COMPANY REORGANIZE - WAREHOUSE LOCATION DETERMINATION · PDF fileNational Seminars of Board of...

National Seminars of Board of Industrial Engineering Indonesia (BKSTI), Yogyakarta, 2000

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COMPANY REORGANIZE - WAREHOUSE LOCATION

DETERMINATION TO MINIMIZING COST OF DISTRIBUTION

AND LOGISTICS

RZ Abdul Aziz, Heri Setiawan, Ch Desi K Industrial Engineering Department MUSI School of Engineering, Palembang, Indonesia

Abstract

Distribution is a complex problem because it involves many factories. One of the important factors in

distribution problems is how to reach the costumer with the possible lowest distribution cost,

therefore, in the effort of company reorganization, the determination of warehouse location has to be

carried out as good as possible. On this paper a model to determine the warehouse location and its

coverage is proposed. The criterion used minimization cost of distribution and logistics which consist

of distribution cost, warehouse’s fixed cost, and operating cost of warehouse. The optimal solution

was solved with heuristic approach

Key word: warehouse, distribution, heuristic

1 INTRODUCTION The problem of determining the location of the warehouse is one of the most important problem in a system of

industry. Hence because decisions about warehouse location will affect the cost of distribution and logistics.

Distribution and logistics is one of the very large cost components in a modern industrial system. A good

decision regarding the location of the warehouse will be able to improve efficiency and minimize distribution

and a logistics cost which means it will increase corporate profits. Inappropriate of warehouse locations will

cause increased costs for distribution and logistics.

So far the company established warehouses located adjacent to the costumer in order to minimize the cost of

distribution and logistics, but because the economic crisis led to a reduced number of costumers (coverage

warehouse) so that the company needs to restructure. One effort in this reorganize is make a decision to choose

which warehouse will be retained or closed.

Many formulas (model) of linear programming that can be used to solve the problems of distribution. One such

model is the transportation model (Lieberman, 1991). But this model only considers the cost of distribution, so

the result of decision of warehouse locations only based on distribution costs.

This paper developed a model that attempted to solve the problem of determining the location of the warehouse

by using a heuristic approach.

2 RESEARCHOBJECTIVES The purpose of this study is to provide a good model for companies in order to reorganize the sustainability of

existing warehouse. Selection of the appropriate warehouse for retained will be able to minimize the cost of the

existing distribution and logistics, as well as to serve costumer better.

3 METHODOLOGY Problem-solving frame work of warehouse site selection and determination of costumer coverage which is based

on cost minimization of distribution and logistics are given in figure 1.


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Figure 1. Solving Problems Schematics

3.1 Model Assumption

This model has assumption as below:

1. Number of items to be distributed from the warehouse to the costumer in this model is assumed to be

constant (fixed)

2. Product to be sent to warehouse is single type.

3.2 Model Formulation

Model formulation that will minimize costs which is associated with the problem of warehouse site selection

and determination of a collection of costumer coverage, consist of three cost elements i.e.:

Distribution costs.

Fixed cost of operation warehouse.

Cost of operation warehouse per amount of products.

Those cost are formulated in form of a mathematical model below:

Minimize the total cost:

MinTC = ∑ ∑ ∑ (∑

)

∑

(1)

Subject to

The capacity of the warehouse i (i.e. number of items allocated from warehouse i

does not exceed warehouse

i capacity)

∑ j = 1, 2, 3, …, n

Determination of data requirements

Warehouse capacity (fixed costs +

operating costsperpernumber

ofitems)

Determination of distribution costs (transport costs)

Determination of minimum total cost

(distribution cost + fixed cost of warehouse +

warehouse per number of items)

Solve the problem

Identify the problem and solution purposes


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The quantity of costumer j (i.e. number of items allocated to the costumer j equal to the costumer inquiry j)

∑ i = 1, 2, 3, …, m

Fixed cost of operation warehouse

{

Model parameter

Tij distribution cost from warehouse i to costumer j

Xij the amount of products at customer j served by warehouse i

Si maximum capacity for warehouse i

TAij the amount of products at customer j

O the cost of operating warehouse

FOi The fixed cost of operation warehouse i

Zi change in fixed costs,

{

Steps that will be taken to obtain the optimal solution based on the above characteristics are as follows:

