (Skjoett-Larsen, 2000). GEAL contracts with a number of 3PLs, specifically trucking companies, to perform its transportation function. Our paper basically determines the specific trucking companies that must be assigned to specific routes, as described in the next section.

3

Problem statement

GEAL manufactures and ships numerous industrial and consumer products including appliance and lighting products. The company has a very large distribution system that includes nine terminals within the USA. The Louisville terminal interfaces with nine origin warehouses, 43 plants for appliance products, seven distribution centres, and 22 plants for lighting products. The entire distribution process is based on a complex transportation network. For years, GEAL has used its wholly owned subsidiary (which is referred to as trucking company 16) and 3PLs to transport products within the USA. For appliance products, GEAL uses 17 trucking companies. GEAL has separate contracts with each trucking company. Each company has different contractual parameters for price, volume, and other service factors. It should be noted that the number of plants, distribution centres, trucking companies and routes are based on the 2005 data provided to us by GE and do not reflect the current numbers of such facilities. Due to GEAL’s ongoing desire to find ways to reduce transportation costs, the company had to deal with logistical problems associated with the trucking of consumer products between manufacturing plants, warehouses and customers. Managers in the

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company realised that they were not allocating the capacity in an optimal fashion to the various trucking companies, including GE’s subsidiary trucking company. They have been using simple, rule of thumb and spreadsheet based tools for allocating routes and volume to each trucking company. In order to better use the total trucking capacity and to minimise the total transportation cost, they wanted to reengineer the entire distribution network structure. After several internal meetings and discussions, GEAL entered into a research agreement with the University of Louisville (UofL) to help solve their distribution problem based on quantitative analysis. Two professors, a graduate research assistant, and two GEAL personnel formed a research group to solve its existing problems.

4

Initial data

Although GEAL ships other industrial and consumer products in addition to appliance and lighting, this project and paper only focuses on the shipment of appliances. Our work could be easily extended to consider other products shipped by GEAL. Invoice level data is available for the 12 months in 2005. Each invoice corresponds to a shipment, and contains its point of origin, destination, distance, carrier used, cost per trip and other information. See Table 1 for definition of terms and example data. Table 1

Definition of terms in appliance products data

Appliance data

Definition example data

Fiscal month

Fiscal calendar month

200512

Fiscal wk

Fiscal calendar week

200549

Bill date

Truck loaded @ R100 on this date

Orig whse

Origin warehouse – R100 Louisville KY

Final city

City of last stop on load

Monroe

Final St.

State of last stop on load

OH

Final Zip

Zip code of last stop on load

Ship MS #

GE shipment number

SCAC

Trucking company SCAC – see deployment origin_SCAC

MMCG

Frt $$

Total freight cost: base cost + stop charges + assessorial + fuel

311

Fuel $$

Total fuel cost

14

Route miles

Mileage travelled for load

135

Route pts.

Total points for load – max points 126

119

Stops

Total stops on load – 1 stop = stop at final only, 2 stops = 1 stop and final, etc.

1

12/5/05 1:35 AM R100

45050 15RI016904

The 17 trucking companies including one GE owned trucking company (#16) serve 701 routes that come under the purview of the Louisville terminal of GEAL. From this initial data, average distance, number of trips, and average cost per trip were computed for each route; in addition, cost per mile was computed for each trucking company.

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The basic set up for the start of the modelling process involved a hypothetical situation: suppose that for the 12-month period associated with the data in the previous section, the shipping load could have been reallocated, what would be the best way to reallocate this load among the trucking companies.

