Optimizing the Unevenness in Production Scheduling Through Mathematical Approach a Case Study

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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 6979(Print), ISSN 0976 6987(Online) Volume 3, Issue 1, January - June (2012), IAEME

74

OPTIMIZING THE UNEVENNESS IN PRODUCTION SCHEDULING

THROUGH MATHEMATICAL APPROACH: A CASE STUDY

S. K. Gupta1, Dr. V. K. Mahna2, Dr. R. V. Singh3, Rajender Kumar41Research Scholar & Associate Professor, Department of Mechanical Engineering, FET, MRIU,

Faridabad, India-1210032Executive Director & Dean Academics, FET, MRIU, Faridabad, India-121003

3Professor & Head, Department of Mechanical Engineering, FET, MRIU, Faridabad, India-1210034Asst. Prof., Department of Mechanical Engineering, FET, MRIU, Faridabad, India-121003

E-Mail: [email protected], [email protected]

ABSTRACT

World over manufacturing has received a great deal of attention in the recent few years for

efficient utilization of resources, because of the market becoming customer oriented. There is

still no consensus on how best to measure and manage production within manufacturing

industries as there are numerous variables which change from industry to industry. In real world,the global competition is forcing entrepreneurs to cut corners on customer deliveries and input

production cost. Under the circumstances production scheduling is an important matterespecially in the organizations wherein the product consists of no. of models of the same

product. This case reveals that the production is either in the form of overproduction or

underproduction as and when compared with planned production. The situation of

underproduction isnt that serious as is the case of overproduction since overproduction isgeneration of unnecessary inventories either in the form of WIP or finished goods. Therefore,

this is nothing except generating a form of waste which is fundamentally against the principles of

Lean Manufacturing. The situation of unnecessary and undesirable inventories results in lockupof funds, which could be otherwise utilized effectively. Mathematical modeling may be an

answer to remove such waviness and unbalances through application of averages, variance anddeviation. The study was conducted and data collected for the purpose of optimization in XYZCompany manufacturing Shock Absorbers with 203 different varieties catering to need of OE

suppliers and replacement market. The most advantageous manufacturing priorities for a given

competitive situation are also discussed in this paper.

Keywords: Quality, Overproduction, Underproduction, Lean Manufacturing, Inventory.

INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING

RESEARCH AND DEVELOPMENT (IJIERD)

ISSN 0976 6979 (Print)

ISSN 0976 6987 (Online)

Volume 3, Issue 1, January- June (2012), pp. 74-91

IAEME: www.iaeme.com/ijierd.html

Journal Impact Factor (2011): 0.8927 (Calculated by GISI)www.jifactor.com

IJIERD

I A E M E


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1.0 INTRODUCTION

Over the last two decades there has been enormous increase not only in demand but also in

production supply of variety of products. In most of the manufacturing industries, the main issue

of productivity is production planning. The materials play an important role so far as itscontribution towards the product and also the cost are concerned. Therefore, a systematic control

is essential so far as materials are concerned to avoid obsolescence, unnecessary storage and

material handling including the delayed deliveries. Figure 1 shows the various inputs toproduction to make the system efficient and effective.

Figure 1 Resources that must be managed effectively

Twenty keys are discussed for workplace improvement in manufacturing industry as shown in

Figure 2 [8]. These keys must be considered in order to achieve continuous improvement. These

20 keys are arranged in a circle that shows the relations between the keys and their influence onthe three main factors: quality, cost, and lead time. The arrangement in the circle is not

categorical, and some keys offer benefits in more than one factor. There are four keys outside the

circle. Three of them (keys 1, 2, and 3) must be implemented before the rest, and key 20 is the

result of implementing the other 19 keys.


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Figure 2 Twenty keys for workplace improvement

The lack of planning generates imbalance in the planned targets and subsequently deliveries. As

a result of this, the customer demand gets nullified resulting into loss of revenues. The uncertain

production plan and scheduling also leads to very heavy inventory of raw materials, WIP andundesired movements of materials. This leads to unnecessary breakup of lots considered for

manufacturing. The result is loss of man-hours, machine-hours, material input and also increase

in the input cost. All these are a type of waste which does not add any value. "A more liberal andextensive reciprocity in the production and sale of commodities is necessary, so that the

overproduction of the organizations can be satisfactorily disposed off to the market.

The problem of unevenness in planning and scheduling can be addressed through process of

categorization of the demand factors pertaining to various models. This categorization shallprovide a whip to the planning and scheduling department to keep a close watch and amend the

actions where-so-ever required. Once, the objective of smoothening the production is achieved

80-85% then it becomes easy to meet the market requirements. This paper addressed the data

bifurcation in which the products are refers to three main categories such as Production at par,

overproduction, underproduction. This paper presents mathematical optimization withapplication of methodology for finding Co-efficient of variation [5].


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2.0 LITERATURE REVIEW

Data filtering has become a key technology for modern production control systems. The goal of

data bifurcation or filtration is a route to the right decision of controlling and optimizing the

production. In order to deal with high variety of products, a very small variety of productsrequires the attention for getting the maximum efficiency. The VED technique is the best

adopted as a routine practice for optimal use of resources and elimination of out of stock

situations in the production house. The VED analysis will facilitate planning department toengage entire energy to limited area only leading to reducing overproduction to bare minimum

including best utilization of funds [2,11].

