ALGORITMA UNTUKTATALETAK FASILITAS

Adaptasi dari materi kuliah TI ITB

OUTLINE

• Introduction• Heuristic Algorithms• Software for layout modelling• Layout issues in modern manufacturing

systems

INTRODUCTION

• A model itself does not provide a solution to a problem

• Algorithms or solution techniques have to be developed to solve a model. An algorithm is a step-by-step procedure that finds a solution to a model and hence to the problem, in a finite number of steps.

• We introduce algorithms that have been developed for the layout problem

INTRODUCTION

• Algorithms developed can be divided into two categories:– Optimal Algorithms (discussed in Ch. 5)– Heuristic Algorithms

• All optimal algorithms developed suffer from disadvantages: the memory and computational time requirements are extremely high increase exponentially as the problem size increases.

• Hence, there are many more heuristic algorithms for solving the layout problem

Heuristic Algorithms

Can be classified into 3 categories:• Construction Algorithms• Improvement Algorithms• Hybrid Algorithms

Construction Algorithms

• MST• CORELAP• PLANET

MST ALGORITHM

Example:[MST]

Example:[MST]

Example:[Output]

CORELAP

• First construction algorithm • Developed by Lee and Moore (1967)• It converts qualitative input data (obtained

from ARC) into quantitative data• CORELAP calculates the total closeness rating

(TCR) for each facility• Facility with the highest TCR is selected and

placed in the centre of the layout

CORELAP

• If two or more facilities share the highest TCR, select one with the highest area (if there is still a tie, select the first such facility).

• Selection of the second facility depends on the interaction with the permanent facility (placed in the layout).

• The temporary facility (unselected facility) with highest adjacency relationship (A, E, I, etc.) with the permanent facility is selected

CORELAP

• The third and subsequent facilities are selected on the basis of their relationship with the permanent facilities.

• The entering facility is placed in the location that maximizes the PR (placement rating) –For an example, see Fig. 6.4

CORELAP

EXAMPLE 2: [ADJACENCY REL]

CORELAP: TCR

CORELAP

Improvement Algorithms

• 2-OPT and 3-OPT• CRAFT• SA-CRAFT (Mulyono dan Iskandar, 1994)

2-Opt Algorithm

Facilities and Sites

Example:[2-Opt Algorithm]

SOLUTION

SOLUTION

SOLUTION

3-Opt Algorithm

CRAFT

• Computerized Relative Allocation of Facility Technique (Armour and Buffa, 1963)

• Up till now, It is still popular and widely used in practice • CRAFT requires the input data:

– Dimension of the building– Dimension of facilities– Flow of material and cost per unit load per unit distance– An initial layout– Restriction on location of facilities (fixed facilities)

Departemen Dummy

• Mengisi bagian yang bersifat umum atau tidak beraturan.

• Menggambarkan area yang tetap di dalam fasilitas dimana departemen tidak. dapat dialokasikan, yaitu tangga elevator, ruang istirahat, tempat alat-alat service, dan lain-lain.

• Menyatakan ruang ekstra dalam fasilitas.• Membantu dalam mengevaluasi lokasi Gang

dalam tata letak.

CRAFT

• Given the initial layout, CRAFT computes the distance between centres of each pair facility and determine the cost of the initial layout.

• CRAFT considers exchanging the location of certain pair of facilities

• The facility pairs considered either have the same area or are adjacent (See Fig. 6.13)

CRAFT:[Estimated Cost]

CRAFT

• Each iteration, CRAFT can examine a maximum n(n-1) possible exchanges, (n=#of facilities)

• The location exchange that result in the greatest estimated cost reduction is made

• The algorithm is stopped if no two-way exchange results in a lower cost.

CRAFT:[Exchange facilities]

CRAFT is also capable of performing:• Three way exchanges• Two-way exchanges followed by three way

exchanges• Three way exchanges followed by two-way

exchanges

CRAFT

• The original version was capable of handling only 40 facilities (Please check the capability of CRAFT in the QSB).

• In general, better the starting solution, the better the final solution.

• This is true with CRAFT also.

Example: [CRAFT]

Example: [CRAFT]

Data InputCRAFT

OUTPUT: [CRAFT]

OUTPUT: [CRAFT]

OUTPUT: [CRAFT]

OUTPUT: [CRAFT]

OUTPUT: [CRAFT]

OUTPUT: [CRAFT]

OUTPUT: [CRAFT]

Hybrid Algorithms

• All improvement algorithms require an initial layout

• The better the starting solution, the better the final solution

• A hybrid algorithm uses a construction algorithm to produce an initial layout and then improve it by an improvement algorithm.

• BLOCPLAN is a hybrid algorithm. • R-MAT (Iskandar, 1985)

BLOCPLAN

• Can develop a single-story or multi-story layout• Can handle quantitative or qualitative data• Can handle a maximum of 18 facilities• Three ways of providing flow data:

– ARC– From-To-Chart– Product-Routing data

• BLOCPLAN converts flow matrix into an equivalent relationship chart by dividing the maximum flow element by 5 (See Table 6.2).

• Then rel chart is used to develop a layout

TABLE 6.2

BLOCPLAN

• BLOCPLAN can develop a layout:– Randomly using a construction algorithm;– Using an embedded improvement algorithm; or – Using an automatic search algorithm

• The improvement algorithm executes an exchange and calculates the adjacency score and the rel-dist score of the new layout.

Adjacency score and Rel-Dist score

BLOCPLAN

• The Criterion used is R-score • R-score=1 – (rel-dist score-LB)/(UB-LB)• UB: Upper Bound LB: Lower Bound• R-score =1 means that the solution is optimal• Hence, BLOCPLAN is trying to develop the

layout with R-score being close to one.

Software for layout modelling

• CORELAP• CRAFT• BLOCPLAN• FactoryCAD• FactoryPLAN• FactoryFLOW(See more in IE Solutions magazine, August

1995)

Layout issues in modern manufacturing systems• The layout problem discussed has been based on

three assumptions:1. The layout problem is two-dimensional2. Information on future manufacturing activities is

known at the time facility design decisions are made

3. The product mix and volume remain fairly constant• These may have been justified in traditional

manufacturing systems but they no longer hold in modern systems

Layout Issues in modern manufacturing systems

• A stable business environment –the traditional manufacturing systems

• A high level of volatility and uncertainty in the current industrial climate

• Effective lifetime of a layout is two years (Nicol and Hollier, 1983)

• The lifetime has decreased further say to one year or less in the past decade

• Due to the high rate of technological innovations as well as the frequent changes in product design and functional demanded by customers

• Re-layout will become more common that layout of new facilities in the future systems (the Dynamic layout problem)

Layout issues

• The layout problem is two-dimensional (This is hold for a manufacturing system)

• It does not apply in an office layout problem –where facilities are usually located in several floors

• Manufacturing systems in the future may have to deal with three-dimensional layout problems –land prices become to high; building a new plant costs ten times more than refurbishing an existing one

Layout issues

• Hence, the manufacturer needs to consider expansion in vertical dimension –transforming a 2-D layout problem into a 3-D layout one.

• The distance between facilities situated in different floors may be nonlinear.

• Many algorithms are available the multifloor problem (e.g. BLOCPLAN, SPACECRAFT, CRAFT 3-D, MULTIPLE)