5.2 Applied Model : Company Case
5.2.3 Application of The Theoretical Model: Including Learning Behaviors of
is because there is no data available related to suppliers’ capacities and the only information on hand about the capacities of suppliers is their improvement potentials. That is why the learning capacities of suppliers’ are used as their capacities while determining their action plans. The model that is discussed in § 5.2.2 is used with incorporating the learning capacities obtained in RQ1 and RQ2. Therefore, only the changes in the model reported in this section.
5.2 Applied Model : Company Case It should be noted that breakpoints must be different for different learning behaviors, and the upper bound for the capacity increase from the on-site visit is different per learning behaviors which will be explained afterwards.
Parameters:
lbjk : Learning behavior of supplier j in topic k, ∀j ∈ J, ∀k ∈ K
icjk(lbjk, sj) : Improvement capacity in topic k for supplier j, ∀j ∈ J, ∀k ∈ K
biin(lbjk, ai) : Break point of line segment n for action i for realized improvement function,
=
F, S and I in learning behavior represent Fast Learner, Slow Learner and Indifferent suppli-ers respectively. Breakpoints and slopes are required for creating piece-wise functions. Break-points are determined by making assumptions. For example, the first break-point for improve-ment increase function is determined as 50% of the improveimprove-ment potential comes from related action for slow learners and indifferent suppliers whereas 40% of the improvement potential comes from the related action for fast learners. This means that a fast learner supplier starts having improvement for a continuous action after allocating capacity of more than 40% of im-provement from respective action. That is why in biin(lbjk, ai)is ai/2and (ai∗ 2/5) for fast and slow learner respectively. The assumption is determined after interviewing with experts, as they also supported that fast learner suppliers start learning earlier than other suppliers.
Slow learner and indifferent suppliers benefit more from buyer involvement as they need guid-ance more than fast learners. 0.18 maximum increase for slow learners, 0.12 maximum increase for fast learners, estimated from historical data for sequence 1 suppliers analyzing effects of on-site visits. This means that the upper bound for learning capacity increase comes from the on-site visit is 0.18 for slow learner suppliers and 0.12 for fast learner suppliers.
The same decision variables, objective function and constraints that are discussed in § 5.2.2 are used for this model
5.2 Applied Model : Company Case 5.2.4 Application of The Theoretical Model: Learning Behaviors with Optimizing On-site
Visits and Investments
The model is built for understanding the effects of another buyer involvement strategy: invest-ments for suppliers. All the assumptions that are represented in the previous section, are also used in this model. Additional decision variables such as investment amounts for suppliers in topics are added to the theoretical model. Furthermore, the effects of investment on suppliers’
capacities must be implemented in the model in order to understand the trade-off between buyer involvement strategies. The effect of investments on suppliers’ learning capacities is modeled as linear-piece wise function. The same procedure while implementing the effect of on-site visits on suppliers’ capacities is followed in this problem. 2 breakpoints are defined in the function. The breakpoints are the same for each supplier but the slopes of the line seg-ments depend on learning behavior and the sequence number of the suppliers. An illustration of the function that is used for learning capacity increase results from investment can be seen in Figure 20.
As can be seen that the slope of the first line segment is bigger than the slope of the second line segment because of the diminishing marginal utility from a monetary unit spent. However, the information related to investments is not available as Philips do not currently invest suppliers directly. Consequently, breakpoints for the function are estimated by using the information related to the cost of conducting on-site visits.
Figure 20: The relationship between investments and learning capacity increase
The same sets are used in this model. The line segment L is also used for investment function.
