Bohr. Omrp. BOHR International Journal of Operations Management Research and Practices Bohr. Omrp. 2583-6420 BOHR 10.54646/bijomrp.2023.20 Case Study Inventory planning for continuous demand materials – A case study in chip manufacturing industry Nhu Phong Nguyen * Phuong Nguyen Nguyen Industrial Systems Engineering, HCM University of Technology, VNU-HCM, Vietnam *Correspondence: Phong Nguyen Nhu, nnphong@hcmut.edu.vn 13 10 2023 2 1 70 76 02 09 2023 11 09 2023 Copyright © 2023 Nhu and Phuong. 2023 Nhu and Phuong

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Inventory is often a valuable asset of a business. Inventory planning is an important function in a manufacturing organization. Improper inventory planning can lead to excess inventory, increasing inventory costs, or lack of inventory, leading to reduced service levels. This article discusses planning inventory for continuous demand spare part materials for a company that assembles microprocessor chips. Spare part materials are classified according to ABC analysis; appropriate planning models for each type of material are used with the goals of minimizing inventory costs and satisfying a desired level of demand.

 inventory planning working stock safety stock ABC analysis fixed order size systems EOQ fixed order interval systems EOI multiple items EOI 1. Introduction

Inventory is a valuable asset of a business. The company under study is a microprocessor chip manufacturing company. The company‘s current inventory cost accounts for 60% of its total production cost. The company considers inventory planning an important function to help cut costs.

The factory operates continuously. The products, after going through the assembly process, will go to the most rigorous inspection steps. With regard to inspection machines, it should be ensured that there are enough spare parts for maintenance so as not to lead to the machine stopping; if the machine stops for a long time, it will lead to late delivery, affecting the company’s service level.

Currently, the maintenance spare parts are not properly planned, leading to the situation that some maintenance spare parts are redundant, increasing inventory costs, some parts are missing, causing the machine to stop and leading to late delivery, and there is a low service level. From 2017 to 2020, out of a total of 990 requests for spare parts to serve testing machines, there are 170 shortages of spare parts. Therefore, the corresponding service level is as follows:

SL = ( 990 - 170 ) 990 = 82.82 ( % )

The 82.82% service level is too low; the company wants to increase the service level to 95%. The company has 55 types of spare parts of continuous demand. This research undertakes the planning of these spare parts, with the objective of minimizing inventory costs and ensuring a desired level of service.

 2. Research methodology 2.1. Inventory planning for continuous demand materials

Continuous demand inventories are those whose demand does not fluctuate much over time (1). Inventory planning is about answering two basic questions: when to order and how much to order. Planning models are used to answer these two basic questions. For high-value materials, the fixed order size model is often used. For average-value materials, the fixed order interval model is often used for each material. For low-value materials, the fixed order interval model for multiple items is often used.

Ferguson et al. (2) applied the EOQ model to inventory management of perishables. Nobil et al. (3) developed the reorder point for the EOQ inventory model with imperfect quality items. Goh (4) constructed an EOQ model with general demand and holding cost functions. Mokhtari (5) developed EOQ for joint complementary and substitutable items. Sebatjane (6) developed an EOQ model for growing items with imperfect quality.

 2.2. Research methodology

The materials under study are continuous demand materials that are planned according to the method of classifying materials by value and applying an appropriate model for each type of material (1). The planning process follows the following steps:

Step 1: Classifying materials according to the ABC analysis.

- Group A includes high-value materials, accounting for about 80% of the total inventory value.

- Group B includes average-value materials, accounting for about 15% of the total inventory value.

- Group C includes low-value materials, accounting for about 5% of the total inventory value.

Step 2: Planning group A materials.

Group A materials are planned according to the fixed order size FOS model, with the following two substeps:

- Planning lot size Q.

- Planning reorder points B.

Lot size Q is planned to minimize inventory costs, according to the economic order size EOQ model as follows:

Q = 2 ⁢ C ⁢ R H = 2 ⁢ C ⁢ R P ⁢ F

where:

- R: annual demand (unit/year).

- P: purchase cost ($/unit).

- C: order cost ($/order).

- H: holding cost ($/unit/year).

- F: holding coefficient (1/year). H = PF

Reorder point B is planned to ensure the desired service level, based on the distribution of demand during lead time M. Reorder point B is determined as follows:

B = μ + S = μ + Z ⁢ σ

where:

- S: safety stock

- Z: safety factor

- σ: standard deviation of lead time demand M.

