Two stages optimization model on make or buy analysis and quality improvement considering learning and forgetting curve

Pratama, Mega Aria; Rosyidi, Cucuk Nur; Pujiyanto, Eko Article Two stages optimization model on make or buy analysis and quality improvement considering learning and forgetting curve Journal of Industrial Engineering and Management (JIEM) Provided in Cooperation with: The School of Industrial, Aerospace and Audiovisual Engineering of Terrassa (ESEIAAT), Universitat Politècnica de Catalunya (UPC) Suggested Citation: Pratama, Mega Aria; Rosyidi, Cucuk Nur; Pujiyanto, Eko (2018) : Two stages optimization model on make or buy analysis and quality improvement considering learning and forgetting curve, Journal of Industrial Engineering and Management (JIEM), ISSN 2013-0953, OmniaScience, Barcelona, Vol. 11, Iss. 4, pp. 794-813, https://doi.org/10.3926/jiem.2615 This Version is available at: https://hdl.handle.net/10419/261676 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ Journal of Industrial Engineering and Management JIEM, 2018 – 11(4): 794-813 – Online ISSN: 2013-0953 – Print ISSN: 2013-8423 https://doi.org/10.3926/jiem.2615 Two Stages Optimization Model on Make or Buy Analysis and Quality Improvement Considering Learning and Forgetting Curve Mega Aria Pratama , Cucuk Nur Rosyidi , Eko Pujiyanto Universitas Sebelas Maret Surakarta (Indonesia) [email protected], [email protected], [email protected] Received: March 2018 Accepted: July 2018 Abstract: Purpose: The aim of this research is to develop two stages optimization model on make or buy analysis and quality improvement considering learning and forgetting curve. The first stage model is developed to determine the optimal selection of process/suppliers and the component allocation to the selected process/suppliers. The second stage model deals with quality improvement efforts to determine the optimal investment to maximize Return on Investment (ROI) by taking into consideration the learning and forgetting curve. Design/methodology/approach: The research used system modeling approach by mathematically modeling a system which consists of a manufacturer with multi suppliers where the manufacturer tries to determine the best combination of their own processes and suppliers to minimize certain costs and provides funding for quality improvement efforts for their own processes and suppliers. Findings: This research provides better decisions in make or buy analysis and to improve the components by quality investment considering learning and forgetting curve. Research limitations/implications: This research has limitations concerning investment fund that assumed to be provided by the manufacturer which in the real system the fund may be provided by the suppliers. In this model, we also do not differentiate between two types of learning, namely autonomous and induced learning. Practical implications: This model can be used by a manufacturer to gain deeper insight in making decisions concerning process/suppliers selection along with component allocation and how to improve the component by investment allocation to maximize ROI. Originality/value: This paper combines two models, which in previous research both models are discussed separately. The inclusion of learning and forgetting also gives a new perspective in quality investment decision. Keywords: quality improvement, quality investment, learning and forgetting curve, return on investment To cite this article: Pratama, M.A., Rosyidi, C.N., & Pujiyanto, E. (2018). Two stages optimization model on make or buy analysis and quality improvement considering learning and forgetting curve. Journal of Industrial Engineering and Management, 11(4), 794-813. https://doi.org/10.3926/jiem.1537 -794- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 1. Introduction In a tight market competition, a manufacturing company must formulate the best strategy to win the competition. According to Mustajib and Irianto (2010), a manufacturing company has to produce not only a good product at a competitive price, but also on-time delivery and fast service to satisfy the customers. But, it becomes a challenge for manufacturing company to fulfill those requirements by improving their production eficiency. Greater eficiency will make a manufacturing company produces their product at lower cost and will get better revenue without compromising the quality (Kumar & Sosnoski, 2009). Generally, a manufacturing company will use their own resources to produce their needed component for final product assembly. It is known as in-house production. By use in-house production method, manufacturing company can maximize the utilization of their production facilities and get better control of the quality and cost. Unfortunatelly by the growth of the market, a manufacturing company is often constrained by their capacities and capabilities to fulfill the market demand. So, to overcome this problem, they usually use an instant solution called outsourcing. According to Belcourt (2006), manufacturing companies were triggered to an outsourcing option since many outsourcing companies provide services on workers, machines or even production activities. But, outsourcing decision is not an easy task. Suppliers have