Product quality improvement model considering quality investment in rework policies and supply chain profit sharing
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Abstract
The aim of this paper is to develop an optimization model for quality improvement by considering quality investment in rework policies and supply chain profit sharing. To improve product’s quality, the decision of process target and its tolerance is important since it directly affects the defective rate, manufacturing cost, and loss to customer due to the deviation of product from its specification. In this research, two rework policies are considered. In the first policy, the rework is done by using the same manufacturing facility, while in the second policy a new process facility was added for rework. Quality improvement in the supply chain environment is also necessary. Hence, profit sharing system is added in the model to strengthen the commitment of the suppliers in improving component quality. In the system, the manufacturer shares the profits to the supplier if the supplier can meet or exceed the quality target specified by the manufacturer. A comparison is given to determine the best quality improvement policy between those two policies considering profit sharing system. From the results of the optimization, the managers can make economic investment decision economically to correct a defective product through cost optimization model and to choose the best option toward the goal of least unit production cost. By using this model, the decision-maker can evaluate any quality investment in order to achieve significant financial return.
Keywords
Quality improvement Quality investment Quality incentive Profit sharing Variance reduction ReworkIntroduction
Recently, manufacturing sector is one of the very rapid growing sectors. In the process, a manufacturing company has to choose the right business strategy in order to compete with others. According to Porter (1980), business strategy is defined as the way companies take to compete in the market with the goal of getting the desired profit. According to Hallgren and Olhager (2006), there are several important aspects for manufacturing companies to compete in the dynamic global competition, namely quality improvement, cost reduction, and on-time delivery. Product quality and cost reduction have been considered as the most common competitive strategies used by many manufacturing companies. The manufacturing companies have to perform quality improvement in their products at minimum cost from time to time. There have been many researches on process quality improvement to minimize cost. One of the important variables in cost minimization is product tolerance value. According to Zhang (1996), tolerance is a critical issue in the design and manufacturing stage of a product, where the determination of tolerance will affect product and process design since the tolerance is the link between product design and manufacturing. This value is important since it serves to limit the variability of product quality around the target characteristics (Mustajib and Irianto 2010). In setting the tolerance, Taguchi (1989) introduced a quadratic loss function that reflects the balance between customers’ loss due to the variation of product performances and producer’s effort to improve the product quality. In Taguchi quality loss concept, quality improvement must be done by reducing the process variance as well as to get the mean value of the process as close as possible to its target.
Several studies have been conducted to combine manufacturing with quality loss cost in a tolerance design model. For example, researchers such as Taguchi et al. (1989), Kapur (1989), Fathi (1990), and Zhang and Hug (1992) have conducted some researches, but they have not considered both manufacturing cost and quality loss simultaneously. Vokurka and Davis (1996) provided a case study of manufacturing scrap reduction through quality improvement. Jeang (1997) developed a tolerance design approach for quality improvement and cost reduction. He minimized the total costs of tolerance and quality loss based on three cost estimation scenarios using response surface methodology. In further research, Jeang (2001) proposed a model for simultaneous optimization of product and process design parameters, which was expressed in a mathematical relationship to link the elements of design target, design tolerance, process mean, and process tolerance in one equation and combined the optimization of parameter and tolerance design over product/process in the early stage of design. For the consideration of reworked items, Chiu and Chiu (2003) presented an economic production quantity model, similar to the optimal lot sizing model, but for defective and scrap rates. Another research by Chiu (2003) considered the influence of the reworking of defective items by allowing backlogging. Chiu (2007) then developed an economic manufacturing quantity model for a case when there are some random defective items produced subject to rework or scrapping. The optimal levels of the lot-size and backlogs were set as the decision variables to minimize expected total cost consisting of setup cost, holding cost, repair cost, disposal cost, and shortage cost.