The new parameters are as follows:
Parameters:
days :Buyer capacity for conducting on site visits in terms of days
budget : Buyer capacity for investments and conducting on-site visits in terms of MU binvl : Break point of line segment l for investment increase function,
5.2 Applied Model : Company Case
sinvjkl(binvl, lbjk, sj) : Slope of line segment l for investment increase function,
=
rinvij :Required investment amount for predecessor action i in supplier j ∀i, j ∈ Ip, J ronsij :Required on-site visit duration for predecessor action i in supplier j ∀i, j ∈ Ip, J
There are several differences with the previous model. Investment strategy is included in the model. Therefore, breakpoints and slopes are defined. The breakpoints are the same for each supplier and defined as 400 and 800 MU. As Philips do not invest suppliers directly, the cost of conducting maximum days of on-site visit is used while determining the breakpoints of the investment function. That is the sum of the fixed and variable cost of conducting 3 days of on-site visits for suppliers. Slopes are different for different line segments as it is modeled as a piece-wise linear function. Slopes also depend on learning capacities and sequence num-ber as it is the case for on-site visit function. The first break-point (400 MU) provides 0.625 of the upper bound whereas the second break-point (800 MU) provides the upper bound as an increase for the learning capacity. The same idea with on-site visit function is used while implementing different learning behaviors and sequence numbers. As slow learner and indif-ferent suppliers benefit more from buyer involvement strategies, their upper bound is bigger than fast learner suppliers. In addition to that, as the sequence number increases the effect of on-site visits decreases but the effect of investment increases. It is because the suppliers in later sequences can be considered as experienced with the sustainability program and investment strategy provides more learning capacity increase than on-site visit strategy.
In addition to that, on-site visit capacity and budget limitation are incorporated as the op-timization is conducted for determining on-site visit duration and investment amounts. In the previous models, on-site visit duration was used as a parameter as it was constant and equal for each supplier. Therefore, budget and on-site visit capacity constraints are included in this model. Also, requirements for implementing predecessor actions are included as the optimization covers assigning predecessor actions to suppliers by considering cost of different strategies. Additional decision variables can be seen as follows:
Decision Variables:
yj =
1, if supplier j visited on site 0, otherwise
, ∀ j ∈ J
5.2 Applied Model : Company Case zjkl= Duration of on-site visit for supplier j in topic k in line segment l
ηjkl= Investment amount in terms of monetary unit for supplier j in topic k in line segment l βjk = Dummy variable representing second line segment must be used for on-site visit increase,
=
γjk = Dummy variable representing second line segment must be used for investment increase,
=
vijk= Dummy variable representing second line segment must be used for realized improvement,
=
wijk= Dummy variable representing third line segment being used for realized improvement function,
=
ρij =Duration of on-site visit allocated for predecessor action i for supplier j , ∀ i, j ∈ Ip, J ζij = Investment amount allocated for predecessor action i for supplier j, ∀ i, j ∈ Ip, J
oij = Dummy binary variable for ensuring either or constraints for supplier j for predecessor action i ,
∀ i, j ∈ Ip, J
Here, the additional decision variables are related to conducting on-site visit strategy, invest-ment strategy and impleinvest-menting either-or constraints for the predecessor action as the pre-decessor action can be implemented either conducting determined days of on-site visits or investing for the supplier depending on the predecessor action. Additional dummy decision variables also used to implement a linear piece-wise function for the capacity increase from investment.
5.2 Applied Model : Company Case
The additional constraints to the previous model are explained in this part. Constraint (3) re-arranged as another buyer involvement strategy, investment, is implemented. The total
ca-5.3 Results pacity is now calculated as the initial capacity depends on learning behavior and suppliers’
sequence number, learning capacity increase result from investments and on-site visits. Con-straint (6) represents that the buyer can not spend on-site visit days if a supplier is not visited on-site. Constraint (7) ensures that the buyer can not allocate on-site visit days to predecessor actions if a supplier is not visited on-site. Constraint (8) represents that buyer can not con-duct on-site visit more than its capacity in terms of days for all the suppliers and predecessor actions. The cost component of investments to suppliers and for the predecessor action is in-cluded in Constraint (9). Constraint (10)-(11) represents that either a predefined number of days of on-site visit or an amount of investment depending on the predecessor action must be completed to assign predecessor action to a supplier. Those predefined numbers are defined as 0 in the models but later different set of parameters are examined in the sensitivity analysis section. Constraints (19)-(21) are for implementing learning capacity increase from investment.
