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One of the best-known Improvement procedures is Craft. One of the best-known Improvement procedures is Craft. Craft was originally presented by Armour and Buffa.Craft was originally presented by Armour and Buffa.

Craft is typical example of a heuristic program based on Craft is typical example of a heuristic program based on quadratic assignment interpretation of the process layout quadratic assignment interpretation of the process layout program. program.

The basic criterion used is the minimization of the cost of The basic criterion used is the minimization of the cost of item movement, where this cost is expressed as a linier item movement, where this cost is expressed as a linier function of distance traveled.function of distance traveled.

CRAFT CRAFT ((Computerized Relative Allocation of Facilities Technique)Computerized Relative Allocation of Facilities Technique)

Prof. Ir. R. Chairul Saleh, M.Sc, Ph.D

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The improvement principle of Craft as follows : The improvement principle of Craft as follows : 1.1. Evaluates a given layout and then considers what the effect Evaluates a given layout and then considers what the effect

will be if department locations are interchange.will be if department locations are interchange.2.2. If improvement can be made by making pair wise exchanges, If improvement can be made by making pair wise exchanges,

the exchange producing improvement is madethe exchange producing improvement is made3.3. The process continue until no improvement can be made by The process continue until no improvement can be made by

pair wise exchanges.pair wise exchanges.

CRAFT CRAFT ((Computerized Relative Allocation of Facilities Technique)Computerized Relative Allocation of Facilities Technique)

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Input CraftInput Craft

Gambar 1. The Craft input format is shown, where each line represented by a punched card. The card is punched with with the sequence of letters representing the various department.

A A A A A B B B A A A A A B B B C C C C D D D D C C C C D D D D

50

40

30

1. Initial Layout and Building OutlineThis may consist of either an arbitrary initial layout or an existing layout, whichever is appropriate. The configuration of the final layout can be significantly affected by the configuration of the initial layout.

Gambar 1. Initial Layout

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A A A A A B B BA A A A A B B BC C C C D D D DC C C C D D D D

Gambar 2. Contoh format Input

In figure 2, one matrix element equals 100 square feet, each row and column equals 10 feet. Given the 4 row and 8 columns, an area of 80 * 40 feet is represented.

2. Number of Departments, respective floor areas, number and location of fixed departments

In common version CRAFT can handle up to 40 different departments. Maximum allowable dimension of 30 * 30.

3. Flow and Distance Data

The flow matrix (from to chart) gives the number of trips made per time period between combination of department. The cost matrix represents the material handling cost required to move one unit of distance between combinations of departments (see figure 3 a).

55

In figure 2, 1 square represents a 100square feet area. Since material handling can be performed in a variety of way, the cost elements need not be the same.

The cost matrix assumes, however, that the appropriate, materials handling equipment has been selected for each move. Since the cost data are expressed as cost per unit distance, it is necessary that the distance unit be the same as the layout scale (see figure 4)

tofrom

A B C D

A - 2 4 4B 1 - 1 3C 2 1 - 2D 4 1 0 -

Figure 3 From-To Chart (Flow Matrix)

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ToFrom

A B C D

A - 1 1 1B 1 - 1 1C 1 1 - 1D 1 1 0 -

Figure 4 Cost Matrix

Method Craft computes total materials handling cost for the initial layout by computing the rectilinear distances between department centroids and computing the resultant flow *cost * distance matrix.

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From figure 1, the centriod location are :

(XA,YA) = (25, 30) (XC, YC) = (20, 10)

(XB,YB) = (65, 30) (XD, YD) = (60, 10)

For example , the rectilinear distance between the centroid coordinate location (XA,YA) and (XB,YB) equals 4030306525YYXX BABA

The resulting distance matrix is given in Figure 5.

tofrom

A B C D

A - 40 25 55B 40 - 65 25C 25 65 - 40D 55 25 40 -

Figure 5. Distance Chart

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-025220D80-6550C 7565-40B

22010080-A

DCBA ToFrom

245

195

180

400

Total

375165170310Total 1020

Figure 6. Total Cost matrix

The total cost or the total distance traveled per unit time equals 1020 feet for the initial layout as shown in figure 6.