many uncertainties in terms of cost, quality and delivery (Teeravaraprug, 2008). Manufacturing company has to choose the suppliers that meet their standard of performance. After manufacturing company selects the appropriate suppliers, there is another problem that follows about how to allocate the components to the selected prcesses and suppliers. Rosyidi, Pratama, Jauhari, Suhardi and Hamada (2016) developed a make or buy analysis model to solve the above problems. In the model, a manufacturing company will be able not only to choose the best alternative that give the minimal cost, but also the allocation for each choosen alternative. The objective function of the model is to minimize the total cost which consists of manufacturing cost, purchasing cost, quality loss, scrap cost, and lateness cost. The manufacturing cost is resulted from the total cost of in-house production activities, while purchasing cost from the total cost of outsourcing activities. Quality loss dealt with the customer quality cost, while scrap cost dealt with the cost from discarding the component which did not conform to the specifications. Lateness cost is the penalty cost for company if they pass the due date to deliver the product to their customer (Rosyidi, Fatmawati & Jauhari, 2016). The model also considered several constraints such as capacity constraint, demand constraint, selected process constraint, stock removal constraint, process sequencing constraint and binary constraint. After manufacturing company makes decision about make or buy and its allocation, they have to maintain or even improve their product quality through quality improvement both in-house and supplier sides. Quality improvement can be done in a manufacturing company by investing some fund to their processes in order to reduce the variance of their final product. The manufacturing company has to know exactly about what kind of investment they have to make. There are some kinds of investments that can be adopted by manufacturing company. The first is technology (machine) investment. According to Dunne, Foster, Haltiwanger and Troske (2004), by investing a new machine or technology, manufacturing company will improve their product quality, productivity, and revenue. The second is human resource investment. According to Blundel, Dearden, Meghir and Sianesi (1999), human resource investment included training, workshop, recruitment etc. In this paper, learning investment is considered to improve product quality by reducing product variance (Moskowitz, Plante & Tang, 2001). In learning concept, two kinds of curves must be considered, namely learning curve and forgetting curve. Learning curve shows the increase of employee’s performances in doing their job through time. On the other hand, forgetting curve occurs when employee gets interruptions in the learning process which will decrease their performance (Jaber & Bonney, 1997). Lower product variance shows the existence of learning, while higher product variance shows the existence of forgetting. The learning and forgetting curve must be integrated in a model to get the best of quality improvement in terms of variance reduction. The best variance reduction in the -795- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 learning investment will maximize the Return on Investment (ROI). The amount of ROI will be used as the objective function of the Second Stage Model (SSM). In this research, those two models above will be solved sequentially to help manufacturing company, not only to choose optimal alternatives between make or buy decision, but also the quality improvement. In practice, this research will contribute to solve the make or buy decisions along with the component allocations and also determine the optimal variance reduction to maximize the ROI. 2. Literature Review 2.1. Previous Research on Make or Buy Deisions Make or buy problem has been attracted many researchers to determine the components that must be produced in-house or outsourced. In addition, many reseachers also have combined the make or buy problem with another topics such as tolerance design, quality loss, Analytic Hierarchy Process (AHP), etc. Chase, Greenwood, Loosli and Hauglund (1990) developed an optimization model to select a process that gives optimal component tolerance in an assembly product. The research was considered to be the earliest model in this topic. Hambali, Sapuan, Ismail and Nukman (2009) developed a model in process selection for composite manufacturing using Analytical Hierarchy Process. Mustajib and Irianto (2010) developed an integrated model for process selection and quality improvment in multi-stage process. Rosyidi, Fatmawati et al. (2016) developed a process selection model to minimize manufacturing cost, quality loss and lateness cost in a make to order manufacturing system. Supplier selection research have also attracted many researchers. For example, Feng, Wang and Wang (2001) developed an optimization model for concurrent selection of tolerance and suppliers. Teeravaraprug (2008) developed a model for outsourcing and vendor selection based on Taguchi loss function. Rezaei and Davoodi (2008) developed a deterministic, multi-item inventory model with supplier selection and imperfect