- μ: expected value of lead time demand M

Assuming lead time demand M has a normal distribution, safety factors Z are defined by service levels SL by Table 1.

Safety factors Z.

SL (%) 90 91 92 93 94 95 96 97 98 99
Z 1.29 1.34 1.41 1.48 1.56 1.65 1.75 1.88 2.05 2.33

Step 3: Planning group B materials.

Group B materials are planned according to the fixed order interval FOI model, with the following two substeps:

- Planning order interval T.

- Planning maximum inventory level E

The order cycle T is planned to minimize inventory costs, according to the economic order interval model EOI as follows:

T = 2 ⁢ C H ⁢ R = 2 ⁢ C P ⁢ F ⁢ R

where:

- R: annual demand (unit/year).

- P: purchase cost ($/unit).

- C: order cost ($/order).

- H: holding cost ($/unit/year).

- F: holding coefficient (1/year). H = PF

The maximum inventory level E is planned to ensure the desired level of service, based on the distribution of demand over the total lead time and cycle time N. The maximum inventory level E is determined as follows:

E = μ + S = μ + Z ⁢ σ

where:

- S: safety stock

- Z: safety factor

- σ: standard deviation of N.

- μ: expected value of N.

Assuming N has a normal distribution, safety factors are defined by service levels by the above table.

Step 4: Planning group C materials.

Group C materials are planned according to the multiple-items fixed order interval model, MFOI, with the following two substeps:

- Planning order interval T for all items in the group.

- Planning maximum inventory level E for each item in the group.

The order cycle T is planned to minimize inventory costs, according to the multiple-items economic order interval model, MEOI, as follows:

T = 2 ⁢ ( C + nc ) F ⁢ ∑ i = 1 n P i ⁢ R i

where:

- n: total number of C-type materials.

- Ri: annual demand of item i (unit/year).

- Pi: purchase cost of item i ($/unit).

- C: integrated order cost for all items ($/order).

- c: partial order cost for each item ($/order).

- F: holding coefficient (1/year).

The maximum inventory level Ei of material i is planned to ensure the desired service level, based on the distribution of demand over the total lead time and cycle time Ni of material i. The maximum inventory level Ei is determined as follows:

E i = μ i + S i = μ i + Z ⁢ σ i

where:

- Si: safety stock of item i.

- Z: safety factor.

- σi: standard deviation of Ni.

- μi: expected valued of Ni.

Assuming Ni has a normal distribution, safety factors are defined by service levels by the above table.

 3. ABC analysis for the company materials

The company has 55 continuous demand spare parts. Data of annual demand R and unit price P are collected, and total annual value RP, percent value PV, and cumulative percent value CPV are calculated as shown in Table 2, (7).

ABC analysis for the company materials.