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Initial model development

Although it was clear that the objective was to minimise total transportation costs, the constraints to be included in our linear programming (LP) model were not well specified. In an attempt to elicit these constraints and also to provide a basis for further discussion with GEAL personnel, we developed four LP models. These models are denoted as Models 1 through 4 in the Appendix. Each of the four models had the same objective function (minimisation of total transportation cost) and the same set of decision variables (total number of trips to be made by each of the 17 trucking companies on each of the 701 routes). The models differed in their constraints. Model 1 restricts the total number of trips on each route equal to its current total number of trips. Other constraints include allowing trucking companies to only serve the routes they currently serve; if one trucking company can serve a route, the lower bound of the number of trips on this route is one, and the upper bound is equal to the current total number of trips made on that route minus the number of trucking companies currently providing service on that route plus one. The latter constraint is to ensure each trucking company currently serving a route continues to make at least one trip. If a trucking company serves more than one route, we use the average cost for that truck-route combination in our model. If a truck is not allowed to serve a specific route, we enforce this restriction by providing a large cost to this route. Model 2 is a slightly modified version of Model 1. The only change is to not require a trucking company currently serving a route to make at least one trip on that route. In other words, the lower bound on number of trips for a trucking company currently serving a route is zero. Models 3 and 4 were developed based on the calculation of cost per mile for each trucking company and average distance for each route. Both use cost per mile and average distance values in the objective function, which once again, minimises the total transportation cost. Cost per mile is calculated by adding all the costs charged on all routes for each trucking company, and then dividing that by the total number of miles this trucking company has travelled on all routes. Average distance is the sample mean value for each route based on GEAL data. Model 3 maintains the total number of trips on each route to its current value. It also limits the load allocated to each trucking company to its available trucking capacity. Model 4 is similar to Model 3, but excludes the trucking capacity constraint.

6

Evolution of models

The initial analysis via the four models indicated that significant potential savings could be achieved by GEAL. This increased the interest level of GEAL personnel in the project.

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A presentation of results to GEAL and further discussion revealed that some real-life assumptions had not been considered. These were added, resulting in the development of four more models. Adding constraints that restricted each trucking company to only serve specific routes in specific states to Model 3 resulted in Model 3a. Similarly, adding these constraints to Model 4 resulted in Model 4a. A presentation of the results and ensuing discussion revealed that much of the short-haul trucking volumes were allocated to long-haul trucking companies. This was because the per mile long haul transportation costs tended to be lower than those for short haul transportation. These long-haul trucking companies currently were not serving any short-haul routes, and by default the model used the same per-mile rate even for short-haul. To rectify this, the GEAL personnel on the project team proposed segmenting costs based on the number of miles for each trucking company on each route. This led to Models 5 and 5a. Model 5 also had these additional constraints. The total number of trips on each route must be equal to its current total number of trips. Each trucking company has a finite trucking capacity. Trucking companies can only serve the routes they are currently serving. For Model 5, the cost for each trucking company on each route was calculated via two steps: Step 1

For trucking company j, first segment the routes based on distance travelled into four categories: 0–100 miles, 100–300 miles, 300–500 miles and above 500 miles separately. Then for each truck-route combination within each segment, divide the total cost charged on all the routes by the number of miles covered by that trucking company to get the cost per mile for each truck-route combination in each segment.

Step 2

For those routes i currently served by trucking company j, the currently available cost values were used; for those routes i currently not served by company j, the corresponding cost values were determined by multiplying the per mile cost values (calculated in Step 1) with the distance for route i. If a trucking company is prohibited from serving a specific route, the cost is set to an arbitrarily large number.

Model 5a was exactly like Model 5, but the trucking capacity constraint for the subsidiary company was removed. This was suggested by the GEAL project team personnel to see whether or not the trucking capacity of its subsidiary company must be increased by purchasing additional trucks and hiring additional drivers.

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Model results

The software used to solve these eight models was LINGO 9.0. Because the amount of input data for some of the models was large, EXCEL was used to store all of the necessary data and let LINGO read these data directly. Most of the models could be solved rather quickly. Similarly, due to the large amount of output data for each new solution, EXCEL was used to store the output.

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The application of linear programming by the GE Company

Appliance products data was used for these eight models. All the new solutions generated by solving these linear programming models resulted in a significant improvement as compared to the current solution (see Table 2). It should be noted that these results are for the 2005 data we obtained from GE. The total cost of the current solution was $9,167,791. Each model produced solutions that reduced this total cost further. Model 4 produced the largest cost saving, which was $3,739,095 (40.79% reduction), followed by Model 3, Model 3a (or Model 4a), Model 5a, Model 5, Model 2 and Model 1. Table 2

Total cost of current solution and eight models Current

Total cost ($)

Model 1

Model 2

Model 3

Model 3a

Model 4

Model 4a

Model 5

Model 5a

9,167,791 8,773,354 8,488,123 6,169,151 6,335,805 5,428,696 6,335,805 7,744,920 7,738,163

Save ($)

394,437

Change (%)

4.3

679,668 2,998,640 2,831,986 3,739,095 2,831,986 1,422,871 1,429,628 7.41

32.71

30.89

40.79

30.89

15.52

15.59

Note: Total cost here means the overall freight expense including base cost, stop charges, assessments and fuel.