The same idea with learning capacity increase for on-site visits is used in constraints (22)-(24).
The line segment can be used only if the previous line segment is fully utilized for a supplier.
The same strategy with modeling improvement potential from actions is used for that function as well. However, the only difference is that on-site visit function has 2 different line segments whereas improvement potential function has 3 different line segments. That is why more con-straints are needed for modeling the improvement coming from assigned actions and allocated capacities.
5.3 Results
For application of the theoretical model of current procedure, with learning behaviors, and with learning behaviors and optimizing buyer involvement strategies, percentage increases from suppliers’ initial score for each supplier and each topic are investigated. In order to compare the effect of optimization, three models are compared. The first model assumes buyer can only conduct on-site visits and the on-site visit duration for suppliers are constant (3 days).
That is why investment strategy is excluded from that model as Philips do not invest suppliers currently. Also, the buyer spends 0.75 days for each topic for each supplier. Therefore, it should be noted that on-site visit duration for suppliers is not optimized as it is already defined as 0.75 days for each topic. Therefore, the same budget(8000 MU) that results from conducting 3 days of on-site visit for each supplier is used. The base model also does not consider learning behaviors of suppliers. Instead, the learning capacities are determined by investigating the suppliers’ historical data. For that purpose, the average increase between each sequence pair for each topic is calculated and used as learning capacities of suppliers. That means if two suppliers are both in their sequence 2, their learning capacities are equal to each other for all topics. In the model with including the learning behaviors, the learning behavior of suppliers are incorporated by using specific learning capacities for each supplier and for each topic by using the learning curves that are obtained in RQ1 and RQ2. Therefore, the model with the sustainability learning behaviors is expected to provide more realistic results. Comparison between learning capacities of the base model and with considering the outputs of RQ1 and
5.3 Results RQ2 can be seen in Appendix N.
In the base model and the model with sustainability learning behaviors, the buyer involvement strategies are not optimized and only on-site visit strategy is considered. However, the model with optimizing buyer involvement strategies incorporates the effect of investment strategy on learning capacities of suppliers, and optimizes both buyer involvement strategy. Consequently, the effects of including the learning behavior of suppliers can be examined by comparing the base model and the model with sustainability learning behaviors, and the effect of optimizing the buyer involvement strategies (investment and on-site visit) can be examined by comparing the second and the model with optimizing buyer involvement strategies as the last model optimizes both buyer involvement strategies.
The base model takes the average improvement amount(historical data) as learning capacities of suppliers, and it assigns actions to suppliers according to that capacity. The model with sus-tainability learning behaviors optimizes action plans according to learning behaviors of sup-pliers. On the other hand, the model with optimizing buyer involvement strategies optimizes how many days to conduct on-site visit and how much money to invest for each supplier in ad-dition to incorporating learning behavior of suppliers. Figure 21 represents the improvement percentages obtained by suppliers in the base model which optimizes only the action plans but not buyer involvement strategy with considering the same learning capacities of all sup-pliers, and Figure 24 represents the improvement percentages in the model with sustainability learning behaviors which optimizes the action plans for each supplier considering their learn-ing behaviors and with different learnlearn-ing capacities for each supplier. Figure 24 represents the improvement percentages in the model with optimizing buyer involvement strategies which determines how many days to allocate for each supplier as on-site visit and how much mone-tary unit to invest in each supplier as financial support to sustainability efforts and the action plans for each supplier considering their learning behaviors.
