Optimization of Space Utilization of Storage Rack System for a Garment Industry using Linear Integer Programming

Optimization of Space Utilization of Storage Rack System for a Garment Industry using Linear Integer Programming

Abhishek. Shetty

Bachelor of Engineering Industrial Engineering and Mangement M.S.Ramaiah Institute of Technology

Bangalore

Vivekanand. V

Assistant Professor

Industrial Engineering And Mangement M.S.Ramaiah Institute Of Technology Bangalore

Animesh. Jain

Bachelor of Engineering Industrial Engineering And Management M.S.Ramaiah Institute Of Technology

Bangalore

Abstract: The garment industry in India faces multiple problems with respective to achieve performance measure such as quality, throughput, cycle time, FGI (Finished Goods Inventory). In order to achieve these performance measures, an optimization model needs to be created with a focus on single or multiple objectives. In the current work, the focus is on obtaining optimal solution with an objective of minimize storage space. This can be obtained by using Integer Linear Programming technique. The objective is to minimize the volume left by means of allocation of various combination of packets of materials in such a way that the constraints of each rack space is considered. Different strategies for allocating various packets of materials were generated and using these strategies, optimal solutions was obtained.

Key words: Optimization, Integer Linear Programming, Garment Industry, Operations Research, Inventory Management, ABC Analysis.

1. INTRODUCTION

   Managing of Inventory takes place at various stages which include raw material inventory stage, WIP (Work In Progress) stage and FGI (Finish Good Inventory) Stage. Managing involves creating an optimal strategy to ensure that objective function which is needed is either minimized or maximized. Currently in the company there is no set practices for allocating materials to the rack based on optimization of storage space. Hence there is a need to create an optimal strategy. In order to achieve, an objective function is used to minimize usage of raw material storage space of the rack system by allocating material in the rack accordingly. To obtain a better understanding about the methodology it is necessary to understand about the raw material storage system.

   It was observed the storage for raw materials was randomly done and there seemed to be a lot of space not being utilized properly simply due to the inconsistency in racks and also the carton boxes in which the raw materials were placed. It was also noticed that the best results under the

   given circumstances was yet to be achieved. The racks were not being properly utilized. The current storage method was not optimized.

   Initially the whole area for raw material storage was observed and the way the packing and combination of different raw materials placed were seen. Also the racks and the boxes were seen and dimensions were taken. It was seen that the boxes were randomly placed based on availability and the racks were also spaced in appropriately.

   It is seen from Fig 1 that raw materials are stored in racks in containers according to their types, however there is no set strategy for allocation of materials in order to optimize rack space. To understand about allocating materials to the rack it is necessary to know the dimension of the rack and dimension of the material package. The dimension of the rack would be considered as part of constraint. Typically when allocating a set of different packaged material to a rack, dimension of the packaged material would be considered to stack and the material were stacked length or breadth wise. Thus when stacking different packets of materials there can be a set of combination which can evolve when onset of material is stacked according to their and other according to their breadth. This allocating strategy is shown in Table 1. Based on these strategies an optimal set of strategies can be found to minimize volume left for a storage rack system.

2. LITERATURE REVIEW

   Allocation problems have been dealt in various books and literature. Taha [1] explains various methods of allocating products, materials in his book on operations research. Rajendran [2] in his paper addresses on how to allocate different bar materials for the required length put forward by the construction site. The paper focuses on different case studies in which one of them focuses on minimization

   of scrap for cutting reinforcement bars to various lengths. There are different types of bars. The bars come in with a particular length which needs to be cut to various lengths based on the requirements put forward by the construction sites.

   In order to minimize the scrap, they have found out the different possible patterns of cutting and have assumed the decision variable to be number of possible different methods of cutting. The objective function is minimization of scraps subjected to the constraints of availability of bars.

   The current paper addresses the problem in a similar however the objective function in our case is to minimize the volume left when we are allocating different boxes based on different strategies in order to minimize the volume left.