Optimization is about utilizing the resources in organized manner to achieve higher efficiency.Optimization is thus, about achieving high utilization, high efficiency and high effectiveness at

bare minimum cost [4]. Mathematical Optimization refers to the selection of a best element

(with regard to some criteria) from some set of available alternatives. In the simplest case, anoptimization problem consists of maximizing or minimizing a real function by systematically

choosing input values from within an allowed set and computing the value of the function. The

generalization of optimization theory and techniques to other formulations comprises a large areaof applied mathematics. More generally, optimization includes finding "best available" values of

some objective function given a defined domain, including a variety of different types of

objective functions and different types of domains.

3.0 CASE STUDY

A study was undertaken in a company manufacturing shock absorbers and having a wide variety

of the product numbering 203. The period of this study was based on a data spread over the

period of last six month as per Annexure 1. Table 1 shows the performance of actual production

as compared with planned production targets. This variation has been graphically representedthrough Bar Chart as given in Figure 3.

Table 1 Gross average monthly production

Months Planned Production Actual Production

Jan12 222521 151431

Feb'12 250428 156504

March'12 266333 152994

April'12 248845 209559

May'12 186317 149798June'12 176038 150009

Average 225080 161716


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Figure 3 Gross average monthly productions

3.1 Inferences

On analysis of data given in Annexure 1, it was found that on an average 13 % production was

inline with the plans ac in Annexure 2, 20% of the production on an average was overproducedi.e. over and above the planned production as in Annexure 3, and in balance cases it wasobserved that 67% of the production was in the category of underproduction as compared to

palmed production as in Annexure 4. The process of straightening the plans is a quite heavy task

therefore, the principles of VED analysis was followed for purpose of categorization so that

effective controls could be introduced. Table 2 shows the VED analysis of over production,under production and production at par. The categorization establishes that production at par is

the lowest followed by overproduction and further followed by under production.

Table 2 Actual Performance

Production Data Actual Model

Contribution

Production at Par 13%

Over Production 20%

Under Production 67%

Total 100%

Variation in Actual & Planned

Production

0

50000

100000

150000

200000

250000

300000

Jan1

2

Feb'1

2

March'1

2

April'12

May'1

2

June'12

Months Detail

ProductionQuantity

Series1

Series2

Series3

Series4


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Figure 4 Pie chart for category bifurcation

The production data reveals over planning as compared to manufacturing capacity. This variation

is almost to the tune of 28% as given in the Figure 3. This over planning will result in

unnecessary pressure on material planning, unnecessary occupancy of space, lockup of funds,obsolescence in spoilage of materials and frequent movement of the stocks. Table 3 provides

comparative analysis of underproduction; overproduction and production at par in terms of no. of

product produced in six months and the contribution of each category so-far-as volumes

manufactured are concerned.

Table 3 Comparative Analysis on Production Data

Production Detail Production Quantity Percentage Contribution

Production at Par 17268 02%

Over Production 353971 36%

Under Production 608547 62%

Total 979786 100%

It is concluded from Table 3 above that the Production Planning and Control Department of saidcompany is working with no exposure to the technological advancements. It is evident that the

Model Contribution

Production at

Par, 13%

Over

Production,

20%

Under

Production,

67%

Production at Par

Over Production

Under Production


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production data doesnt match with the planned production. In most of the categories, it is

underproduction followed with overproduction and further very small percentage matching withthe planned data.

The data was further analyzed and it was observed that there is a huge variation from thestandard deviation. This was further normalized with the help of mathematical modeling and the

details are as per enclosed table. This normalized solution can remove the waviness to a great

extent by introducing controls on categorized items only. Table 4 gives details regardingcategory-wise breakup of VED analysis. This table establishes that a mere control of 35 items

out of 203 items (17%) will help in eliminating the imbalances in the production and improving

the overall performance.

Table 4 Results Summary Sheet

Sr.No. Description Total No. of Items Category Bifurcation

Items for Control

V E D Total

1 Under Production 135 23 (17%) 4 7 12 23

2 Over Production 41 12 (30%) 3 4 5 12

3 Balanced 27 0 0 0 0 0

Total 203 35 7 11 17 35

Table 5 is based on optimized data including the percentage smoothness of both categories i.e.

over production and under production. The category of overproduction being serious in nature

has been smoothened to an extant of 92% with control on 12 items (0.6% of total varieties).

Table 5 Optimization Results

ProductionDetail

Total Produced Quantity Optimized Quantity PercentageContributionNo. of

ProductsQuantity No. of

ProductsQuantity

OverProduction

41 353971 12 326937 92%

UnderProduction

135 608547 23 277961 28%

Total 176 962518 35 704898 73%

4.0 CONCLUSION

In this competitive globalization, almost all the manufacturing organizations realize the value of

on time delivery of their products to market or stockholders. The amount of product varieties wasfound under production to be tune of 67%, over production 20% and remaining 13% production

just matching with the actual plans giving rise to huge build up of inventories all around. This

also results in non compliance of deliveries and thereby an unsatisfied customer. Underproduction is the confirmation of living in dreams while it is quiet evident that the planned data

is much beyond capacities and therefore away from realm. This statement is further confirmed


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by the fact that the data depicts 62% of quantities produced are underproduction as compared

with planned production. The situation is not so serious except that there is extra amount ofburden for procurement to cater the needs of the planned production. Similarly, the fate of over

production is also bad as it results in build up of unnecessary inventories either in the form of

WIP or finished goods. This is contrary to fundamental principles of Lean Manufacturing. Theamount of over production is to the tune of 36% of the item produced. The co-efficient of

variation when applied to this situation optimizes the given data in a fashion that mere strict

control of 9 % of the items produced can provide smoothness up to 38% and further control of8% of items can remove waviness up to 35%. Therefore, the overall results can be improved up

to 73% by controlling 35 items as given in the table above.