Based on the known information, Model 5 and Model 5a have the most realistic constraints; hence the results for these two models are more reasonable. Model 5 reduced the total cost by $1,422,871 and made a 15.52% improvement. Using Model 5a, GEAL could save $1,429,628, which is a 15.59% reduction over their current expenditures. The total cost of current solution and eight models are given in Table 2 and Figure 1. Figure 1 Comparison of total cost for current solution and eight models (see online version for colours)

Currently, Company 16 has the largest number of trips on all routes it served, with a value of 3,254 trips. After running each of the eight models, new solutions regarding number of trips for each trucking company for each model were obtained (Table 3). Also, the comparison between the current costs on all routes for each trucking company and that given by the eight models is provided in Table 4.

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For Company 16, the volume on all routes it served was increased from 3,254 to 3,300 for Model 5 and to 4,195 for Model 5a. In other words, Company 16 not only keeps its business, but also increases its overall business by 1.41% and 28.92% respectively for Models 5 and 5a. The increased business to Company 16 suggests that GEAL can decrease trucking costs by using the new solutions given by the linear programming models. Its subsidiary can improve its distribution activity by handling more trucking volume than current. Based on the current overall number of trips in Table 3, Companies 12 and 15 are 16’s two largest competitors. Company 12 has total 2,549 trips on all routes and Company 15 has 2,376. The results of Model 5 and Model 5a show that Company 12 loses its business to 496 trips and 491 trips respectively, which means that it cannot be competitive with Company 16 any longer. But for Company 15, its business increases to 2,700 trips for both Model 5 and Model 5a. This improvement for Model 5 and Model 5a is 13.64% as compared with current solution. At the same time, the improvement for Company 16 based on Model 5 and Model 5a are 1.41% and 28.92%. Although Company 16 does not have a greater business improvement than Company 15 on Model 5, it does have greater improvement on Model 5a. However, based on Model as 5 and 5a, Company 11 makes 3,359 trips and 2,916 trips, respectively, which indicates that it would become the main competitor for Company 16. Especially for Model 5, Company 11 even has larger number of total trips on all routes than Company 16. In order to reach the goal that minimises the total cost among all trucking companies, Company 16 has to give up some business to some companies, e.g., Company 11. This strategy of outsourcing more business to 3PLs helps reduce the overall shipping cost. Table 3

Number of trips for 17 trucking companies – current solution and results from eight models Current solution