The objective of CRAFT is to minimized materials handling cost, where this cost is obtained as a linear function of distance traveled.

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Pair wise ExchangePair wise Exchange

CRAFT applies the pair wise exchange heuristic. It considers exchange of the centroid locations for those departments which either are same area or have a common border. The interchange that produces the greatest anticipated reduction in total cost is determined and the department are interchanged.

Craft considers a possible interchange of departments A and B. If we make this interchange we obtain the layout given in Figure 7.

Figure 7 . Layout after Interchange of Department A and B

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As can be seen the new centroid coordinates for departments A and B are

(XA,YA) = (55, 30) ((XB,YB) = (15, 30)

But in estimating total cost CRAFT simply interchanges the original coordinates yielding (XA,YA) = (65, 30) and ((XB,YB) = (25, 30). The resulting distance chart and corresponding cost matrix are given in Figure 8.

tofrom

A B C D

A - 40 65 25B 40 - 25 55C 65 25 - 40D 25 55 40 -

Figure 8. Distance Chart

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The total cost is estimated by CRAFT to be 1060.after exchanging department A and B. Craft decides that interchanging department A and B is not advantageous due to an anticipated increase of 40 in total cost. Figure 9, the matrix total cost after first iteration occurred.

ToFrom

A B C D

A - 80 260 100B 40 - 25 165C 130 25 - 80D 100 55 0 -

Total

440

230

235

155Total 270 160 285 345 1060

Figure 9. Total Cost Chart

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Interchange A and K results in a estimated cost of 995. Interchange A and D produces a cost estimated of 1095. The department B and K are not the same area, and do not have a common border, consequently CRAFT does not consider an interchange of B and K. Interchanging B and D results in a total cost of 945, while interchanging K and D produce a total cost of 1040. Consequently, CRAFT considers the best interchange to be and will introduce the change in the layout.

Interchanging the centroid location of departments B and D yields the layout of Figure 10.

Dept DDept A

Dept C Dept B

Figure 10. First improved Layout after exchange of B and D

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Since B and D are not the same size, we notice that department D is no longer rectangularly shaped and that the department centroids were not exchanged exactly. Rather a short calculation shows that

(XA,YA) = (25, 30) (XC, YC) = (20, 10)

(XB,YB) = (55,10) (XD, YD) = (67.5, 25)

Due to the change of the centroid locations, the distance chart for the new layout needs to be recomputed (see figure 11). On the multiplying the flow values of figure 3 and the distance values in figure 11, we obtain a total cost of 985, rather the estimated cost of 945.

tofrom

A B C D

A - 50 25 47.5B 50 - 35 27.5C 25 35 - 62.5D 47.5 27.5 62.5 -

Figure 11. Distance chart for first improved layout

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CRAFT continues evaluating pair wise interchanges and finds that interchanging departments A and B give the greatest estimated cost reduction with an estimated total cost of 945. Figure 12 give second improved layout having the following centroid location :

Figure 12. Second Improved Layout after exchanging A and B

(XA,YA) = (49,18) (XC, YC) = (20, 10)

(XB,YB) = (15,30) (XD, YD) = (67.5, 25) The estimated cost for this layout is 945; computation of the actual cost, however, yield a value 969.

Applying the pair wise interchange on the second improved layout indicates K and D should be interchanged. The estimated cost is 927 for exchange of K and D. K and D have the same area, their centroids will be exchange exactly and the true total cost will be 927.

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CRAFT makes the indicated exchange of department locations, which yield the layout shown in figure 13.

Dept CDept B

Dept D Dept A

In performing the pair wise interchange calculations for the third improved layout, CRAFT finds that no pair wise interchange will produce an estimated total cost less than 927. Consequently, the search terminates with the layout shown in Figure 13

Figure 13. Third Improved Layout