In the manufacturing process, it is commonly known that items vary in their performances due to some inevitable random variations, such as material, operator, method, or process. Quality inspection processes are generally conducted only at the final stage of the production process. With this only final-stage inspection process, it will make the defect product in the preceding process stage become undetected. The inspection at each stage of the production process is needed to reduce this problem. Inspection, which is usually accomplished using manual method, has been intensively replaced by the use of simple yet effective sensor technology. This technology has made in process or between-process inspection become feasible. In this way, the defect parts or components can be detected earlier to avoid bigger problems (Irianto 1996). In the process, defective products may need to be reworked so as to conform with the specifications. The model of overall inspection policy of each process was carried out previously by Lo and Tang (1990), especially for products with expensive components, in which each process should be carefully inspected before proceeding to the subsequent process. A research on inspection policy and rework was done by Irianto (1996). There were two policies proposed in the research: (i) using the same production process facility for rework/correction process, and (ii) using different rework/correction facility. The model considered the economic and investment aspects. In the first policy, no additional investment for quality improvement was considered. While in the second policy, the investment value of quality improvement was calculated from the investment of additional separate rework facilities. The model was then extended by Irianto and Rahmat (2008) by including the process selection in make-to-order company by considering inspection and rework at the same production line facility. Then, Irianto (2009) added consideration to the model with the imperfection on the inspection process. Jerusalem et al. (2016) proposes a new comprehensive model for process selection. It incorporates both offline and online quality controls, an excellent balance between the costs, tolerance as a quality requirement, and delivery time.
However, in Irianto’s work, the model tends to select the second policy since it gives more benefit in the long term than the first policy. Thus, in this research we will enhance the first policy by adding quality investment to improve the quality of the process in terms of variance reduction. Quality investment models have been developed by Abdul-Kader et al. (2008, 2010).They conducted a research to model the possibility of reducing the cost of rework/scrap by adding quality investment. They adopted an investment which is expressed as the function of mean and variance. This quality investment model was also used by Chen and Tsou (2003), which was originally used as the basis of modeling the investment defined by Hong and Hayya (1993) and Ganeshan et al. (2001). Rosyidi et al. (2016a) developed a quality improvement model by variance reduction in component using learning investment. The model can be used to solve the problem of investment allocation to improve the quality of a product. Further, Rosyidi et al. (2016b) developed an investment allocation model for quality improvement to reduce component variances at manufacturer and supplier side to maximize the return on investment.
In addition to quality improvement in the form of rework policy selection and optimal investment value as mentioned previously, quality improvement in the supply chain environment is also necessary. Profit sharing system can be used in the supply chain to strengthen the commitment of the suppliers in improving component quality. In the system, the manufacturer shares the profits to the supplier if the supplier can meet or exceed the quality target specified by the manufacturer in the form of incentives. With this system, the suppliers will make their best effort to improve their product quality while minimizing costs throughout the supply chain. Profit sharing model in this research refers to the model of Kusukawa et al. (2006). In their research, profit sharing or rebates are given by the manufacturer or second-tier supplier to the first-tier suppliers who are capable of improving the quality so that the quality of the supplier process exceeds the quality target set by the manufacturer. Hence, the optimal quality targets must be achieved by the supplier to obtain optimal profit sharing. Research on the provision of incentives in improving process performance is also done by Overvest and Veldman (2008). They proposed a managerial incentives model to managers who can deliver the innovation or improvement in process performance using Cournot competition scheme. Furthermore, Veldman and Gaalman (2013) developed a model to determine the effect of incentive strategies for product quality and process improvement using game theory models in competition between two managers.
There are some other aspects that considered in several supply chain models regarding profit sharing. Panda et al. (2015) analyzed coordination of a manufacturer–distributer–retailer supply chain, where the manufacturer exhibited corporate social responsibility (CSR). In manufacturer–Stackelberg game setting, the paper proposed a contract bargaining process to resolve channel conflict and to distribute surplus profit among the channel members. Modak et al. (2015) proposed a two-echelon duopolistic retailers supply chain model with recycling facility considering Cournot and collusion behaviors of the retailers. The paper explored channel coordination and profit distribution in a two-layer socially responsible supply chain that consisted of a manufacturer and two competitive retailers. Further, Modak et al. (2018a) developed a model with three different structures of two-echelon closed-loop supply chain (CLSC) under price and product quality-dependent deterministic demand environment where product price, quality level, and recycling rate were considered as the decision variables. They also developed in other research a model that dealt with a manufacturer–retailer supply chain considering the cost of greenhouse gas (GHG) emission during manufacturing process (Modak et al. 2018b). Revenue sharing contract and asymmetric Nash bargaining strategy were used in that research to resolve channel conflict and to share surplus profit between the channel members.