REFERENCES

1. Dilworth, J. B., (1993). Production and Operations Management: Manufacturing andServices. Mc-Graw Hill Publication, 4th Edition.

2. Grewal C.S. and Sareen K.K. (2006). Development of model for lean improvement: Acase study of automobile industry. Industrial Engineering Journal, Vol. 35(5), pp. 24-

27.3. Hines, P., Rich, N. & Esain, A. (1997). "Creating a Lean Supplier Network: A

Distribution Industry Case". Proceedings of the Logistics Research Network Conference,

Huddersfield, U.K.: University of Huddersfield, pp. 60-77.

4. Khare, S. (2006). Optimizing the Organization: Unleashing the potential of practices,processes and people. Tata Mc-Graw Hill Publishing Company Limited, New Delhi, pp.

2-10.

5. Kobayashi, I. (1998). 20 Keys to Workplace Improvement. Productivity Press,Cambridge, revised edition, MA.

6. Ohno, T. (1988). "Toyota Production system: Beyond Large Scale Production".

Productivity Press, Cambridge, MA.7. Pavnaskar, S.J., Gershenso, J.K and Jambekar, A.B. (2003). "Classification scheme for

lean manufacturing tools, International Journal of Production Research, Vol. 41, pp.

3075-3090.8. Sardana, S., Kumar, R., Bajwa, M. and Gulati, P. (2011). Application of SPC tool for

finding variation in the Process Output (A Case Study). International Journal ofIndustrial Engineering Research and Development, ISSN: 0976-6987, Vol. 2, Iss. 1,

May-Oct., 2011, pp. 46-58.

9. Schroeder, R. G., (1993). Operations Management: Decision making in the OperationsFunction,Mc-Graw Hill Publication, 4th Edition.

10.Stevenson, W.J. (1996). Production and Operations Management, Irwin McGraw-Hill,5th ed., New York.11.Womack, J.P., and D.T. Jones, From Lean production to the Lean Enterprise, Harvard

Business Review, pp. 93-103(1994).


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Annexure 1: Planned Production V/S Actual Performance from time period of January to June, 2012

Sr. No. Part No.January February March April May June

Plan Actual Plan Actual Plan Actual Plan Actual Plan Actual Plan Actua

1 3558 7304 1458 10708 1260 15448 3144 7000 2485 7582 3726 6956 2828

2 3504 4848 2574 9078 5286 12292 4000 8000 3594 11956 4650 12256 7240

3 3543 4020 1074 7946 984 10962 2334 5000 2946 4554 2340 4364 2742

4 3712 12964 10124 17846 12799 22547 13024 18023 20688 18835 16700 8385 9538

5 6222 2770 1280 6290 2450 7340 3340 5000 2650 4380 1980 4100 3076

6 3542 5350 2820 5732 672 9560 2568 4000 5134 1986 1992 1644 1506

7 3510 852 84 2070 0 4870 1132 2000 780 2770 1218 3562 0

8 3549 4758 2244 6214 1218 11496 4170 4000 4482 2522 3384 2138 2882

9 3371 3840 0 0 0 4100 1188 5412 612 100 247 100 156

10 6201 0 0 2000 0 4000 0 1500 0 1500 0 1500 0

11 3407 400 0 1400 0 1400 0 1900 0 2350 0 2900 0

12 4119 600 0 1100 68 1032 0 1332 0 1732 50 1982 152

13 3519 606 0 906 396 510 0 2910 828 4682 1866 2816 2814

14 4134 800 0 1300 0 1300 0 1300 0 1550 324 1376 860

15 3329 400 0 900 0 900 0 1100 0 1500 84 1816 686

16 6203 3000 1919 5439 2318 2382 1338 1644 1296 948 719 229 299

17 3727 6290 2164 8224 4730 8494 6810 3500 6564 2430 2388 5158 5798

18 4123 400 0 900 0 900 0 1100 0 1340 100 1440 392

19 4122 600 0 1100 0 1100 100 1000 0 1120 128 1192 404

20 3720 5220 3400 6850 4130 6830 3440 9090 8610 3000 5121 3279 4090

21 6225 0 188 2000 0 500 0 2000 936 1764 0 1764 1431

22 3380 1800 0 0 0 700 0 2200 0 800 420 780 684

23 6202 3000 1758 6116 2981 2426 1440 1886 1942 600 542 58 450

24 4136 600 0 1100 0 1100 0 1100 0 1600 876 1024 81125 4127 600 0 1100 0 1100 0 1500 494 1206 492 714 582