1. All warehouses are taken into account for seeking possible solutions then done calculation total costs

2. Perform reduction in the number of warehouses in N number of combination, and then calculate the total

cost (distribution costs, fixed cost of operation warehouse and cost of operating warehouse per amount of

products) of each N combination

3. Compare all the total cost obtained, and hence minimum total cost is found.

From equation (1) in case changes in fixed costs is binary (0.1) where this expense present if warehouse is used

and zero if the warehouse is not used, where as the cost of warehouse operations per number of items is constant,

thus by joining segment 1 and 2 of equation (1) resulting equation 2

Min TC = ∑ ∑

∑

(2)

Subject to

The capacity of the warehouse i (i.e. number of items allocated from warehouse i

does not exceed

warehouse i capacity)

∑ j = 1, 2, 3, …, n

The quantity of costumer j (i.e. number of items allocated to the costumer j equal to the costumer inquiry j)

∑ i = 1, 2, 3, …, m

Fixed cost of operation warehouse.

{

3.3 Distribution Cost

Distribution cost can be identified as follows:

1. Distance between warehouse to costumer

2. Cost of sending product per kilometer

Thus the cost of distributing the amount of product from the warehouse to the costumer is:

(3)

Model parameter


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the cost of distribution between warehouse i to costumer j

the cost of sending product per kilometer

dij distance between warehouse i to costumer j

So the cost of distribution is a function of the cost of sending product related to the distance. Variable of

distance used in this paper is based on the results of research.

3.4 The Cost of Operating Warehouse

The Cost of Operating Warehouse is the costs of goods maintenance in warehouse and other cost. cost for

operation warehouse consists of two parts, namely:

Fixed cost i.e. cost of conducting the maintenance and operation of physical facilities.

Cost for operation warehouse per amount of product i.e. increased linearly with the amount of product

Step Calculations of total costs (distribution costs, fixed cost of operating warehouse, and cost of

operating warehouse per amount of products)

Heuristic methods are used to optimize the number of warehouse locations and the coverage by working steps as

follows:

Step1 Selection of the first warehouse:

The distribution of product at each warehouses is done by using a transport model, assumed all the

warehouse sustained, then calculate

BT0 = ∑ ∑ ∑ (∑

)

∑

Go to step 2

Step2 Examination of the capacity of warehouse

If the total number of warehouse capacities minus the sum of all goods = ψ, and ψ>Min(warehouse), go

to step3; if not, proceed to step 5.

Step3 Reduction in the number of warehouse

Perform reduction in the number of the warehouse by performing a combination of reduction in the

warehouse, on the condition of the entire warehouse capacity greater than or equal to the sum of all

goods. then count

BT(k)n =∑ ∑ ∑ (∑

)

∑

For each combination of reduction in the warehouse, go to step 4.

Step 4 Examination of the total cost

BTk = Min (BT(k)n)

BTk > BTk-1, Go to step 5. If not, repeat step 3

Step 5 Assignment

Total cost (BTk-1) is the minimum total cost and will be known to the warehouse that is used and the

amount of coverage to meet the needs of consumers j, then the optimization has been completed and the

problem has been solved.

4 MODEL APLICATION Distribution and logistic model formulated above then applied to a company which is doing reorganizing to

minimize the cost. The company has a number of warehouse N and costumer M, the data’s are as follows:

Data on the number and capacity of each warehouse. These data set first. The number and capacity of the

warehouse that will be examined are as follows;


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Table 1. The number and capacity of each Warehouse

No. Warehouse Warehouse Capacity (Ton)

1 Warehouse-1 120

2 Warehouse-2 120

3 Warehouse-3 120

4 Warehouse-4 120

5 Warehouse-5 70

6 Warehouse-6 120

7 Warehouse-7 80

8 Warehouse-8 120

9 Warehouse-9 120

10 Warehouse-10 120

11 Warehouse-11 90

12 Warehouse-12 100

13 Warehouse-13 60

14 Warehouse-14 40

The distance data between warehouse and the costumer shown in appendix 1

Distribution costs per number of goods (tons) per kilometer are Rp 1,622.- per ton per kilometer. Data of

distribution cost from each warehouse to the costumer is shown in appendix 2

Data on the amount of product (tons) was needed by every costumer is shown in Table 2