   Additionally ABC classification was applied and allocation was accordingly done based on these classification.

3. PROBLEM DESCRIPTION:

   As mentioned earlier in the introduction section, the rack space is not optimally utilized and packaged material are allocated based on a random basis or wherever there is space availability. Hence there is a need for systematic and scientific way of allocation with the objective of optimal utilization of rack space.

   In addition to the above mentioned the classification of materials werent applied and this adds to further problems.

   For the solution of the above-identified problems, ABC classification and an OPERATIONS RESEARCH model using Integer linear programming method, which is done for optimization, were recommended for the same

4. PROBLEM OBJECTIVE

   The objective of this study is to allocate materials optimally based on the current scenario (No ABC classification), ABC Classification, AB and C classification and then comparing all these combinations and suggesting best practices.

   Figure1: Raw Material Storage

   Figure 2 : Rack Dimensions

5. METHODOLOGY:

Figure 3 : Methodology

1. ANALYSING THE RAW MATERIAL STORAGE AWAREA

   Figure 4: Raw Materials

   Material	Quantity(pcs.)	Value(Rs.)	Pieces/Packet(pcs.)	Boxes / Material(pcs.)	Packet dimensions(cm)
   Button	2249582	3616272	864	2603	19*15*3
   Pu Patch	176515	690734	500	353	36*26*3
   Rivet	471095	643283	5000	942	22*19*3
   Stud	57768	150976	5000	58	22*19*3
   Tag	672342	2012751	1000	672	36*26*3
   Leather Patch	35221	347296	500	70	36*26*3
   Carry Bag	83650	356510	1000	17	51*42*10
   Zip	434966	2641242	1000	435	20*25*3
   Label	1547692	863435	500	3095	20*20*3
   Number of racks in avialable : 152
   Number of racks in use : 132
   Rack Dimensions(cm) : 60*46*60

   Material	Quantity(pcs.)	Value(Rs.)	Pieces/Packet(pcs.)	Boxes / Material(pcs.)	Packet dimensions(cm)
   Button	2249582	3616272	864	2603	19*15*3
   Pu Patch	176515	690734	500	353	36*26*3
   Rivet	471095	643283	5000	942	22*19*3
   Stud	57768	150976	5000	58	22*19*3
   Tag	672342	2012751	1000	672	36*26*3
   Leather Patch	35221	347296	500	70	36*26*3
   Carry Bag	83650	356510	1000	17	51*42*10
   Zip	434966	2641242	1000	435	20*25*3
   Label	1547692	863435	500	3095	20*20*3
   Number of racks in avialable : 152
   Number of racks in use : 132
   Rack Dimensions(cm) : 60*46*60

   Where

   Figure 5: Strategy allocations

2. INTEGER LINEAR PROGRAMMING AND ABC ANALYSIS

3. INTEGER LINEAR PROGRAMMING

Linear Programming (LP) is a mathematical procedure for determining optimal allocation of scarce resources. It is a special case of mathematical programming (mathematical optimization). Linear programming deals with a class of programming problems where both the objective function to be optimized is linear and all relations among the variables corresponding to resources are linear.

Any LP problem consists of an objective function and a set of constraints. A function is a thing that does something.

In the problem stated by the company it was the rack space for material allocation which was required to be optimized.

1. The decision variables are the various strategies used in allocating the boxes based on the rack dimensions

2. The objective function is to minimize the volume left based on the allocation strategy

3. The constraints are the total number of boxes available for various products (Calculated based on availability and there should be minimum availability)

Based on the various strategy, the calculation below shows the coefficients to be used for the constraints. Figure 5 shows an excel table sheet on how coefficients are allocated for each strategy and a particular product. It should be noted from the calculation below that based on the strategy allocated and the rack dimension the coefficients are calculated. The below figure is example of solver table without ABC Classification.