Model 1

Model 2

Model 3

Model 3a

Model 4

Model 4a

Model 5

Model 5a

1

5

1

-

-

-

-

-

-

-

2

521

415

391

-

-

-

-

158

158

3

13

50

61

-

-

-

-

135

135

4

44

27

21

-

-

-

-

19

19

5

837

413

383

-

-

-

-

117

61

6

17

234

252

11,598

12,424

-

12,424

17

17

7

501

409

385

-

-

-

-

656

289

8

72

72

72

900

74

12,498

74

74

74

9

9

2

-

-

-

-

-

-

-

10

46

769

784

-

-

-

-

50

50

11

1,723

2,607

2,626

-

-

-

-

3,359

2,916

12

2,549

1,692

1,587

-

-

-

-

496

491

13

165

384

402

-

-

-

-

1,324

1,314

14

338

347

341

-

-

-

-

-

-

15

2,376

1,301

1,341

-

-

-

-

2,700

2,700

16

3,254

3,753

3,834

-

-

-

-

3,300

4,195

17

28

22

18

-

-

-

-

93

79

10,245

865,296

187,515

21,793

28,493

5

6

7

8

9

10

1,929,080

22,441

15

16

17

9,167,791

1,309,000

14

Total

177,839

192,845

13

558,733

648,805

4

2,590,953

66,523

3

12

21,067

2

11

3,424

533,731

1

8,773,354

16,220

2,066,286

799,239

155,834

356,009

1,973,534

1,125,875

386,700

12,319

187,515

537,784

138,717

287,960

73,449

78,994

566,913

9999

Model 1

8,488,123

11,938

2,028,519

800,658

141,593

315,307

1,895,192

1,091,594

392,706

0

187,515

493,785

149,357

262,191

29,962

96,337

591,460

0

Model 2

6,169,150

0

0

0

0

0

0

0

0

0

1,154,255

0

5,014,894

0

0

0

0

0

Model 3

6,335,805

0

0

0

0

0

0

0

0

0

192,203

0

6,143,602

0

0

0

0

0

Model 3a

5,428,696

0

0

0

0

0

0

0

0

0

5,428,696

0

0

0

0

0

0

0

Model 4

6,335,805

0

0

0

0

0

0

0

0

0

192,203

0

6,143,602

0

0

0

0

0

Model 4a

7,744,920

52,172

1,499,116

1,720,547

0

535,798

815,650

1,849,219

16,666

0

192,275

536,259

12,082

49,516

24,025

203,426

238,161

0

Model 5

7,738,163

44,974

2,030,710

1,721,353

0

528,101

812,113

1,638,731

16,666

0

192,275

243,045

12,082

32,494

24,025

203,426

238,161

0

Model 5a

Table 4

Current

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Cost for each trucking company on all routes

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Based on Model 5a, Company 16 can increase its business by $101,630 over a 12-month period. But for Model 5, although Company 16 can serve more trips, the total cost for it decreased by $429,964. Companies 11 and 15, the two largest competitors of Company 16, have increased their total business. Company 11 increases total cost from $558,733 to $1,849,219 for Model 5 and to $1,638,732 for Model 5a. The related percentage improvements are 230% and 193%. For Company 15, its improvements are $411,548 (31.4%) for Model 5 and $412,353 (31.5%) for Model 5a. We emphasise again that all of the above results are based on 2005 data.

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Tools for viewing data in an interactive fashion

Use of the eight linear programming models can result in large potential savings to GEAL. In order to make these models usable by company analysts not trained in LINGO, we developed a user friendly interface as well as an EXCEL file tool. Both tools are useful for making decisions on trucking strategies based on the optimisation solution given by eight different models for appliance products. The interface programme is developed using Microsoft Visual and is based on three query conditions. The first one is to query by the name of one trucking company; the second one is to query by the final city in a route; and the third one is to query by one state. The results of the three queries contain: the information of routes (final city and final state), trucking companies servicing these routes and the number of trips made for the current solution and those produced by the eight models. The greatest benefit of this interface programme is that people in GEAL need not look at all the data in separate spreadsheets at once. With the help of this tool, they can check the current allocation or those suggested by each of the eight models. In addition, they can compare their current solution with any model(s) solution(s) or one model solution with another model solution. Using these three query conditions, they can search the relative information much easier and faster. Besides this interface programme, an EXCEL file based tool, especially for results of Models 5 and 5a, was developed at the specific request of GEAL. GEAL personnel making trucking capacity allocation decisions do not have a background in operations research and LP modelling. They are comfortable using spreadsheets and wanted a spreadsheet based optimisation tool. The spreadsheet we developed has 17 columns corresponding to the 17 trucking companies and 2,804 rows corresponding to the 701 routes. It shows the current solution, Model 5 solution, Model 5a solution and the solution entered by GE personnel. All the ‘current solution’ rows show the number of trips made by each trucking company according to the decisions made by GEAL personnel. All Model 5 and Model 5a rows have the optimal solutions produced by solving Models 5 and 5a, respectively. There are also blank cells that initially contain all 0’s, which are in ‘new’ rows. Again, at the suggestion of the GEAL team personnel, this feature was added so that users can experiment with their own solution as given by the number of trips for each trucking company on each route. For the new solution provided by the users, this tool automatically calculates related summary information such as overall total cost, cost for each route, number of trips and cost for each trucking company.

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GEAL has begun using this EXCEL file tool to make trucking decisions, i.e., to assign the volume for each trucking company route by route. Using our tool, they compare the current solution, the solution of Model 5 and Model 5a at the same time. GEAL personnel may want to make minor alterations to the optimal solution given by the integer programming models by adding some real-world considerations. After the company analysts do this, the related summary is provided by this tool in the new solution row. They can then readjust their decisions based on the summary information. Because of the development of these two tools, people from GEAL feel comfortable in using them for making decision on a regular (monthly) basis.