i Spare parts R (u) P ($/u) RP ($) PV (%) CPV (%) Group
1 P3TIU394 850 2259 1920150 4.68 4.68 A
2 P1TIU379 800 2259 1807200 4.40 9.08
3 P18AP598 800 2255 1804000 4.39 13.47
4 P18TIU378 210 8576.26 1801015 4.39 17.86
5 P28TIU344 200 8576.26 1715252 4.18 22.04
6 P3TIU348 760 2250 1710000 4.16 26.2
7 P44TESTER122 300 5091.94 1527582 3.72 29.92
8 P18TESTER191 290 5091.94 1476663 3.60 33.52
9 P1TESTER125 280 4968.81 1391267 3.39 36.91
10 P18TIU371 500 2695 1347500 3.28 40.19
11 P3TESTER102 300 4308.72 1292616 3.15 43.34
12 P1TIU360 155 7871.2 1220036 2.97 46.31
13 P44TIU301 300 4007.3 1202190 2.93 49.24
14 P3TIU354 150 7871.2 1180680 2.88 52.12
15 P1TESTER105 260 4308.72 1120267 2.73 54.85
16 P28TESTER185 200 5091.94 1018388 2.48 57.33
17 P28AP511 380 2490 946200 2.30 59.63
18 P3TESTER175 160 4968.81 795010 1.94 61.57
19 P18TIU376 60 13207.49 792449 1.93 63.5
20 P1TIU400 350 2131.39 745987 1.82 65.32
21 P3TIU362 50 13505.97 675299 1.64 66.96
22 P28TIU357 50 13207.49 660375 1.61 68.57
23 P44TIU388 50 13207.49 660375 1.61 70.18
24 P1TESTER200 266 2478.26 659217 1.61 71.79
25 P18TESTER190 50 11964.01 598201 1.46 73.25
26 P28TIU320 230 2512.37 577845 1.41 74.66
27 P44AP538 560 900 504000 1.23 75.89
28 P28TESTER100 35 13830 484050 1.18 77.07
29 P44TESTER165 35 13830 484050 1.18 78.25
30 P18TESTER103 35 13830 484050 1.18 79.43
31 P1HK620 1400 340 476000 1.16 80.59
32 P18HK645 1400 340 476000 1.16 81.75 B
33 P44HK656 1400 340 476000 1.16 82.91
34 P3TIU365 1000 450 450000 1.10 84.01
35 P1TIU340 1000 450 450000 1.10 85.11
36 P3HK677 1700 250 425000 1.03 86.14
37 P3TESTER192 170 2478.26 421304 1.03 87.17
38 P18TIU386 900 452 406800 0.99 88.16
39 P44TESTER178 34 11964.01 406776 0.99 89.15
40 P1AP554 200 2007 401400 0.98 90.13
41 P44TIU376 180 2162 389160 0.95 91.08
42 P3AP587 700 547.68 383376 0.93 92.01
43 P28TIU390 160 2351.97 376315 0.92 92.93
44 P28TESTER199 30 11964.01 358920 0.87 93.8
45 P44TIU340 960 337.63 324125 0.79 94.59
46 P44TIU302 1500 209 313500 0.76 95.35
47 P1AP590 500 547.68 273840 0.67 96.02 C
48 P44TIU304 150 1782 267300 0.65 96.67
49 P18TIU381 150 1662 249300 0.61 97.28
50 P28HK691 600 400 240000 0.58 97.86
51 P44TIU314 800 289 231200 0.56 98.42
52 P1AP577 200 1112 222400 0.53 98.95
53 P3AP582 190 1112 211280 0.5 99.45
54 P28TIU385 300 621.6 186480 0.44 99.89
55 P18TIU327 110 440 48400 0.11 100
Total 41066787.8 100.00

The table above shows that out of 55 continuous supplies, there are 31 group A materials, accounting for about 80% of the total inventory value, 15 group B materials accounting for about 15% of the total inventory value, and 9 group C materials, accounting for about 5% of total inventory value.

 4. Inventory planning for A items

According to the above planning model, Group A materials are planned according to the FOS model. Among the 31 group A materials, P3TIU394 is selected for planning, and other materials are similarly planned.

4.1. Lot size Q planning

Lot size Q is planned according to the following steps:

- Collect data and estimate parameters.

- Plan the lot size.

The parameters of the model include R, P, C, and H. The average annual demand R and unit purchase cost P of the material are collected as follows:

R = 850 ⁢ ( u / y ) P = 2259 ⁢ ( $ / u )

Order costs are analyzed into many components (8); these components are estimated as shown in Table 3. After the component costs are estimated, the order cost is estimated by summing these component costs.

Estimation of order cost.

Cost components Value ($/order)
Cost of finding suppliers Search costs 20
Contact costs 20
Equipment cost 10
Costs to create orders Paper and ink costs 4
Phone costs 5
Fax machine costs 4
Printer cost 2
Facility cost 10
Software support costs 50
Import and export costs 200
Receiving cost Inspection cost 10
Warehouse import cost 10
Labor costs 10
Total 355

The holding cost H can be estimated through the purchasing cost P and the holding coefficient F.

H = P ⁢ F

The holding coefficient F is analyzed into many components (9); these components are estimated as shown in Table 4. After the components are estimated, the holding coefficient is estimated by summing these components.

Estimation of holding coefficient.

Cost components Percentage
Capital costs Loan costs 5%
Loss of capital opportunity 3%
Warehouse costs Insurance 1%
Tax 0%
Machinery cost 1%
Labor cost 0.5%
Storage space costs Company space costs 3%
Outsourcing space costs 3%
Risk and opportunity loss Obsolete 1%
Damage in storage 1%
Shortage 1%
Total 20%

With the parameters estimated above, the optimal lot size of P3TIU394 is determined as follows:

Q * = EOQ = 2 ⁢ C ⁢ R PF = 2 * ⁢ 355 * ⁢ 850 2259 * ⁢ 0.2 = 36.55 ≈ 37 ⁢ ( u ) 4.2. Reorder point planning

Reorder point B is planned according to the following steps:

- Collect data of service levels and lead time M.