Table 2. The amount of product needed for each customer

No. Costumer Demand (Ton)

1 Customer-1 17

2 Customer-2 129

3 Customer-3 13

4 Customer-4 19

5 Customer-5 15

6 Customer-6 27

7 Customer-7 56

8 Customer-8 16

9 Customer-9 8

10 Customer-10 14

11 Customer-11 32

12 Customer-12 9

13 Customer-13 110

14 Customer-14 20

15 Customer-15 11

16 Customer-16 10

17 Customer-17 106

18 Customer-18 12

19 Customer-19 15

20 Customer-20 31

21 Customer-21 6

22 Customer-22 24

23 Customer-23 10

24 Customer-24 13

25 Customer-25 7

Total 730

The cost of warehouse operations is the cost of goods maintenance in warehouse and other costs. The cost

of warehouse operation consists of : fixed cost and operating cost per amount of product. o Fixed cost of operating warehouse is the cost of personal to conduct maintenance and operation of

physical facilities is shown in Table 3.


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Table 3 Fixed cost of every warehouse

No. Warehouse Fixed cost (Rp)

1 Warehouse-1 120590




5 Warehouse-5 81738










o Warehouse operating costs per amount of product is the cost of warehouse operation that rises linearly

with the capacity of each warehouse; for every warehouse this costs are similar i.e. Rp.135.127 per ton.

Selection of warehouse site and coverage area using heuristic procedure to minimize warehouse site

selection models. Input of this model is a matrix of distribution cost and warehouse operating cost.

Problem-solving procedure is presented in tabular form, which is the result of step by step calculation.

Calculations start with selection of the warehouse location to be closed, then increase the number of

closed warehouse locations to get the total minimum cost. Any increase in the number of closed warehouse

checked first to see the possibility of the best partner warehouse locations. The best combination is shown

in table 4 and figure 2.

Table 4 Total cost of selection warehouse location

Sustain warehouse Combination of

warehouse closed Distribution cost

Warehouse

operation cost Total cost

1,2,3,4,5,6,7,8,9,10,11,12,13,14 - 7,290,890 1,979,716 9,270,606

1,3,4,5,6,7,8,9,10,11,12,13,14 2 7,320,086 1,726,912 9,046,998

1,4,5,6,7,8,9,10,11,12,13,14 2,3 7,370,368 1,531,569 8,901,937

1,4,5,6,8,9,10,11,12,13,14 2,3,7 7,399,564 1,371,749 8,771,313

1,4,5,6,8,9,10,12,13,14 2,3,7,11 7,495,262 1,235,979 8,731,241

1,4,5,6,8,10,12,13,14 2,3,7,11,9 7,800,198 1,123,122 8,923,320

Figure 2. Total Cost Graph

01,000,0002,000,0003,000,0004,000,0005,000,0006,000,0007,000,0008,000,0009,000,000

10,000,000

Distribution cost

Warehouse operation cost

Total cost


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Table 5 Distribution of goods to costumers from the sustained warehouse

Customer Warehouse

1 4 5 6 8 9 10 12 13 14

Customer-1 - - - 17 - - - - - -

Customer-2 - 120 - - - 9 - - - -

Customer-3 - - 13 - - - - - - -

Customer-4 - - - - - 19 - - - -

Customer-5 15 - - - - - - - - -

Customer-6 - - - - - - - - 27 -

Customer-7 - - - - - - 56 - - -

Customer-8 - - - - - - 16 - - -

Customer-9 - - - 8 - - - - - -

Customer-10 - - 14 - - - - - - -

Customer-11 - - - - - - 32 - - -

Customer-12 - - - 9 - - - - - -

Customer-13 - - - - 110 - - - - -

Customer-14 20 - - - - - - - - -

Customer-15 - - - - - - 11 - - -

Customer-16 - - - 10 - - - - - -

Customer-17 - - 16 39 - - - 51 - -

Customer-18 - - 12 - - - - - - -

Customer-19 - - 15 - - - - - - -

Customer-20 - - - 31 - - - - - -

Customer-21 - - - 6 - - - - - -

Customer-22 - - - - - - - 24 - -

Customer-23 - - - - 10 - - - - -

Customer-24 - - - - - - - - - 13

Customer-25 - - - - - - - - - 7

5 CONCLUSIONS AND FURTHER STUDY Based on calculations and problem solving the conclusions are as follow:

1. The number of warehouse which was closed are 2,3,7, and 11, while those preserved is warehouse number

1,4,5,6,8,9,10,12,13, and 14 with coverage area below:

Warehouse Amount of product (Ton) Costumer coverage area

Warehouse-1 35 D-5, D-14

Warehouse-4 120 D-2

Warehouse-5 70 D-3, D-10, D-17, D-18, D-19

Warehouse-6 120 D-1, D-9, D-12, D-16, D-17, D-20, D-21



Warehouse-10 115 D-7, D-8, D-11, D-15


Warehouse-13 27 D-6


2. Total cost of the warehouse optimization and its coverage area is Rp, 107,373,951.- per year which consists

of distribution cost of Rp.7,495,262.- per year, fixed cost of Rp. 1,235,979.- per year, and warehouse

operation cost of Rp. 98,642,710.- per year.

Further study of this research can be done by neglecting the existing assumptions as follows:


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1. Add the number of items, in this paper only single type of item but for further study could done on some

types of item.

2. Revenue gained from the closure of a warehouse is not only seen from the warehouse fixed cost as

presented on this paper.

REFERENCES

1. Abdul Hayat : The use of heuristic methods in the determination of collection warehouse coverage area in

PT Pan Java Bottling Company. Under graduate Thesis, Industrial Engineering Dept. of Bandung Inst. Of

Tech. ,1985.

2. Ballou, Ronald H : Business Logistic Management, prentice-Hall, Inc., Engelwood Cloffs, New Jersey,

1973

3. Bazaraa, Mokhtar S.,Jarvis, john j., and Sherali, Hanif D : linear programming and network flows, John

Wiley and Sons, New York, 1990

4. Eilon, Samuel., Watson-gandy, C.D.T., and chistofides, Nicos: Distribution Management : Mathematical

Modeling and Practical Analysis. Hafner, New York, 1971

5. Lieberman, Gerald J., and Hillier, Frederick S : introduction to mathematical programming, McGraw-Hill,

1991

6. RZ Abd Aziz : Optimization of Depots Location and Allocation of Bus in Each Depots also on any Routes

in Jakarta Transportation Company, Master Thesis, Engineering and Management Industry Department

Bandung Inst, of Tech., 1997.

7. Woodward, Frank H : Transportation Management, Pustaka Binaman Pressindo, Jakarta, 1991.


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Appendix 1

Table 6. Distance between warehouse and costumer (km)

No Customer Warehouse

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 Customer-1 55 25 26 53 17 16 25 27 26 52 54 25 48 65