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Preliminary results of the implementation

After the development of the eight models and the two tools and after implementing an electronic bidding system for its vendors (trucking companies), GEAL began to implement the research results into its operations. Initially, they only applied the models on specific routes rather than all the routes. They indicated that during the initial runs of the model they could obtain about $100,000 of savings for specific routes. They now use the tool to generate solutions for each month and based on the savings identified by the optimisation model, they calibrate their truckload allocation decisions for the following month. Some comments from the company include: •

The tool has been very helpful in creating a holistic view for the transportation managers to manage their carriers.

•

It provides a quick and easy way to see interaction effects of decisions and really helps to comb through opportunities that otherwise we would have missed.

•

While in the beginning we may have thought that the tool could provide a ‘one time’ benefit, we now see that the tool needs to be constantly worked as input variables change.

•

To this end we have made utilising the tool a part of the standard monthly operating procedures for the transportation managers.

10 Final discussion We have developed eight transportation models to help GEAL reallocate its truckload in an optimal fashion. Each of the models has the same objective function – to minimise the total shipping cost – but with a different set of constraints. These models provided a mechanism to communicate with GE, thereby allowing the university personnel on the project team to arrive at a realistic model for planning purposes. The most realistic model (Model 5) indicates that GEAL can save 15.52% of its shipping cost. Two graphical user interfaces to assist the management in applying the optimisation models in their operations were also developed. The feedback from the company showed that over $100,000 of savings for specific routes would be obtained with initial runs of the models.

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Some quantitative improvements on the routes allocation problem at GEAL have been achieved, but there are still several directions we can explore to advance our work. First, the optimisation models can be extended by including more realistic factors/constraints, such as the limited number of drivers of each carrier, backhaul problem and so on. Also, we may revaluate the way (data available/retrograde method) we developed the models and enrich the content of the models and the insights they deliver. Another aspect we can explore is to look at the cost structure for each carrier and the distance on each route. In the existing models, we simply use the average cost and distance, which can be substituted by more sophisticated formulations. Last but not least, currently we only consider one objective to minimise the total shipping cost. In a further study, we could include other critical objectives in the supply chain, such as increasing the service quality of the carriers.

Acknowledgements Work presented in this paper was supported in part by a research contract with GE Corporation and is based on 2005 data. We thank Kenny Pritchett for his assistance during the data collection and modelling phases of this project.

References Ahn, H. and Kaminsky, P. (2005) ‘Production and distribution policy in a two-stage stochastic push-pull supply chain’, IIE Transactions, Vol. 37, No. 7, pp.609–621. Ambrosino, D. and Scutella, M.G. (2005) ‘Distribution network design: new problems and related models’, European Journal of Operational Research, Vol. 165, No. 3, pp.610–624. Campbell, J.F. (1993) ‘One-to-many distribution with transshipments: an analytic model’, Transportation Science, Vol. 27, No. 4, pp.330–340. Ko, H.J., Ko, C.S. and Kim, T. (2006) ‘A hybrid optimization/simulation approach for a distribution network design of 3PLS’, Computers and Industrial Engineering, Vol. 50, No. 4, pp.440–449. Leahy, S.E., Murphy, P.R. and Poist, R.F. (1995) ‘Determinants of successful logistical relationships: a third-party provider perspective’, Transportation Journal, Vol. 35. No. 2, pp.5–13. Parthanadee, P. and Logendran, R. (2006) ‘Periodic product distribution from multi-depots under limited supplies’, IIE Transactions, Vol. 38, No. 11, pp.1009–1026. Sheu, J. (2006) ‘A novel dynamic resource allocation model for demand-responsive city logistics distribution operations’, Transportation Research, Vol. 42, No. 6, pp.445–472. Skjoett-Larsen, T. (2000) ‘Third party logistics–from an interorganizational point of view’, International Journal of Physical Distribution and Logistics Management, Vol. 30, No. 1, pp.112–127. Stefansson, G. (2006) ‘Collaborative logistics management and the role of third-party service providers’, International Journal of Physical Distribution and Logistics Management, Vol. 36, No. 2, pp.76–92. Van Roy, T.J. (1989) ‘Multi-level production and distribution planning with transportation fleet optimization’, Management Science, Vol. 35, No. 12, pp.1443–1453. Wang, W., Fung, R.K. and Chai, Y. (2004) ‘Approach of just-in-time distribution requirements planning for supply chain management’, International Journal of Production Economics, Vol. 91, No. 2, pp.101–107.