- Estimate parameters Z, μ, and σ.

- Plan safety stock S and reorder point B.

At a service level of 95%, the factor of safety is determined as follows:

Z = 1 , 64

Data of lead time demand M are collected; the expectation and standard deviation of M are estimated with the following results:

μ = 153 , σ = 16

Safety stock S and reorder point B are calculated as follows:

S = Z ⁢ σ = 1 , 64 × 16 = 26 , 24 B = μ + S = 153 +  26 , 24 = 179 , 24

Collect data, estimate parameters, and do the same calculation for the remaining materials. Inventory plans for group A materials are all shown in Table 5.

Inventory plans for group A materials.

i Materials R (u/y) P ($/u) L (d) Q (u) B (u)
1 P3TIU394 850 2259 63 37 148
2 P1TIU379 800 2259 63 35 139
3 P18AP598 800 2255 63 35 139
4 P18TIU378 210 8576.26 133 9 77
5 P28TIU344 200 8576.26 133 9 73
6 P3TIU348 760 2250 35 35 73
7 P44TESTER122 300 5091.94 42 14 35
8 P18TESTER191 290 5091.94 42 14 34
9 P1TESTER125 280 4968.81 133 14 103
10 P18TIU371 500 2695 35 26 48
11 P3TESTER102 300 4308.72 133 16 110
12 P1TIU360 155 7871.2 42 8 18
13 P44TIU301 300 4007.3 42 16 35
14 P3TIU354 150 7871.2 42 8 17
15 P1TESTER105 260 4308.72 133 15 95
16 P28TESTER185 200 5091.94 42 12 23
17 P28AP511 380 2490 63 23 66
18 P3TESTER175 160 4968.81 133 11 59
19 P18TIU376 60 13207.49 42 4 7
20 P1TIU400 350 2131.39 42 24 40
21 P3TIU362 50 13505.97 42 4 6
22 P28TIU357 50 13207.49 42 4 6
23 P44TIU388 50 13207.49 42 4 6
24 P1TESTER200 266 2478.26 133 20 97
25 P18TESTER190 50 11964.01 98 4 13
26 P28TIU320 230 2512.37 42 18 27
27 P44AP538 560 900 56 47 86
28 P28TESTER100 35 13830 42 3 4
29 P44TESTER165 35 13830 42 3 4
30 P18TESTER103 35 13830 42 3 4
31 P1HK620 1400 340 56 121 216
5. Inventory planning for B items

According to the above planning model, group B materials are planned according to the FOI model. Among the 15 group B materials, P18HK645 is selected for planning, and other materials are similarly planned (10).

5.1. Order interval T planning

Order interval T is planned according to the following steps:

- Collect data and estimate parameters.

- Plan the order interval T

The parameters of the model include R, P, C, and H. The average annual demand R and unit purchase cost P of the material are collected as follows:

R = 1400 ⁢ ( u / y ) P = 340 ⁢ ( $ / u )

Similar to group A materials, the ordering cost of group B materials is estimated with the following results.

C = 355 ⁢ ( $ )

The holding cost H could be estimated by the holding cost factor F, which is estimated similar to the class A material above.

F =  20 %

With the above estimated parameters, the optimal ordering period of P18HK645 is determined as follows:

T * = 2 ⁢ C PFR = 2 × 355 340 × 0.2 × 1400 = 0.086 ⁢ ( year ) ≈ 31 ⁢ ( day ) 5.2. Max inventory level E

The maximum inventory level E is planned according to the following steps:

- Collect data of service level SL and demand N.

- Estimate parameters Z, μ, and σ.

- Plan safety stock S and maximum inventory E.

At the company’s required service level of 95%, the factor of safety is defined as follows:

Z = 1 , 64

The demands in total lead time and cycle time N of P18HK645 are collected, from which the expected values and standard deviations are estimated as follows:

μ =  309 , σ = 11

The amount of safety stock and the maximum inventory level are calculated as follows:

S = Z ⁢ σ = 1 , 64 × 11 = 18 , 04 E = μ + S = 309 + 18 , 04 = 327 , 04

Collect data, estimate parameters, and do the same calculation for the remaining materials. Inventory plans for group B materials are all shown in Table 6.