2 Customer-2 19 10 19 10 18 18 12 15 14 19 23 18 34 34

3 Customer-3 36 13 13 18 10 11 12 22 17 16 16 13 38 36

4 Customer-4 28 2.1 14 25 10 9 3 4 2 25 28 13 26 40

5 Customer-5 2 26 37 15 34 33 25 28 26 32 38 37 32 32

6 Customer-6 30 28 35 32 24 23 28 26 27 37 39 35 5 47

7 Customer-7 28 17 22 10 20 20 16 22 24 5 8 22 40 26

8 Customer-8 37 30 34 11 32 32 30 32 33 8 5 34 52 15

9 Customer-9 40 15 6 28 4 3 14 16 17 27 29 6 36 48

10 Customer-10 42 16 10 22 9 10 15 24 20 19 19 11 40 39

11 Customer-11 36 18 16 14 16 17 17 24 26 11 12 17 50 35

12 Customer-12 28 10 10 20 6 6 9 14 13 22 23 10 36 40

13 Customer-13 30 8 19 28 15 15 9 4 6 31 32 18 22 44

14 Customer-14 10 18 30 13 26 25 17 20 18 26 30 30 24 29

15 Customer-15 39 26 18 14 20 21 25 28 30 11 10 19 52 33

16 Customer-16 42 16 8 30 6 5 15 16 17 27 31 7 36 50

17 Customer-17 40 15 4 26 1.5 2 14 20 18 26 26 3 40 46

18 Customer-18 38 14.5 13 19 11 12 13.5 22 18.5 16 16 13 39 36

19 Customer-19 38 12 12 20 8 9 11 20 16 17 18 12 38 37

20 Customer-20 36 10 6 23 2 1 11 14 13 25 25 5 36 44

21 Customer-21 28 13 14 14 10 10 12 20 17 14 16 14 36 31

22 Customer-22 52 22 10 30 15 16 21 26 25 23 24 11 54 50

23 Customer-23 35 42 52 24 50 50 42 40 42 21 22 52 52 2

24 Customer-24 33 38 49 20 48 48 38 38 39 20 20 49 50 1

25 Customer-25 32 7 18 29 14 14 8 2 4 30 32 17 23 44


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Appendix 2

Table 7. Distribution cost between warehouse to costumer

No Customer Warehouse

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 Customer-1 89210 40550 42172 85966 27574 25952 40550 43794 42172 84344 87588 40550 77856 105430

2 Customer-2 29196 16220 30818 16220 29196 29196 19464 24330 22708 30818 37306 29196 55148 55148

3 Customer-3 58392 21086 21086 29196 16220 17842 19464 35684 27574 25952 25952 21086 61636 58392

4 Customer-4 45416 3406 22708 40550 16220 14598 4866 6488 3244 40550 45416 21086 42172 64880

5 Customer-5 3244 42172 60014 24330 55148 53526 40550 45416 42172 51904 61636 60014 51904 51904

6 Customer-6 48660 45416 56770 51904 38928 37306 45416 42172 43794 60014 63258 56770 8110 76234

7 Customer-7 45416 27574 35684 16220 32440 32440 25952 35684 38928 8110 12976 35684 64880 42172

8 Customer-8 60014 48660 55148 17842 51904 51904 48660 51904 53526 12976 8110 55148 84344 24330

9 Customer-9 64880 24330 9732 45416 6488 4866 22708 25952 27574 43794 47038 9732 58392 77856

10 Customer-10 68124 25952 16220 35684 14598 16220 24330 38928 32440 30818 30818 17842 64880 63258

11 Customer-11 58392 29196 25952 22708 25952 27574 27574 38928 42172 17842 19464 27574 81100 56770

12 Customer-12 45416 16220 16220 32440 9732 9732 14598 22708 21086 35684 37306 16220 58392 64880

13 Customer-13 48660 12976 30818 45416 24330 24330 14598 6488 9732 50282 51904 29196 35684 71368

14 Customer-14 16220 29196 48660 19464 42172 40550 27574 32440 29196 42172 48660 48660 38928 47038

15 Customer-15 63258 42172 29196 22708 32440 34062 40550 45416 48660 17842 16220 30818 84344 53526

16 Customer-16 68124 25952 12976 48660 9732 8110 24330 25952 27574 43794 50282 11354 58392 81100

17 Customer-17 64880 24330 6488 42172 2433 3244 22708 32440 29196 42172 42172 4866 64880 74612

18 Customer-18 61636 23519 21086 30818 17842 19464 21897 35684 30007 25952 25952 21086 63258 58392

19 Customer-19 61636 19464 19464 32440 12976 14598 17842 32440 25952 27574 29196 19464 61636 60014

20 Customer-20 58392 16220 9732 37306 3244 1622 17842 22708 21086 40550 40550 8110 58392 71368

21 Customer-21 45416 21086 22708 22708 16220 16220 19464 32440 27574 22708 25952 22708 58392 50282

22 Customer-22 84344 35684 16220 48660 24330 25952 34062 42172 40550 37306 38928 17842 87588 81100

23 Customer-23 56770 68124 84344 38928 81100 81100 68124 64880 68124 34062 35684 84344 84344 3244

24 Customer-24 53526 61636 79478 32440 77856 77856 61636 61636 63258 32440 32440 79478 81100 1622

25 Customer-25 51904 11554 29196 47038 22708 22708 12976 3244 6488 48660 51904 27574 37306 71368

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