26 3528 1000 0 3050 717 933 0 1000 813 187 0 0 0

27 3366 1520 1144 1880 192 2688 1280 1000 456 1344 1512 532 292

28 3367 1090 330 2260 800 2460 730 1000 1262 538 450 788 650

29 3526 1500 0 3000 1177 323 113 350 200 150 18 0 0

30 6151 4000 3731 5586 2994 0 1892 358 511 2647 0 2647 2302

31 3435 728 240 0 0 1000 0 2500 444 0 0 600 354

32 4126 600 0 1100 100 1000 244 956 388 768 332 436 204

33 3344 880 278 0 0 1032 0 2032 0 750 960 990 876

34 3379 1300 0 0 0 600 0 1100 0 750 480 470 264

35 3457 0 0 400 0 800 0 400 0 800 0 1200 14436 3455 0 0 400 0 800 0 400 0 800 0 1200 156

37 3473 0 0 400 0 800 0 400 0 800 0 1200 186

38 3598 500 258 742 180 1062 474 500 0 1000 0 1500 1146

39 3527 700 0 2250 413 637 332 500 409 91 0 0 0

40 3513 1000 0 2000 1280 720 88 0 0 0 0 2000 1368

41 3512 730 0 1730 924 806 0 0 0 0 0 2000 1449

42 3569 1310 90 0 0 150 0 650 0 450 0 550 174


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43 3358 1480 280 0 0 220 0 1020 0 800 384 816 828

44 6284 5716 5588 5132 3612 3120 3072 3048 1946 0 0 0 0

45 3423 2200 880 0 0 1000 60 940 408 0 0 0 0

46 6282 400 0 3600 2872 1198 841 957 597 1560 640 1520 1507

47 6145 6718 4604 3215 2038 0 98 352 856 1000 816 684 786

48 6278 500 0 1000 0 1500 800 300 0 300 110 190 170

49 6160 0 0 300 0 600 0 600 0 600 0 600 0

50 3472 0 0 400 0 800 0 400 192 608 0 1008 372

51 6171 1634 1180 0 0 780 396 1234 72 0 0 1000 456

52 4120 400 0 400 68 332 0 332 0 582 72 810 192

53 3599 500 306 696 306 890 306 500 294 706 0 1206 836

54 3715 1040 590 820 270 550 0 800 920 1680 1290 2740 2166

55 6170 1980 1100 0 0 2320 360 4460 3980 0 984 0 0

56 3751 860 540 1570 910 1760 700 500 610 900 790 1110 950

57 3453 0 0 400 0 800 0 400 0 800 390 810 654

58 3221 700 0 1200 575 1125 0 625 900 725 875 350 275

59 3570 800 354 0 0 500 0 1000 348 200 36 264 0

60 3520 0 0 0 0 0 0 2000 0 0 0 0 0

61 3536 0 0 0 0 0 0 0 0 0 0 2000 0

62 4135 400 0 900 116 784 220 564 464 300 180 220 260

63 3383 1000 429 2400 937 63 0 550 721 0 0 0 0

64 6236 0 0 0 0 0 0 600 0 600 0 1200 486

65 3337 400 0 0 0 500 0 1000 0 0 0 0 0

66 3748 0 0 500 0 1500 324 1676 1602 122 108 600 522

67 6228 775 905 0 0 2000 300 1700 1477 223 0 223 409

68 3357 730 280 0 0 500 0 1000 300 0 0 0 0

69 6198 1200 258 950 290 652 654 0 0 0 0 0 0

70 3726 620 610 700 460 1440 190 900 750 800 830 570 620

71 6169 2700 1780 0 0 2560 1652 1408 1500 0 180 0 0

72 6215 1383 297 2586 2509 359 841 0 0 431 0 431 0

73 3280 4920 4920 6810 6180 6630 4490 8640 8464 8276 8576 6200 7338

74 6237 100 0 0 0 380 0 980 600 380 0 1280 1153

75 3227 700 600 0 0 380 0 780 792 500 216 884 288

76 6135 0 0 200 0 500 0 500 336 164 0 164 0

77 6235 359 0 0 0 680 0 680 536 144 143 0 0

78 3732 400 0 0 0 500 0 500 228 0 0 0 0

79 3103 620 250 0 0 550 252 1098 684 300 264 0 0

80 6157 2400 2129 270 160 750 589 161 80 981 758 523 255

81 3107 0 0 500 0 500 0 500 420 0 0 0 082 6269 200 0 176 504 183 0 183 243 410 291 909 0

83 6259 0 0 0 0 0 0 0 0 500 0 800 288

84 3232 0 0 300 0 300 0 2800 2400 0 0 0 0

85 6161 0 0 200 200 200 200 200 200 200 200 200 200

86 3101 500 0 200 0 1200 996 1050 984 0 0 0 0

87 6289 0 0 0 0 0 0 0 0 2502 1631 871 804

88 3252 600 610 200 0 700 0 1100 1064 200 192 0 0


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89 3208 930 250 0 0 500 288 612 600 0 0 0 0