Figure 21: Improvement percentages for each topic and for each supplier in the base model
The comparison of Figure 21 and 22 demonstrates that the improvement percentages are not equally distributed over the suppliers as there are differences in terms of learning capabilities of suppliers. In the base model, the total increase in sustainability score is 14.7% whereas it is
5.3 Results
Figure 22: Improvement percentages for each topic and for each supplier in the model with sustainability learning behaviors
Figure 23: Deviation of improvement percentages when the learning behavior is included
calculated as 15.2% when the base is taken as the initial sustainability scores. Therefore, the model with sustainability learning behaviors is not only providing more realistic solution but also a better one in terms of improvement percentages. Also, by assuming the same learning capacity for suppliers, the chance of not using the full potential of suppliers or overusing the potential are very likely. Figure 23 represents the difference between average improvement percentages for each supplier. In the Figure 23, positive percentage values represent that sup-pliers do not use their full potential with the action plan without considering learning behavior of suppliers. This means that provided action plan do not fully utilize the supplier’s learning capability. On the other hand, negative percentage values demonstrate that the action plans assigned to those suppliers are not within their capacity limitation. Therefore, it is very likely that these suppliers may not comply with the given action plans. The results show that 7%
of deviation in the average sustainability increase can be expected if the learning behavior of suppliers are not used. The further comparison of the initial learning capacities in the base model and the model with learning behaviors is examined in Appendix N.
The comparison of Figure 22 and 24 demonstrates that the total improvement percentage en-hances by using the buyer involvement strategies efficiently. It can be seen that nearly all suppliers increases their improvement percentages in each topic. It is also interesting to exam-ine how much the sum of all scores change after optimizing the buyer involvement strategies.
5.3 Results
Figure 24: Improvement percentages amount for each topic and for each supplier in the model with optimizing buyer involvement strategies
The total sustainability score increases from 15.2% to 19.7% compared to the initial scores of the suppliers after optimizing the buyer involvement strategies. That means the sum of initial scores for all suppliers increases by 19.7% after optimizing the buyer involvement strategies.
It should be noted that the models use the same amount of budget(8000 MU).
Sensitivity Analysis
In order to see the effects of buyer involvement strategies, the budget of the buyer changed, and the total improvement percentage is recorded. The budget first determined as 0, which means buyer cannot support its suppliers but it can still provide action plans. After that, the budget increases with the step size of 8000 MU which is the initial level of budget for the base model. However, buyer’s capacity for conducting on-site visit kept constant at 30 days. Figure 25 demonstrates the impact of the buyer’s budget on the total improvement percentage. As can be seen, there is a decreasing return to scale. It is expected as the marginal utility of buyer involvement strategies on the improvement amount decreases. Therefore, the effect of increas-ing budget must be decreasincreas-ing. Also, after MU, increasincreas-ing budget does not contribute to the improvement amount.
Figure 25: Sensitivity analysis of buyer’s budget on the total improvement percentage As buyer’s capacity for conducting on-site visit can be changed by increasing or decreasing the
5.3 Results number of assessors, the impact of on-site visit capacity in terms of days must be examined.
For that purpose, two different analysis are conducted. In the first analysis, the budget kept constant at 8000 MU as it is the initial level of budget in the models, and the buyer’s capacity for conducting on-site visits are changed from 0 to 50 with step size of 10. The result can be seen in Figure 26. It can be seen that, as the number of days for on-site visit increases, the total improvement percentage increases. However, there is a decreasing return to scale which is also expected. In the second analysis, the budget kept constant at 52000 MU and the buyer’s
Figure 26: Sensitivity analysis of on-site visit capacity on total improvement amount capacity for conducting on-site visits are changed from 0 to 50. Figure 26 represents the result when the budget is 8000, and Figure 27 demonstrates the result when the budget is 52000 MU.
The effect of increasing the number of days for on-site visit is also decreasing return to scale in the second analysis. However, when Figure 26 and Figure 27 are compared, when the budget of buyer is bigger, marginal improvement percentage coming from each additional number of days for on-site visit increases. As can be seen from Figure 27, 32% increase in sustainability scores of the suppliers compared to the initial scores can be achieved by increasing the on-site visit capacity further. It can be further supported that when buyers involve in the improvement process, higher return can be achieved. It is also important to see that after days are determined as 40 when the budget is 8000, the further increase in capacity does not provide any benefit.
Figure 27: Sensitivity analysis of on-site visit capacity on the total improvement percentage
5.3 Results It is also interesting to see the effect of required on-site visit days and investment amount
5.3 Results It is also interesting to see the effect of required on-site visit days and investment amount