In this paper, we develop a mathematical model that can be used to determine the optimal tolerance, rework policy, and profit sharing that should be given by the manufacturer or second-tier supplier to the first-tier suppliers. The main contribution of this research lies in the integration of profit sharing, learning, and facility investment in a quality investment decision model which will make the suppliers commit to the efforts of quality improvements and the manufacturer gains maximum benefits from those sharing and investments. A numerical example is given in this paper to show the application of the proposed model. This research will be beneficial to a decision-maker in companies engaged with manufacturing in the global competition and respond to managerial issues related to production and business decisions.
Problem definition
A manufacturing company needs to improve their product quality by reducing the component variance of their manufactured products. To reduce the variance, an inspection and rework process of defective items need to be done. In this case, the manufacturer has two options: (1) using the same facility to rework the defective items, or (2) adding separate rework facility. In this paper, we assume the reworked product still has the probability to be defect, so it can be reworked multiple times until it meets the required specification. The first policy is chosen due to its simplicity, that is, reworking the defect units by using the existing facility. In this first policy, quality investment is made by considering learning investment to reduce the variance. This investment can be used for training, technological improvements, as well as other efforts related to the variance reduction. The second policy has two advantages. It may have higher capacity due to uninterrupted process in main facility of production process and the rework can be done better than the process in the main production line. However, the second policy needs a big additional investment to purchase and setup of new facility.
Our concern in this paper is the quality improvement in a product to minimize costs related to the improvement effort and the quality investment related to both policies. Trade-off between two conflicting objectives, which is cost and quality, is unavoidable. This happens because the company has to spend more on quality costs and manufacturing costs to make a better quality product. The quality loss in terms of the inspection and rework cost is integrated and then minimized to obtain the optimal tolerance value for each policy based on their most economical performance. This optimization procedure not only leads us to set the most economical tolerance and profit sharing, but also simultaneously helps the management in selecting or evaluating the policies concerning inspection and rework to improve the product quality.
Model formulation
External quality loss cost formulation
Manufacturing cost formulation
The next cost component comes from the production line. It is assumed that all defective products can be reworked with the same facilities that already exist or with the addition of rework facility. Since the rework is only done for the defective product, the total cost of the correction depends on the tolerance value t. Inspection costs also need to be considered. This cost comes from all the products that are inspected, both defective and good ones. Therefore, the tolerance value also affects the cost of inspection because the defective product also needs to be re-inspected.
Number of good, corrected, and inspected products
- 1.
If \({{tp \le tc \cdot \overline{{P_{1} }} } \mathord{\left/ {\vphantom {{tp \le tc \cdot \overline{{P_{1} }} } {\left( {1 - \overline{{P_{2} }} } \right)}}} \right. \kern-0pt} {\left( {1 - \overline{{P_{2} }} } \right)}}\), then \(n_{{p_{2} }} \le t/tp\)
- 2.
Otherwise \({{n_{{p_{2} }} \le T} \mathord{\left/ {\vphantom {{n_{{p_{2} }} \le T} {\left( {{{t_{c} \cdot \overline{{P_{1} }} } \mathord{\left/ {\vphantom {{t_{c} \cdot \overline{{P_{1} }} } {\left( {1 - \overline{{P_{2} }} } \right)}}} \right. \kern-0pt} {\left( {1 - \overline{{P_{2} }} } \right)}}} \right)}}} \right. \kern-0pt} {\left( {{{t_{c} \cdot \overline{{P_{1} }} } \mathord{\left/ {\vphantom {{t_{c} \cdot \overline{{P_{1} }} } {\left( {1 - \overline{{P_{2} }} } \right)}}} \right. \kern-0pt} {\left( {1 - \overline{{P_{2} }} } \right)}}} \right)}}.\)
From Eq. (15), we can observe that without quality investment, the output of the second policy is higher than the first.