90 6156 0 0 100 0 250 75 525 520 530 0 530 442

91 3354 1250 370 0 0 0 0 0 0 0 0 0 0

92 3562 400 0 500 378 1522 954 736 930 100 0 0 120

93 3730 0 0 800 800 0 0 0 0 0 0 0 0

94 3267 500 480 0 0 500 0 900 624 0 0 0 0

95 3733 140 0 140 0 140 117 23 0 0 0 460 0

96 6227 0 0 0 0 122 0 1922 1630 292 0 3292 3231

97 3240 5064 4800 7264 4840 7424 8020 2404 2690 2300 3220 1080 1220

98 3417 10 0 0 0 0 0 700 130 570 470 0 0

99 6211 0 0 300 0 300 0 300 0 300 528 0 0

100 3343 2080 1712 0 0 100 0 100 0 100 0 100 102

101 6175 1389 799 590 463 727 662 322 591 0 0 150 0

102 3735 140 0 140 0 140 67 73 66 0 0 300 0

103 3364 0 0 0 0 0 0 0 0 500 136 864 600

104 6194 0 0 5000 4572 428 229 199 0 5500 5379 0 386

105 3418 68 0 0 0 0 0 500 0 500 492 0 42

106 4129 0 0 0 0 0 0 0 0 200 16 334 0

107 3262 1000 770 1230 1080 1150 1030 0 0 0 0 0 0

108 3263 500 500 0 0 0 0 0 0 0 0 0 0

109 3456 500 500 0 0 0 0 0 0 0 0 0 0

110 3345 800 720 0 0 0 0 500 0 0 0 0 84

111 3729 0 0 0 0 0 0 0 0 0 0 600 132

112 4314 1096 996 3000 2880 12 288 3324 2976 1084 945 3139 3108

113 3365 0 0 0 0 0 0 500 376 624 310

114 6127 0 0 100 0 100 0 500 576 600 324 676 646

115 3382 0 0 0 0 0 0 750 425 325 175 0 59

116 3511 4906 3906 5710 5562 5798 4080 1000 3966 648 1086 3412 2466

117 3226 400 400 0 0 0 0 0 0 0 0 0 0

118 3360 400 400 0 0 0 0 0 0 0 0 0 0

119 3361 400 400 0 0 0 0 0 0 0 0 0 0

120 3736 0 0 0 0 0 0 0 0 200 200 200 200

121 3128 1000 600 0 0 0 0 500 504 0 0 0 0

122 6186 170 100 170 180 0 0 0 0 260 0 260 204

123 3419 32 0 0 0 0 0 300 0 300 240 0 36

124 6178 0 0 0 0 0 0 0 0 300 300 50 50

125 3725 860 520 0 0 0 10 0 0 0 0 0 0

126 6162 0 0 1810 1218 592 806 0 0 150 203 0 0

127 3260 120 0 0 0 500 488 512 324 0 0 0 0128 3749 0 0 1000 950 1550 1470 1080 990 880 680 1200 1310

129 6154 3289 2616 673 710 0 339 0 0 0 0 0 0

130 3317 700 444 0 0 0 0 0 0 0 0 0 0

131 3721 950 1090 800 710 890 870 720 720 700 500 1200 1130

132 6261 0 0 0 0 0 0 0 0 200 0 200 163

133 3228 130 0 0 0 0 0 500 396 0 0 0 0

134 3229 300 0 0 0 0 0 0 0 0 0 0 72


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135 4133 600 0 1100 756 444 270 174 635 0 442 0 0

136 3427 0 0 0 0 200 200 0 0 0 0 0 0

137 6184 0 0 0 0 0 0 0 0 100 0 500 400

138 6240 0 0 0 0 0 0 0 0 0 0 500 300

139 3424 1400 1206 0 0 0 0 0 0 0 0 0 0

140 3234 760 830 500 200 300 70 1730 2060 820 780 1050 1036

141 3246 500 485 200 144 56 0 56 0 0 0 0 0

142 6131 150 160 300 240 60 0 60 0 0 0 119 120

143 6283 7652 5568 6084 7310 2880 3516 5764 5685 0 132 0 0

144 3452 500 340 0 0 0 0 0 0 0 0 0 0

145 3438 0 0 0 0 150 0 150 180 0 0 300 288

146 4117 0 0 0 0 50 50 50 50 50 50 0 0

147 3484 0 0 0 0 0 0 0 0 0 0 100 100

148 3416 70 70 0 0 0 0 0 0 0 0 0 0

149 6193 0 0 0 0 0 0 0 0 0 0 2000 2000

150 3102 0 0 0 0 0 0 0 0 500 500 0 0

151 6144 1100 900 350 550 0 0 0 0 0 0 300 300

152 3476 260 260 0 0 0 0 0 0 0 0 0 0

153 3175 200 200 0 0 0 0 0 0 0 0 0 0

154 3353 180 180 0 0 0 0 0 0 0 0 0 0

155 3475 1600 1836 0 0 224 0 224 212 0 0 0 0

156 6260 0 0 0 0 0 0 0 0 500 500 0 0

157 3251 0 0 0 0 150 150 0 0 0 0 0 0

158 3350 0 0 0 0 0 0 0 0 400 400 0 0

159 3351 0 0 0 0 0 0 0 0 600 600 0 0

160 3737 0 0 0 0 0 0 0 0 150 150 0 0

161 6204 300 300 220 80 0 80 0 0 0 0 240 300

162 6212 0 0 1500 1500 1000 1000 0 0 0 0 0 0

163 3241 0 0 0 0 0 0 0 0 0 0 50 60

164 6138 180 220 200 0 200 192 8 192 0 0 0 0

165 6268 500 248 270 543 0 0 0 0 0 0 0 0

166 4115 0 0 0 0 0 0 0 52 0 0 0 0

167 6190 0 0 0 0 0 0 0 91 150 0 150 265

168 4309 0 0 0 0 0 0 0 100 0 0 0 0

169 3714 0 0 0 0 0 0 0 0 25 0 0 140

170 4321 1000 920 2000 1950 0 0 600 0 0 0 500 1368

171 6257 0 25 0 60 0 0 0 0 0 50 0 20

172 4128 0 0 0 0 0 0 0 0 0 156 0 0

173 4113 0 0 0 0 100 0 100 100 100 210 0 156174 6124 0 0 200 144 56 0 56 192 0 0 48 192