quality. Sabatini, Jauhari and Rosyidi (2011) developed a supplier selection model based on tolerance allocation to minimize purchasing cost and quality loss. Rosyidi, Murtisari and Jauhari (2016) developed a concurrent optimization model for supplier’s selection, tolerance and component allocation with fuzzy quality loss. Furthermore, the research on both process and supplier selection or make or buy problem have been conducted by following reseachers. Bajec and Jakomin (2010) discussed about the importance of make or buy decisions for a company. Rosyidi, Akbar and Jauhari (2014) developed a make or buy analysis model on tolerance design to minimize manufacturing cost and quality loss. The research was based on previous models developed by Chase et al. (1990) and Feng et al. (2001). Rosyidi, Pratama, Jauhari, Suhardi and Hamada (2015) and Rosyidi, Puspitoningrum, Jauhari, Suhardi and Hamada (2016) developed a make or buy analysis model with multi-stage manufacturing process to minimize manufacturing cost and taguchi quality loss (2015) and also fuzzy quality loss (2016). Pratama and Rosyidi (2017) developed a make or buy decision model with multistage manufacturing process and supplier imperfect quality. Rosyidi, Pratama et al (2016) developed a make or buy analysis model in a multi-stage manufacturing processes. The model will become a basis for this research as the first stage model. The output of this model will become the input for the second stage model of this research. 2.2. Previous Research on Quality Improvement with Learning and Forgetting Curve Quality improvement has become the concerns of many researchers due to its importance in customer satisfaction. But, in this research we focus on quality improvement research in its relation with quality cost and investment for the quality, learning, and forgetting. Tsou and Chen (2005) and Zhu, Zhang and Tsung (2007) developed quality improvement model by considering quality cost. They developed a model to improve product quality considering production and quality cost, in terms of lot sizing decision. Bernstein and Kok (2009) developed a dynamic cost reduction through process improvement in assembly networks. -796- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 In quality improvement studies, the role of learning curve can not be ignored. Actually, learning curve has been used in many fields. For example, Womer (1979) developed a model about learning curves, production rate, and program cost. Cunningham (1980) used the learning curve as a management tool. Fine (1986) studied about quality improvement and learning curve in a productive system. Moskowitz et al. (2001) developed a model on allocation of quality improvement targets based on investments in learning. Serel, Dada, Moskowitz and Plante (2002) conducted a research about quality investment under autonomous and induced learning. Rosyidi, Jauhari, Suhardi and Hamada (2016) developed a variation reduction model for quality improvement to minimize investment and quality costs by considering suppliers’ learning curve. Later, Rosyidi, Nugroho, Jauhari, Suhardi and Hamada (2016) developed an optimization model about quality improvement through variance reduction of component by investment allocation in learning. The applications of learning curve in those researches above have not been considered forgetting curve in the model. To find a better result, we have to include not only learning curve but also forgetting curve. Learning and forgetting curves have been used in various fields of research. Li and Cheng (1994) developed a model of economic production quantity by considering learning and forgetting aspects. Jaber and Bonney (1997) conducted a study of the relationship between learning curve and forgetting curve. Jaber and Bonney (2003) developed a lot sizing model considering learning and forgetting aspects to improve product quality. Badiru (1995) conducted a multivariate analysis of learning and forgetting effects on product quality. This research, especially the SSM will develop based on learning and forgetting curves. 3. Model Development 3.1. System Description In this research, we develop two models, namely First Stage Model (FSM) and Second Stage Model (SSM). The output of FSM will become the input for SSM. FSM is an optimization model in make or buy analysis to select an alternative between in-house, outsource, or both. This model also determines the component allocation for every decision. Once the number of components are determined, those components will be inspected to ensure their quality and will be assembled into the finished product. Based on the results of the allocation, the variance of every single component is known which will be used as the input of SSM. An investment is needed to improve the component quality through variance reduction, especially the learning investment. According to Zollo and Winter (2002) learning investment is the company's effort to improve quality by doing learning and training. In the learning process, there is a time that the operators’ capability will decrease due to the interruption in production activities known as forgetting. Hence, we have to consider both learning and forgetting in variance reduction model. Moreover, SSM