Internal failure cost, prevention and appraisal cost, and rebate
The concept of rebate assumes that the optimal quality target with rebate is higher than the quality level without rebate. The quality target and rebate values for each supplier are set by the manufacturer. If the quality level of supplier j exceeds a predetermined quality target, supplier j will receive a rebate from the manufacturer or supplier of the next related tier.
- 1.
When supplier j achieved the optimal quality target value q_{j}** after setting rebate, quality cost of supplier j can be minimized.
- 2.
When quality cost of supplier j after setting rebate is minimized, cost reduction ratio between quality cost of supplier j with rebate and that without rebate is equivalent to cost reduction ratio of total quality cost obtained from the whole supply chain system with rebate.
- 3.
Target of supplier j, Tj, is set as a higher value than the optimal quality target value of supplier j without rebate, q_{j}*.
Total cost formulation
The value of optimal tolerance t* can be obtained by minimizing Eq. (40) with respect to t.
Quality improvement model with learning investment for Policy 1
After determining the optimal tolerance, we add a learning investment model to determine the amount of quality investment required for quality improvement to minimize the production cost. Hence, the model will provide simultaneous joint decisions to achieve optimal process setting, which are optimal investment and optimal variance and mean values after the investment. By adding the investments, there will be a reduction in cost.
The optimal investment value I_{1} and the optimum variance can be obtained by minimizing Eq. (47) and by substituting the optimum tolerance value previously obtained.
Quality improvement model with investment for Policy 2 and rework policy selection
Numerical example
Target process mean m | 402 mm |
Current process mean μ | 402.86 mm |
Current standard deviation σ_{1} | 0.66 |
Standard deviation of rework facility σ_{2} | 0.53 |
The best variance that can be achieved after quality improvement σ_{L} | 0.55 |
Total manufacturing time T | 10,000 unit time duration |
Processing time/unit t_{p} | 10 time duration |
Rework time/unit t_{c} | 10 time duration |
Inspection time/unit t_{i} | 1 time duration |
Processing cost/unit c_{p} | $2 |
Rework cost/unit c_{c} | $2 |
Inspection cost/unit c_{i} | $0.3 |
Taguchi loss constant K | $1 |
Variance curve constant α | 0.00362 |
Mean curve constant β | 0.0105 |
Cost of investment adding rework facility | $225 |
Fixed cost and variable cost for operating the correction facility and rework per unit product are assumed to be $40 and $2, respectively.
Quality failure cost of each supplier
Failure cost ($) | |||||
---|---|---|---|---|---|
j/i | 1 | 2 | 3 | 4 | 5 |
1 | 3 | 0 | 0 | 0 | 0 |
2 | 0 | 2 | 0 | 0 | 0 |
3 | 2 | 0 | 4 | 0 | 0 |
4 | 0 | 2 | 0 | 3 | 0 |
5 | 0 | 0 | 3 | 3 | 5 |
Prevention and appraisal cost of each supplier
Appraisal and prevention cost ($) | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 (manufacturer) | |
m _{ j} | 2.7 | 2.2 | 2.8 | 2.3 | 2.6 |
b _{ j} | 1 | 1.5 | 1.3 | 2 | 1.2 |
Optimization results at the manufacturer side
Rework Policy 1 | Rework Policy 2 |
---|---|
Optimal tolerance = 1.432 mm | Optimal tolerance = 1.255 mm |
Total cost/unit = $7.58 | Total cost/unit = $7.83 |
Investment quality = $108.615 | Investment quality = $ 225 |
Amount produced before investment = 970 units | |
Amount produced after investment = 978 units | Amount produced = 996 units |
Investment quality/unit = $0.111 | Investment quality/unit = $ 0.226 |
Optimal mean after investment = 402.27 mm | Process mean after investment = 402.86 mm |
Optimal variance after investment = 0.626 | Process variance after investment = 0.53 |
Total cost of quality of each supplier before rebate
Sj | q* | Failure cost ($) | Prevention and appraisal ($) | Total before rebate ($) |
---|---|---|---|---|
S1 | 0.894 | 0.32 | 3.70 | 4.02 |
S2 | 0.867 | 0.27 | 3.70 | 3.97 |
S3 | 0.911 | 0.57 | 4.46 | 5.03 |
S4 | 0.836 | 0.76 | 4.61 | 5.37 |