Z = Total volume left after allocation

1= Number of packets for a rack for part P1 using strategy 1

2= Number of packets for a rack for part P1 using strategy 2

3= Number of packets for a rack for part P1 using strategy 3

4= Number of packets for a rack for part P1 using strategy 4

5= Number of packets for a rack for part P1 using strategy 5

8= Number of packets for a rack for part P1 using strategy 8

10= Number of packets for a rack for part P1 using strategy 10

12= Number of packets for a rack for part P1 using strategy 12

13= Number of packets for a rack for part P1 using strategy 13

18= Number of packets for a rack for part P1 using strategy 18

20= Number of packets for a rack for part P1 using strategy 20

3= Number of packets for a rack for part P2 using strategy 3

6= Number of packets for a rack for part P2 using strategy 6

8= Number of packets for a rack for part P2 using strategy 8

15= Number of packets for a rack for part P2 using strategy 15

16= Number of packets for a rack for part P2 using strategy 16

19= Number of packets for a rack for part P2 using strategy 19

6= Number of packets for a rack for part P3 using strategy 6

16= Number of packets for a rack for part P3 using strategy 16

5= Number of packets for a rack for part P4 using strategy 5

9= Number of packets for a rack for part P4 using strategy 9

11= Number of packets for a rack for part P4 using strategy 12

12= Number of packets for a rack for part P4 using strategy 12

4= Number of packets for a rack for part P5 using strategy 4

18= Number of packets for a rack for part P5 using strategy 18

2= Number of packets for a rack for part P6 using strategy 2

3= Number of packets for a rack for part P6 using strategy 3

7= Number of packets for a rack for part P6 using strategy 7

13= Number of packets for a rack for part P6 using strategy 13

14= Number of packets for a rack for part P6 using strategy 14

15= Number of packets for a rack for part P6 using strategy 15

X1-Strategy for allocating Buttons Only

Number of packets of Buttons (A1 )= 3*4*19= 228 packets

The number of buttons are calculated based on rack dimensions and the button box dimension

19

= Number of packets for a rack for part P6

using strategy 19

Volume left = 16*46*60 = 44160 cm3

4= Number of packets for a rack for part P7 using strategy 4

16= Number of packets for a rack for part P7 using strategy 16

17= Number of packets for a rack for part P7 using strategy 17

3= Number of packets for a rack for part P8 using strategy 3

= Number of packets for a rack for part P8 using strategy

X2 – Strategy for allocating Buttons, Rivets

Number of packets of Buttons = 19*2*3= 114 packets

Number of packets of Rivets = 19*2*2= 76 packets

The number of buttons and rivets are calculated based on rack dimensions and the button box dimension

7

11

= Number of packets for a rack for part P8

7

using strategy 11

Volume left = (10*46*60) + (44*8*60) = 48720 cm3

13= Number of packets for a rack for part P8 using strategy 13

14= Number of packets for a rack for part P8 using strategy 14

19= Number of packets for a rack for part P8 using strategy 19

20= Number of packets for a rack for part P8 using strategy 20

9= Number of packets for a rack for part P9 using strategy 9

10= Number of packets for a rack for part P9 using strategy 10

17= Number of packets for a rack for part P9 using strategy 17

OBJECTIVE FUNCTIONS

Min Z =

11+22+33+44+55+66+77+88+99+1010

= =1

S.T CONSTRAINTS

=

=

1 Total number of boxes for part P1

In a similar way coefficients can be calculated for the remaining set of strategy

5.5 BJECTIVE FUNCTIONS & CONSTRAINTS

Min Z=11+22+33+44+55+66+77+88+

99+1010

=

=

Min Z = 1

S.T CONSTRAINTS WITHOUT ABC CLASSIFICATION

For buttons:

=

=

1 Total number of boxes for buttons 228×1+114×2+57×3+57×4+114×5+76×7+114×8+114×10+171x

12+114×13+57×18+114×20 2603

For zip:

Total number of boxes for zip

Total number of boxes for part P2

=1

=1

19×3+19×6+38×8+19×15+19×16+19x 435

=

=

1 Total number of boxes for part P3

=1

=1

Total number of boxes for part P4

For tag:

1 Total number of boxes for tag

=1 Total number of boxes for part P5

=1

=1

Total number of boxes for part P6

=1

=1

Total number of boxes for part P7

=

38×6+19×16 672

For label:

Total number of boxes for part P8

1 Total number of boxes for label

=1

=

=

=

1 Total number of boxes for part P9

5.4 CALCULATION

Number of racks available: 152 Number of racks in use: 132

Rack Dimensions (cm): 60*46*60 (L*B*H)

The values and combinations were obtained by the following calculation.

38×5+76×9+76×11+38×12 3095

For PU patch:

=

=

1 Total number of boxes for PU patch 19×4+38×18353

For Revit:

=

=

1 Total number of boxes for Revit 76×2+38×3+76×7+38×13+76×14+114×15+38×19942

For leather patch:

=

=

1 Total number of boxes for leather patch 19×4+19×16+19×17 70

For stud:

=

=

1 Total number of boxes for stud 38×3+76×7+76×11+38×13+76×14+76×19+76×20 58

For carry bag:

=1

=1

Total number of boxes for carry bag 5×9+5×10+5×17 17

WITH ABC CLASSIFICATION

For AB classified materials For buttons:

=

=

1 Total number of boxes for buttons

228×1+114×2+114×3+171×4+57×5+38×6+57×8+

114×10 2603

For zip:

=

=

1 Total number of boxes for zip 38×3+38×7+19×10 435

For tag:

=

=

1 Total number of boxes for tag 19×6+38×8+38×9 672

For label:

=

=

1 Total number of boxes for label 76×2+38×4+114×5+76×7+38×9+38×10 3095

For C classified materials For PU patch:

=

=

1 Total number of boxes for PU patch

19×3+19×4+19×5+19×6+19×7353

For Revit:

=

=

1 Total number of boxes for Revit 76×1+76×3+38×7+38×8+38×10942

For leather patch:

=

=

1 Total number of boxes for leather patch 19×2+19×5+19×870

For stud:

=

=

1 Total number of boxes for stud

76×1+76×4+38×7+38×8+38×958

For carry bag:

=

=

1 Total number of boxes for carry bag 5×2+5×6+5×9+5×1017

1. RESULT

   Solving the obtained data through solver

   Solver was used to find out the best combination among the materials in terms of rack space to optimize space.

   Calculation was done in two methods

   1. Without ABC Classification

   2. With ABC Classification.

SOLVER TABLE (WITHOUT ABC CLASSIFICATION)

Figure 6 : Solver results without ABC classification By using this technique 20 racks were saved.

SOLVER TABLE (WITH ABC CLASSIFICATION)

Solver table for AB classified materials

Figure 7 : Solver results with ABC classification for AB classified material

Solver table for C classified materials

Figure 8 : Solver results with ABC classification for C classified material

By using this technique we saved 2 more racks.

CONCLUSION:

After implementing the ABC classification and applying the optimized solution for allocation of materials in the rack it was observed that the method recommended and applied would bring down the number of racks in use. The optimized solution would help to allocate materials in a planned order which would be feasible in use.

The table below shows the number of racks in use in before and after implementation of ABC and AB &C classifications

Table 1: Results

It is seen that by means of applying optimization technique

20 rack space is saved. It was also seen that ABC classification uses the least number of racks after optimization. Thus ABC classification with the optimization technique applied for storage is to be adopted in order to achieve the best results.

REFERENCES:

1. H.A.Taha , Operations Research: An Introduction, 8th Edition,

   Mcgraw Hill, 2008

2. S. Rajendran, Application of Linear Programming Techniques for Construction Site Problems : Some Case Studies, CE&CR, DEC 1995

3. Everett E. Adam, Ronald J.Ebert, Production and Operations Management: Concepts, Models and Behavior,5th Edition Sage Publication, 1993