also considers learning cycle, which comprises of several periods. In a single learning cycle, it is assumed that there will be an interruption as the place for forgetting process. This learning cycle is useful to give a break to a learning process in every cycle. The example of break time includes worker's change of work shift and production process interruption due to no orders placed by customers. The number of learning cycles used in the system will depend on the decision of the manufacturing company. The number of learning cycles can be determined from the beginning of the process or they can be stopped when the variance reduction target has been achieved. The description of this system is shown in Figure 1. -797- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 Figure 1. General System Description -798- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 3.2. Model Formulation 3.2.1. Notations QL: Current Quality Loss Cost Q*L: Quality loss cost after the learning and forgetting L*cik : Optimal learning investment m: Machine index k: Component index σ 2Ri** : Variance after the learning and forgetting d0: Current memories b(t ) : Interruption time l *ik : Optimal Learning rate g(t ) : Learning Periods LCik : Learning investement lik : Learning rate Pik : Proportion of variance reduction LCik Max : Maximum fund in cycle i LC(i – 1)k Max : Maximum fund in cycle i-1 LC *(i – 1)k : Optimal learning investment in cycle i – 1 j: Supplier index χk: Component allocation from selected alternative I: Learning cycle index A: Quality Loss Cost Coefficient σ 2Ri : Assembly product variance di: Residual Memories after forgetting fi: Forgetting rate σ 2ik*: Component variance after learning Ie: Cost coefficient for the exponential investment function LC *ik :Optimal learning rate for each component and cycle 3.2.2. Objective Function The model formulation will focus on second stage model. For more detail about the FSM in terms of objective function, decision variables and model constraints, one can refer to Rosyidi, Pratama et al. (2016). The objective function of SSM in this research is to maximize the ROI. The optimal allocation of learning investment is obtained based on the optimal proportion of variance reduction that maximizing ROI as formulated in Equation (1). There are three costs considered in the model to obtain the ROI, namely the current quality loss, quality loss after the learning and forgetting, and optimal learning investment. Current quality loss is formulated in Equation (2). (1) -799- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 (2) The next cost considered in the objective function is quality loss after the occurrence of learning and forgetting. Before formulating this cost, first we have to find the component variance after learning and forgetting. Quality loss after the occurrence of learning and forgetting is formulated in Equation (3). (3) Component variance after the occurrence of learning and forgetting can be obtained by calculating residual memories after forgetting occurs in every cycle as formulated in Equation (4). (4) Then, component variance after the occurrence of learning and forgetting can be obtained by Equation (5). (5) Assembly variance after the occurrence of learning and forgetting is formulated in Equation (3) and can be obtained with Equation (6). (6) Component variance after the learning process is formulated in Equation (7). (7) Optimal learning rate for each component and cycle are obtained from Equation (8). (8) Cost coefficient for the exponential investment function is formulated in Equation (9) below. (9) Learning investment for each component and cycle obtained from the following equation below. (10) Proportion of variance reduction (pik) in Equation (10) is the decision variable in the SSM. Learning rate for each component and cycle can be obtained by following equation. (11) The optimal learning investment can be found by considering optimal learning rate in Equation (8) and Learning investment in Equation (10). Equation (12) shows the formula. (12) -800- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 In every learning cycle, there will be a maximum investment fund. The maximum fund for cycle i can be obtained by determining the difference between maximum found at cycle i – 1 with optimal learning investment at cycle i – 1 for each component. Equation (13) shows the formula. Equation (13) shows the formula. (13) Based on the calculation of each cost above, then the return on investment can be calculated as in Equation (14). (14) 3.2.3. Model Constraints This SSM considers two constraints, namely learning investment and learning rate constraints. Learning rate constraint is used to ensure that the maximum fund provided by the company is greater than learning investment cost for each component. Equation (15) shows this constraint formula. (15) Optimal learning rate constraint is used to ensure that the company will get further variance reduction. To meet this requirement, the optimal learning rate must be equal or greater than the current learning rate. Equation (16) shows this constraint formula. (16) 4. Numerical Example A numerical example is used in this research to show how the model works in a case. The