S5 | 0.879 | 1.36 | 4.70 | 6.07 |
Total cost of quality of each supplier after rebate
Sj | qi** | Failure cost ($) | Prevention and appraisal ($) | Rebate ($) | Total after rebate ($) |
---|---|---|---|---|---|
S1 | 0.945 | 0.16 | 3.70 | 0.65 | 3.21 |
S2 | 0.931 | 0.14 | 3.70 | 0.67 | 3.17 |
S3 | 0.925 | 0.41 | 4.27 | 0.65 | 4.03 |
S4 | 0.885 | 0.48 | 4.45 | 0.63 | 4.30 |
S5 (1) | 0.978 | 0.68 | 4.41 | 0.37 | 4.72 |
S5 (2) | 0.982 | 0.66 | 4.41 | 0.38 | 4.69 |
Rebate component of each supplier
Sj | Tj | κ_{j}($) | Uj ($) |
---|---|---|---|
S1 | 0.894 | 2.67 | 0.51 |
S2 | 0.867 | 1.73 | 0.55 |
S3 | 0.911 | 3.20 | 0.61 |
S4 | 0.836 | 2.13 | 0.53 |
S5 (1) | 0.879 | 3.72 | 0.00 |
S5 (2) | 0.879 | 3.73 | 0.00 |
Quality cost reduction ratio of each supplier
Sj | Total before rebate ($) | Total after rebate ($) | Reduction ratio of quality cost (%) |
---|---|---|---|
S1 | 4.02 | 3.21 | 20 |
S2 | 3.97 | 3.17 | 20 |
S3 | 5.03 | 4.03 | 20 |
S4 | 5.37 | 4.30 | 20 |
S5 (1) | 6.07 | 4.72 | 22 |
S5 (2) | 6.07 | 4.69 | 23 |
Figure 8 shows the effect of α to the optimal variance after investment on the rework Policy 1. The figure shows that the greater the value of α, the optimal variance becomes smaller. This is because α is influenced by the amount of training, technological improvement, and other things related to the reduction in variance, which means the quality is also better so that the optimum variance is also getting smaller.
From the model presented in this paper, several managerial implications can be stated. First, the managers can make economic investment decisions economically to correct the defective product through cost optimization model and to choose the best option toward the goal of least production cost. Second, they also can determine the optimal profit sharing or rebates that should be given by the manufacturer or second-tier suppliers to the first-tier suppliers capable of improving the quality. Hence, the quality of supplier process can be maintained and improved continuously.
Conclusion
In this paper, we presented two policies of quality improvement in a manufacturing process which performs inspection and rework considering profit sharing in the supply chain. In the first policy, the rework was done using the same manufacturing facility, while in the second policy additional process facility was added for the rework. For the first policy, we integrated two cost models comprising tolerance model and quality investment model. In addition to quality improvement in the form of rework policy selection and optimal investment value as mentioned previously, quality improvement in the supply chain environment is also necessary. The profit sharing system is used in the supply chain to increase the efforts of suppliers in quality improvement. This system is performed by providing a share of the manufacturer’s profits to the supplier if the supplier can meet or exceed the quality target specified by the manufacturer in the form of incentives. With this system, the suppliers will try to improve their product quality while minimizing costs throughout the supply chain of quality in order to run more efficiently. By minimizing the sum of total costs, the optimal tolerances, quality investment, and the optimal profit sharing or rebates that should be given by the manufacturer or second-tier supplier to the first-tier suppliers capable of improving the quality can be obtained for both policies.
In the numerical example, it was shown that this model is applicable in the manufacturing process and showed how the model reacts and managerial implications to the changes in the parameters such as Taguchi loss constant K, α, appraisal cost, and internal failure cost. It can be used as a guideline for managers in analyzing the choices of process improvement. For further research, the model can be extended by considering multistage processes, inspection, and corrections. Another consideration can be given by considering other distributions rather than normal distribution, such as uniform and exponential.
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