The application of linear programming by the GE Company

Appendix Parameters R

total number of routes

M

total number of trucking companies

cij

cost for making a trip by trucking company j on route i

Ni

number of trips made on route i over the data period

Ti

set of trucking companies currently serving route i

CARD(Ti)

the number of members in set

Si

set of trucking companies allowed to serve route i

cj

cost per mile for trucking company j

di

distance on route i

Kj

maximum number of trips made by trucking company j

Pj

total number of miles currently served by trucking company j

Decision variable xij

number of trips to be made by trucking company j on route i

Model 1 Minimise R

Z1 =

∑∑c x

ij ij

i =1 j∈Si

Subject to

∑x

ij

= Ni

i = 1, 2,..., R

j∈Si

1 ≤ xij ≤ Ni − CARD(Ti ) + 1 xij ≥ 0

i = 1, 2,..., R

Model 2 Minimise R

Z2 =

∑∑c x

ij ij

i =1 j∈Si

i = 1, 2,..., R j ∈ Si

j ∈ Si

51

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Subject to

∑x

= Ni

ij

i = 1, 2,..., R

j∈Si

xij ≥ 0

i = 1, 2,..., R

j ∈ Si

Model 3 Minimise R

M

∑∑ c d x

Z3 =

j i ij

i =1 j =1

Subject to M

∑x

= Ni

ij

i = 1, 2,..., R

j =1 R

∑x

≤ Kj

ij

j = 1, 2,..., M

i =1

xij ≥ 0

i = 1, 2,..., R

j = 1, 2,..., M

Model 3a Minimise R

Z 3a =

M

∑∑ c d x

j i ij

i =1 j =1

Subject to M

∑x

ij

= Ni

i = 1, 2,..., R

j =1 R

∑x

ij

≤ Kj

j = 1, 2,..., M

i =1

xij ≥ 0

i = 1, 2,..., R

j ∈ Si

xij = 0

i = 1, 2,..., R

j ∉ Si

xij ≥ 0

i = 1, 2,..., R

j = 1, 2,..., M

The application of linear programming by the GE Company

Model 4 Minimise R

Z4 =

M

∑∑ c d x

j i ij

i =1 j =1

Subject to M

∑x

= Ni

ij

i = 1, 2,..., R

j =1

xij ≥ 0

i = 1, 2,..., R

j = 1, 2,..., M

Model 4a Minimise R

Z 4a =

M

∑∑ c d x

j i ij

i =1 j =1

Subject to M

∑x

= Ni

ij

i = 1, 2,..., R

j =1

xij ≥ 0

i = 1, 2,..., R

j ∈ Si

xij = 0

i = 1, 2,..., R

j ∉ Si

xij ≥ 0

i = 1, 2,..., R

j = 1, 2,..., M

Model 5 Minimise R

Z5 =

M

∑∑ c x

ij ij

i =1 j =1

Subject to

53

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X. Yang et al. M

∑x

= Ni

ij

i = 1, 2,..., R

j =1 R

∑x

≤ Kj

ij

j = 1, 2,..., M

i =1

xij ≥ 0

i = 1, 2,..., R

j ∈ Si

xij = 0

i = 1, 2,..., R

j ∉ Si

xij ≥ 0

i = 1, 2,..., R

j = 1, 2,..., M

Model 5a Minimise R

Z5a =

M

∑∑ c x

ij ij

i =1 j =1

Subject to M

∑x

ij

= Ni

i = 1, 2,..., R

j =1 R

∑x

ij

≤ K j (This constraint does not apply to GE's subsidiary)

i =1

xij ≥ 0

i = 1, 2,..., R

j ∈ Si

xij = 0

i = 1, 2,..., R

j ∉ Si

xij ≥ 0

i = 1, 2,..., R

j = 1, 2,..., M

j = 1, 2,..., M