example in this research refers to the case in Cao, Mao, Ching and Yang (2009) with some adjustments of the parameters to fit the model. In this research, the product consists of three components: Revolution axis, End shied nut and Sleeve. Figure 2 shows the dimensional chain of the assembly. The dimension of the revolution axis (x1), end shield nut (x2), and sleeve (x3) are 38 mm, 42 mm, and 80 mm, respectively. To maintain good performance, a gap of x0 (the important quality characteristic) with a tolerance of 0.2 mm is required. In this numerical example, it is assumed that the manufacturing company has two stages of the production process (cell) used to produce the three components. Each stage of the process has three identical machines. Each machine and supplier have different characteristics in term of manufacturing costs, processing time and tolerance. Table 1. shows the machine characteristics in cell 1, whereas Table 2. shows the machine characteristics in cell 2. Table 3. shows the characteristics of each supplier. Table 4. shows the machine's production capacity and supplier capacity and Table 5. shows the sequence of processes for each component. Some of the parameters used in this numerical example include the process capability index (Cp) which is assumed to be the same of 1.25 for each machine and supplier. The quality loss cost coefficient (A) is assumed to be IDR. 2,000,000/ unit. The component scrap cost is assumed to be IDR 15,000/unit and the cost of assembly scrap is IDR. 25,000/unit. Customers place an order of 1,000 units with a due date for 35 days (8 working hours). If the company completes the order by more than the due date a penalty in term of lateness cost of IDR. 250/minute will be beared. The assembly time is assumed to be 3 min/unit. Using the first stage model, the company can determine which machine and/or supplier will be selected and the allocation of each component to each selected machine and/or supplier to minimize the total cost comprises of manufacturing cost, purchase cost, quality loss cost, scrap cost and lateness cost. -801- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 b ( t ) Quality Loss Cost Revolution Axis End Shield Nut Sleeve 2 IDR. 61,702,323 IDR. 44,569,698 IDR. 65,781,519 3 IDR. 67,602,658 IDR. 48,659,053 IDR. 72,113,040 4 IDR. 78,095,635 IDR. 55,561,190 IDR. 83,460,979 5 IDR. 84,318,824 IDR. 60,359,662 IDR. 90,023,387 Table 25. Effects of interruption time to the quality loss b ( t ) Variance Reduction Percentage Revolution Axis End Shield Nut Sleeve Total 2 51.96% 43.57% 47.12% 47.55% 3 41.27% 42.54% 36.77% 40.19% 4 19.83% 26.42% 21.71% 22.65% 5 11.17% 10.31% 2.72% 8.07% Table 26. Effects of Interruption time to the variance reduction b ( t ) Return on Investment Revolution Axis End Shield Nut Sleeve Total 2 132.45% 84.66% 114.92% 110.17% 3 54.95% 41.93% 67.38% 54.46% 4 45.80% 26.25% 41.39% 3720% 5 25.22% 17.54% 18.14% 19.96% Table 27. Effects of Interruption time to the ROI In addition to the effect on the cost of quality loss, the changes in interruption time (b(t )) will also affect the variance reduction percentage obtained by the company. Table 26 shows the effect of changes of b(t ) on the variance reduction percentage. From Table 26, we can see that each value of b(t ) will increase, while the variance reduction percentage will decrease. For example, when the value of b(t ) is 4 periods, the variance reduction percentage for the Revolution Axis is 19.83%, and when the value b(t ) increases to 5 periods, the variance reduction percentage at that component decreases to 11.17%. The similar results are obtained for all other components. This occurs because the addition of the interruption time (b(t )) will increase the variance in which the greater the decrease of the variance, the lower the reducttion percentage. The change of interruption time will also affect to the ROI. Table 27 shows the effect of b(t) changes on the ROI. Table 27 above shows that each value of b(t ) increases, the percentage of ROI obtained will decrease. For example, when b(t ) is 4 periods, the total ROI is 37.20%, and when b(t ) increases to 5 periods, the total ROI decreases to 19.96%. Similarly for all ROI on each other components. This occurs because the addition of the interruption time (b(t )) will affect the increase in variance, and the greater the gap of variance that should be reduce make the investment costs increased. It is why the ROI obtained by the company reduced. Figure 3 and Figure 4 shows the effect of b(t ) changes on the variance reduction percentage and the ROI respectively. -808- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 Figure 3. Effects of interruption time to variance reduction Figure 4. Effects of interruption time to The ROI 5.2. Learning cycle ( i ) analysis The learning cycle (i ) is one of the important parameters considered in this model. The learning cycle is useful to give a break to a learning process in every cycle, so the forgetting process will occur. The number of learning cycles used will depend on the decision of the manufacturing company. The number of learning cycles can be determined in advanced at the beginning of the cycle and will stop when the variance reduction target has been achieved. i