175 6136 0 0 200 180 20 0 20 120 0 0 80 192

176 3129 0 0 0 0 0 0 0 0 0 0 0 180

177 3244 0 0 300 300 0 0 0 0 0 0 730 918

178 6279 0 0 0 100 0 0 0 0 0 0 0 93

179 4118 0 0 0 0 0 0 0 200 0 0 0 0

180 6216 0 0 300 430 0 75 0 0 0 0 0 0


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181 6229 959 1077 0 220 0 0 0 0 0 0 1200 1093

182 3316 1100 680 0 0 150 0 650 528 6 0 0 948

183 6132 0 0 300 216 84 60 24 0 0 0 84 476

184 3700 0 0 0 0 0 0 0 168 932 960 0 72

185 3176 0 0 0 0 0 0 0 0 0 0 0 276

186 6158 0 0 0 291 0 0 0 0 0 0 0 0

187 3245 0 0 200 204 0 0 0 0 0 0 539 828

188 6143 2300 2380 920 1055 565 619 546 635 1200 1055 745 857

189 3713 0 0 0 0 0 0 0 0 0 354 0 0

190 3224 300 810 0 0 0 0 0 0 0 0 0 0

191 3247 150 150 0 0 0 0 0 0 0 0 0 648

192 3900 4522 4160 5000 4416 7234 5328 9306 11481 4325 4848 2627 4018

193 3220 0 1560 1740 1296 84 0 84 236 0 0 3050 3360

194 6133 1000 1830 2040 2796 8 0 8 0 0 0 0 0

195 3711 6124 6286 7428 7650 8278 5198 9000 11402 8598 9740 1858 2824

196 6288 0 0 0 0 0 0 0 0 2080 4704 0 648

197 3289 4192 4872 2000 2769 4520 6334 0 0 0 0 1000 1152

198 3728 8820 7554 13266 14511 8795 9120 6675 7840 5680 7416 4714 5414

199 4315 270 3780 1600 1331 270 420 0 0 0 0 0 552

200 6241 3140 4470 8170 8210 7460 7780 5080 8280 1850 3206 3244 3636

201 6213 5000 4770 0 1798 0 0 12300 13099 0 0 7200 11668

202 3601 0 4050 200 975 0 3750 6250 7512 5800 5600 4200 4055

203 6226 5000 3921 0 2220 11114 20147 16167 16595 15500 21560 2200 2789

Total 222168 154119 252657 158864 267603 154674 248765 209795 187781 151738 175828 15065

Annexure 2 Planned V/s Actual Production: Production at Par Optimization

Sr.No.

Product Code Plan Production Actual Production

1. 6204 760 760

2. 6161 1000 1000

3. 3730 800 800

4. 3263 500 500

5. 3456 500 500

6. 3226 400 400

7. 3360 400 400

8. 3361 400 400

9. 3736 400 400

10 3427 200 200

11. 3484 100 100

12. 3416 70 70

13. 3251 150 150

14. 3350 400 400

15. 3351 600 600


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16. 3737 150 150

17. 6212 2500 2500

18. 6178 350 350

19. 4117 150 150

20. 6193 2000 2000

21. 3102 500 500

22. 6144 1750 1750

23. 3476 260 260

24. 3175 200 200

25. 3353 180 180

26. 3475 2048 2048

27. 6260 500 500

Total 17268 17268

Annexure 3: Analysis of Planned V/s Actual Production: Underproduction Optimization

Sr. No. Code Total Deviation AverageProd

Deviationin days

%ageContribution

Cumulative%agePlan Actual

1 3558 54998 14901 40097 2484 -484 9.08 9.08

2 3504 58430 27344 31086 4557 -205 7.04 16.12

3 3543 36846 12420 24426 2070 -354 5.53 21.65

4 3712 98600 82873 15727 13812 -34 3.56 25.21

5 6222 29880 14776 15104 2463 -184 3.49 28.7

6 3542 28272 14692 13580 2449 -166 3.07 31.77

7 3510 16124 3214 12910 536 -723 2.94 34.71

8 3549 31128 18380 12748 3063 -125 2.89 37.6

9 3371 13552 2203 11349 367 -927 2.56 40.16

10 6201 10500 0 10500 0 0 2.39 42.55

11 3407 10350 0 10350 0 0 2.34 44.89

12 4119 7778 270 7508 45 -5005 1.69 46.58

13 3519 12430 5904 6526 984 -199 1.52 48.1

14 4134 7626 1184 6442 197 -979 1.45 49.55

15 3329 6616 770 5846 128 -1367 1.36 50.91

16 6203 13642 7889 5753 1315 -131 1.30 52.21

17 3727 34096 28454 5642 4742 -36 1.27 53.4818 4123 6080 492 5588 82 -2044 1.26 54.74