Inventory plans for group B materials.

i Materials P ($/u) R (u/y) L (d) T (d) E (u)
1 P18HK645 340 1400 49 31 309
2 P44HK656 340 1400 56 31 337
3 P3TIU365 450 1000 63 32 262
4 P1TIU340 450 1000 56 32 243
5 P3HK677 250 1700 49 33 385
6 P3TESTER192 2478.26 170 133 33 78
7 P18TIU386 452 900 35 34 171
8 P44TESTER178 11964.01 34 98 34 12
9 P1AP554 2007 200 42 34 42
10 P44TIU376 2162 180 105 35 69
11 P3AP587 547.68 700 133 35 324
12 P28TIU390 2351.97 160 63 35 43
13 P28TESTER199 11964.01 30 98 36 11
14 P44TIU340 337.63 960 91 38 341
15 P44TIU302 209 1500 35 39 304
6. Inventory planning for C items

According to the above planning model, the nine class C materials are planned according to the MFOI model.

6.1. Order interval T planning

Order interval T for all class C items is planned according to the following steps:

- Collect data and estimate parameters.

- Plan the order interval T.

The average annual demand Ri and unit purchase cost Pi of the materials are collected as shown in Table 7.

Average annual demand Ri and unit purchase cost Pi of the materials.

i Materials Pi ($/u) Ri (u) PiRi ($)
1 P1AP590 547.68 500 273,840
2 P44TIU304 1782 150 267,300
3 P18TIU381 1662 150 249,300
4 P28HK691 400 600 240,000
5 P44TIU314 289 800 231,200
6 P1AP577 1112 200 222,400
7 P3AP582 1112 190 211,280
8 P28TIU385 621.6 300 186,480
9 P18TIU327 440 110 48,400
Total 1,930,200

The integrated order cost C, the partial order cost c, and holding coefficient F are estimated as follows:

C = 889 ⁢ $ / o ⁢ r ⁢ d ⁢ e ⁢ r , c = 355 ⁢ $ / o ⁢ r ⁢ d ⁢ e ⁢ r , F = 20 %

The economic order cycle of all group C materials is calculated as follows:

T * = 2 ⁢ ( C + nc ) F ⁢ ∑ i = 1 n P i ⁢ R i ⁢ 2 ⁢ ( 889 + 9 * ⁢ 355 ) 0.2 * ⁢ 1930200 ⁢ 0.1455 ⁢ ( y ) ≈ 53 ⁢ ( d ) 6.2. Max inventory level E

The maximum inventory level Ei of each material is planned according to the following steps:

- Collect data on service levels SL and demand Ni.

- Estimate the parameters Z, μi, and σi.

- Plan safety inventory Si and maximum inventory level Ei.

At the company’s required service level of 95%, the factor of safety is defined as follows:

Z = 1 , 64

The demand Ni of group C materials is collected, from which the expected values and standard deviations are estimated as shown in Table 8.

Expected values and standard deviations of Ni.

i Items μ i σ i
1 P1AP590 258 11
2 P44TIU304 36 4
3 P18TIU381 39 4
4 P28HK691 167 10
5 P44TIU314 194 12
6 P1AP577 64 5
7 P3AP582 61 3
8 P28TIU385 95 9
9 P18TIU327 27 2

The amount of safety stock and the maximum stock level are calculated according to the following models.

S i = Z ⁢ σ i E i = μ i + S i

The calculation results are as shown in Table 9.

Safety stock and the maximum stock level of class C materials.

i Items S (u) Ei (u)
1 P1AP590 18 275
2 P44TIU304 7 43
3 P18TIU381 6 45
4 P28HK691 17 185
5 P44TIU314 19 213
6 P1AP577 9 73
7 P3AP582 5 66
8 P28TIU385 15 111
9 P18TIU327 4 31
7. Conclusion

The article develops inventory plans for 55 spare parts that are in constant demand for a chip manufacturing company, with the goal of minimizing inventory costs and achieving a service level of 95%. ABC analysis divides these 55 spare parts into 31 Class A materials, 15 Class B materials, and 9 Class C materials.

The 31 Class A spare parts are planned under fixed lot size models. The 15 Class B spare parts are planned according to fixed order interval models. The 9 Class C spare parts are planned according to the fixed lot size model for multiple items.

The research has the advantage of applying operation research models to achieve cost objectives and service level requirement. But the downside is that demand distributions have not been determined, so the service level may not be as calculated. In addition, the study did not apply to evaluate actual effectiveness. Future research is to determine demand distributions so that service levels can be accurately calculated. Research also needs to be applied in practice to evaluate its practical effectiveness.

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