Quality Loss Costs Revolution Axis End Shield Nut Sleeve 1 Rp. 19,779,503 Rp. 14,146,748 Rp. 21,120,635 2 Rp. 18,881,193 Rp. 13,495,992 Rp. 20,163,384 3 Rp. 16,708,921 Rp. 11,988,236 Rp. 17,832,894 4 Rp. 13,867,877 Rp. 10,042,085 Rp. 14,778,779 Table 28. Effects of learning cycles to quality loss i Variance Reduction Percentage Revolution Axis End Shield Nut Sleeve Total 1 5.78% 1.13% 3.64% 5.78% 2 14.11% 5.49% 17.99% 14.11% 3 30.39% 29.35% 27.90% 30.39% 4 42.08% 36.88% 44.58% 42.08% Table 29. Effects of learning cycles to varianvce reduction -809- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 In this scenario, the learning cycle parameters (i ) are assumed to be to 1, 2, 3, and 4 cycles. The addition of the learning cycle affects the quality loss as shown in Table 28. From Table 28 above we can see that each addition of i will decrease the quality loss. When total cycle is 3, the quality loss for Revolution Axis component is IDR. 16,708,921, and when the cycle increases to 4, the value of quality loss on that component decreases to IDR. 13,867,877. Similar patterns are found for all other components. This occurs because the more learning cycles are used, the value of the variance of the product will continue to reducing. The addition of the learning cycles used also affects to variance reduction percentage. Table 29 shows the influence of learning cycles to variance reduction percentage. From Table 29 above it can be seen that each addition of the learning cycles (i ) makes the variance reduction percentage increasing. For example, when the number of i is 3 cycle, the variance reduction percentage for Revolution Axis component is 30.39%, and when the value of i is added to 4 cycle, the variance reduction percentage on that component increases to 42.08%. Similarly for all other components. This happens because the more learning cycles are used, the value of the variance of the product will continue to reduce. Of course, the variance reduction percentage will be greater. As the objective function of this second stage model to maximize the return on investment, this change of learning cycle also affects the ROI. Table 30 shows the effect of i on the ROI. From Table 30 above we can see that the addition of the number of learning cycles (i ) will increase the ROI. The resulting ROI is the accumulated ROI value of the n-cycle. For example, with 4 learning cycles, the ROI is 146.03%. The value is the accumulation of ROI from the first cycle until the fourth cycle. The increased of ROI comes from the greater variance reduction percentage, even though in the same time there will be an increase in the learning investment cost. Figure 5 shows the influence of learning cycle to the variance reduction percentage while the influence of learning cycle on the ROI is shown in Figure 6. Cycle Return on Investment 1 77.53% 2 117.50% 3 134.15% 4 146.03% Table 30. Effects of learning cycle to the ROI Figure 5. Effect of learning cycle to the Variance Reduction Figure 6. Effects of learning cycle to the ROI 6. Conclusions This research proposed two stages optimization model on make or buy analysis and quality improvement considering learning and forgetting curves. The first stage model was used to determine the optimal process/suppliers selection and component allocation to the selected process/suppliers. The variance from the first stage model then became the input for the next second stage model. The second stage model was used to -810- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2615 determine the optimal investment of quality improvement to maximize the ROI considering learning and forgetting curve. The SSM in this research gave better results compared with the previous model without forgetting curve. The SSM gave higher benefit in term of quality improvement with a consequence that the company has to spend higher learning investment. Hence the SSM is suitable for a company which has a production cycle with some learning and forgetting in the cycle and needs to continuously perform quality improvement by investment in learning. From the results of sensivity analysis, the model is quite sensitive to the parameters of the model. The increase of the interruption time will reduce the amount of ROI. More learning cycle will also increase the amount of ROI. Hence, before a manufacturing company uses this model, a careful data collection and processing must be done. For the future research, this study can be extended by differentiate between induced and autonomous learning. Moreover, this research can also be extended by using dynamic forgetting rate. Declaration of Conflicting Interests The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding This research was funded by Research Grant from The Institute of Research and Community Services Universitas Sebelas Maret Surakarta under Graduate Scheme with Contract Number 543/UN27.21/PP/2018. References Badiru, A.B.(1995). Multivariate analysis of the effect of learning and forgetting on product quality. International Journal of Production Research, 33(3), 777-794. https://doi.org/10.1080/00207549508930179 Bajec, P., & Jakomin, I.A. (2010). Make-or-buy decision process for outsurcing. 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