19 4122 6112 632 5480 105 -1561 1.24 55.98

20 3720 34269 28791 5478 4799 -34 1.23 57.21

21 6225 8028 2555 5473 426 -386 1.23 58.44

22 3380 6280 1104 5176 184 -844 1.17 59.61

23 6202 14086 9113 4973 1519 -98 1.12 60.73

24 4136 6524 1687 4837 281 -516 1.09 61.82


15/18


88

25 4127 6220 1568 4652 261 -534 1.07 62.89

26 3528 6170 1530 4640 255 -546 1.05 63.94

27 3366 8964 4876 4088 813 -151 0.95 64.89

28 3367 8136 4222 3914 704 -167 0.92 65.81

29 3526 5323 1508 3815 251 -455 0.88 66.69

30 6151 15238 11430 3808 1905 -60 0.86 67.55

31 3435 4828 1038 3790 173 -657 0.85 68.4

32 4126 4860 1268 3592 211 -510 0.82 69.22

33 3344 5684 2114 3570 352 -304 0.80 70.02

34 3379 4220 744 3476 124 -841 0.79 70.81

35 3457 3600 144 3456 24 -4320 0.78 71.59

36 3455 3600 156 3444 26 -3974 0.78 72.37

37 3473 3600 186 3414 31 -3304 0.77 73.14

38 3598 5304 2058 3246 343 -284 0.74 73.88

39 3527 4178 1154 3024 192 -472 0.69 74.57

40 3513 5720 2736 2984 456 -196 0.68 75.25

41 3512 5266 2373 2893 396 -219 0.66 75.91

42 3569 3110 264 2846 44 -1940 0.64 76.55

43 3358 4336 1492 2844 249 -343 0.64 77.19

44 6284 17016 14218 2798 2370 -35 0.63 77.82

45 3423 4140 1348 2792 225 -373 0.63 78.45

46 6282 9235 6457 2778 1076 -77 0.62 79.07

47 6145 11969 9198 2771 1533 -54 0.62 79.69

48 6278 3790 1080 2710 180 -452 0.61 80.3

49 6160 2700 0 2700 0 0 0.61 80.91

50 3472 3216 564 2652 94 -846 0.60 81.51

51 6171 4648 2104 2544 351 -218 0.59 82.1

52 4120 2856 332 2524 55 -1368 0.57 82.67

53 3599 4498 2048 2450 341 -215 0.55 83.22

54 3715 7630 5236 2394 873 -82 0.54 83.76

55 6170 8760 6424 2336 1071 -65 0.52 84.28

56 3751 6700 4500 2200 750 -88 0.49 84.77

57 3453 3210 1044 2166 174 -373 0.49 85.26

58 3221 4725 2625 2100 438 -144 0.47 85.73

59 3570 2764 738 2026 123 -494 0.45 86.18

60 3520 2000 0 2000 0 0 0.45 86.63

61 3536 2000 0 2000 0 0 0.45 87.0862 4135 3168 1240 1928 207 -280 0.43 87.51

63 3383 4013 2087 1926 348 -166 0.43 87.94

64 6236 2400 486 1914 81 -709 0.43 88.37

65 3337 1900 0 1900 0 0 0.43 88.8

66 3748 4398 2556 1842 426 -130 0.41 89.21

67 6228 4921 3091 1830 515 -107 0.41 89.62


16/18


89

68 3357 2230 580 1650 97 -512 0.37 89.99

69 6198 2802 1202 1600 200 -240 0.36 90.35

70 3726 5030 3460 1570 577 -82 0.35 90.7

71 6169 6668 5112 1556 852 -55 0.35 91.05

72 6215 5190 3647 1543 608 -76 0.34 91.39

73 3280 41476 39968 1508 6661 -7 0.35 91.74

74 6237 3120 1753 1367 292 -140 0.33 92.07

75 3227 3244 1896 1348 316 -128 0.30 92.37

76 6135 1528 336 1192 56 -639 0.27 92.64

77 6235 1863 679 1184 113 -314 0.27 92.91

78 3732 1400 228 1172 38 -925 0.26 93.17

79 3103 2568 1450 1118 242 -139 0.25 93.42

80 6157 5085 3971 1114 662 -50 0.25 93.67

81 3107 1500 420 1080 70 -463 0.24 93.91

82 6269 2061 1038 1023 173 -177 0.23 94.14

83 6259 1300 288 1012 48 -633 0.22 94.36

84 3232 3400 2400 1000 400 -75 0.22 94.58

85 3101 2950 1980 970 330 -88 0.22 94.8

86 6289 3373 2435 938 406 -69 0.21 95.01

87 3252 2800 1866 934 311 -90 0.21 95.22

88 3208 2042 1138 904 190 -143 0.21 95.43

89 6156 1935 1037 898 173 -156 0.20 95.63

90 3354 1250 370 880 62 -428 0.19 95.82

91 3562 3258 2382 876 397 -66 0.19 96.01

92 3267 1900 1104 796 184 -130 0.18 96.19

93 3733 903 117 786 20 -1209 0.18 96.37

94 6227 5628 4861 767 810 -28 0.17 96.54

95 3240 25536 24790 746 4132 -5 0.16 96.7

96 3417 1280 600 680 100 -204 0.16 96.86

97 6211 1200 528 672 88 -229 0.16 97.02

98 3343 2480 1814 666 302 -66 0.15 97.17

99 6175 3178 2515 663 419 -47 0.15 97.32

100 3735 793 133 660 22 -893 0.14 97.46

101 3364 1364 736 628 123 -154 0.14 97.6

102 6194 11127 10566 561 1761 -10 0.13 97.73

103 3418 1068 534 534 89 -180 0.13 97.86

104 4129 534 16 518 3 -5828 0.12 97.98105 3262 3380 2880 500 480 -31 0.12 98.1

106 3345 1300 804 496 134 -111 0.11 98.21

107 3729 600 132 468 22 -638 0.11 98.32

108 4314 11655 11193 462 1866 -7 0.10 98.42

109 3365 1124 686 438 114 -115 0.10 98.52

110 6127 1976 1546 430 258 -50 0.09 98.61


17/18


90

111 3382 1075 659 416 110 -114 0.09 98.7

112 3511 21474 21066 408 3511 -3 0.09 98.79

113 3128 1500 1104 396 184 -65 0.08 98.87

114 6186 860 484 376 81 -140 0.08 98.95

115 3419 632 276 356 46 -232 0.08 99.03

116 3725 860 530 330 88 -112 0.08 99.11

117 6162 2552 2227 325 371 -26 0.07 99.18

118 3260 1132 812 320 135 -71 0.07 99.25

119 3749 5710 5400 310 900 -10 0.07 99.32

120 6154 3962 3665 297 611 -15 0.06 99.38

121 3317 700 444 256 74 -104 0.06 99.44

122 3721 5260 5020 240 837 -9 0.06 99.5

123 6261 400 163 237 27 -262 0.05 99.55

124 3228 630 396 234 66 -106 0.05 99.6

125 3229 300 72 228 12 -570 0.05 99.65

126 4133 2318 2103 215 351 -18 0.04 99.69

127 6184 600 400 200 67 -90 0.04 99.73

128 6240 500 300 200 50 -120 0.04 99.77

129 3424 1400 1206 194 201 -29 0.04 99.81

130 3234 5160 4976 184 829 -7 0.04 99.85

131 3246 812 629 183 105 -52 0.04 99.89

132 6131 689 520 169 87 -59 0.03 99.92

133 6283 22380 22211 169 3702 -1 0.03 99.95

134 3452 500 340 160 57 -85 0.03 99.98

135 3438 600 468 132 78 -51 0.02 100

Total 1050366 608547 441819

Annexure 4: Analysis of Planned V/s Actual Production: Overproduction Optimization

Sr. No. CodeTotal

Deviation AverageProd

Deviation indays

%ageContributio

n

Cumulative%age

Sr. No.

1 3241 50 60 10 10 30 0.01 0.01

2 6138 588 604 16 101 5 0.02 0.04

3 6268 770 791 21 132 5 0.03 0.07

4 4115 0 52 52 9 180 0.08 0.15

5 6190 300 356 56 59 28 0.08 0.23

6 4309 0 100 100 17 180 0.15 0.38

7 3714 25 140 115 23 148 0.17 0.55

8 4321 4100 4238 138 706 6 0.21 0.76

9 6257 0 155 155 26 180 0.23 0.99

10 4128 0 156 156 26 180 0.23 1.22

11 4113 300 466 166 78 64 0.25 1.47

12 6124 360 528 168 88 57 0.25 1.72


18/18


91

13 6136 320 492 172 82 63 0.26 1.98

14 3129 0 180 180 30 180 0.27 2.25

15 3244 1030 1218 188 203 28 0.28 2.53

16 6279 0 193 193 32 180 0.29 2.82

17 4118 0 200 200 33 180 0.3 3.12

18 6216 300 505 205 84 73 0.31 3.43

19 6229 2159 2390 231 398 17 0.35 3.77

20 3316 1906 2156 250 359 21 0.37 4.15

21 6132 492 752 260 125 62 0.39 4.53

22 3700 932 1200 268 200 40 0.4 4.94

23 3176 0 276 276 46 180 0.41 5.35

24 6158 0 291 291 49 180 0.44 5.78

25 3245 739 1032 293 172 51 0.44 6.22

26 6143 6276 6601 325 1100 9 0.49 6.71

27 3713 0 354 354 59 180 0.53 7.24

28 3224 300 810 510 135 113 0.76 8

29 3247 150 798 648 133 146 0.97 8.97

30 3900 33014 34251 1237 5709 7 1.85 10.82

31 3220 4958 6452 1494 1075 42 2.23 13.05

32 6133 3056 4626 1570 771 61 2.35 15.4

33 3711 41286 43100 1814 7183 8 2.71 18.11

34 6288 2080 5352 3272 892 110 4.89 23.01

35 3289 11712 15127 3415 2521 41 5.11 28.12

36 3728 47950 51855 3905 8643 14 5.84 33.96

37 4315 2140 6083 3943 1014 117 5.9 39.85

38 6241 28944 35582 6638 5930 34 9.93 49.78

39 6213 24500 31335 6835 5223 39 10.22 60

40 3601 16450 25942 9492 4324 66 14.2 74.2

41 6226 49981 67232 17251 11205 46 25.8 100

Total 287118 353971

Documents

Optimizing the Unevenness in Production Scheduling Through Mathematical Approach a Case Study