5.2 Applied Model : Company Case
5.2.2 Application of The Theoretical Model: The Base Model
In the base model, suppliers’ learning capacities are assumed to be same as the information is assessor-dependent and subjective. Therefore, the average improvement amounts for each sequence and each topic is used for suppliers’ learning capacities in the base model. In addition to that, buyer capacity in terms of MU and on-site visits is also incorporated. As there are a limited number of assessors available at Philips, the maximum number of on-site visit duration for all the suppliers must be defined to limit the number of site visit days. Conducting on-site visits also results in costs as there are travel costs and the daily cost of assessors. Therefore, the budget of the buyer must also be used as a constraint in the model. Improvement potentials result from satisfying actions are calculated from Philips’ database. The effects of on-site visits on suppliers’ improvement amounts are estimated by analyzing the sustainability scores of suppliers before and after having the on-site visits. It is found that the suppliers that are in sequence 1, increase their sustainability scores by 12% on the average after having the on-site visits. Therefore, the assumption for the effects of on-site visits on suppliers’ capacities is made by using this information. Assumptions of the applied models can be seen in Table 23.
Sets:
I :Set of actions for suppliers J :Set of suppliers
K :Set of topics (Environment, Health Safety, Business Ethics, Human Capital) Ick:Subset of continous actions for topic k, Ick⊆ I
Ibk :Subset of binary actions for topic k, Ibk⊆ I Ip :Subset of predecessor actions, Ip ⊆ I
Pi:Set of successors of action i, Pi ⊆ I L = 1, 2 :Set of line segment for On-site visit
N = 1, 2, 3 :Set of line segment for realized improvement function
As can be seen in the sets, there are two different line segment set used in this model. Set L is used for on-site visit and investment functions whereas set N is used for improvement function. The main difference is that Set L has 0 and 1 whereas Set N has 0,1 and 2 as the
5.2 Applied Model : Company Case
Table 23: Assumptions of the models Cost of
actions
The improvement amount results from actions are considered as the cost of actions.
They are derived from the database at Philips, not supplier-specific as the
improvement potential from an action is defined as an increase in the sustainability score. Suppliers need to allocate their capacities to obtain improvement from actions.
Suppliers’
Capacity
As Philips do not consider the learning capacities of suppliers, they are determined from historical data by calculating average improvement amount for each supplier in each topic and each sequence. Therefore, suppliers are assumed to have the same learning capacity in the base model. However, the learning capacities of the suppliers are incorporated in the later models as their learning capacities were estimated from their learning curves. Therefore, the learning capacity is dependent on learning behavior and the sequence number of suppliers. In that way, time and budget constraints at the supplier side implicitly incorporated into the model as the information was not available in the database at Philips.
Buyer’s Capacity
Buyer assumed to allocate 3 days of on-site visit per supplier. Interviews with experts revealed that this assumption is valid for considering the current practice.
Cost of On-site Visit
Derived from average minimum daily employee wage in China (Which is considered as 20 MU/day2). In Philips, as the assessors are assumed to earn 8 times more than average employee wages in China, the cost of conducting a day of the on-site visit is assumed as the daily wage of assessors which is 160 MU/day. In addition to daily cost, there is a fixed cost component of conducting an on-site visit. The fixed cost
component assumed as conducting 2 days of an on-site visit by interviewing with experts at Philips.
Buyer’s Budget
Buyer is assumed to have a budget that can be allocated to investments and on-site visits. As the base model uses conducting 3 days of on-site visits per each supplier, the budget is calculated according to the information. As there are 10 suppliers in scope, the buyer needs to conduct 30 days of on-site visits. Consequently, the buyer assumed to have 8000 MU which results from conducting 3 days of on-site visit for each supplier.
Effects of On-site Visit
One of the buyer involvement strategies is considered as on-site visit. The longer an assessor spend her time at a supplier, the more increase in capacity of suppliers until the maximum point which is defined as 3 days. according to experts as the maximum duration of an on-site visit is defined as 3 days at Philips. The effect is also different depending on the sequence number and learning behavior of suppliers.
Effects of Investment
One of the buyer involvement strategies is considered as investments to suppliers. The more monetary unit invested in suppliers, the more increase in capacity of suppliers until the maximum point. The maximum point is defined by using the cost of conducting on-site visits. As the maximum duration is 3 days for conducting on-site visits, it results in 800 MU. Therefore, the maximum point for investment is defined as 800 MU for each topic as well for scalability purposes. The effect is also different depending on the sequence number and learning behavior of suppliers.
Predecessor Actions
Predecessors actions can be assigned to suppliers if the buyer either conducts the estimated days of on-site visit or invests in estimated MU on suppliers. As the information is not available at Philips, it is assumed as there is not a need for investment or conducting on-site visit to implement predecessor actions. However, different values for cost values and required days of on-site visit are later tested in sensitivity analysis section as there is not a clear information related to cost of the predecessor action.
Hourly wage for suppliers in China is estimated as 20 RMB (2.5 Euros)(https://www.china-briefing.
com/news/minimum-wages-china-2020/)
5.2 Applied Model : Company Case improvement function has 3 line segments meaning that 3 different slopes. Breakpoints refer to the points where slope changes. Therefore, number of line segment will be equal to number of break points in the function. Figure 17 represents relationship between allocated capacity to an action and obtained improvement.
Figure 17: Relationship between allocated capacity and obtained improvement
In order to obtain improvement from continuous actions, suppliers need to allocate a minimum capacity. In the Figure 17, the x-axis represents the decision variable how much capacity must be allocated to action i by supplier j. After the capacity allocation, the improvement amount is modeled by using a linear-piecewise function. That is why there are line segments where the slopes are different. To determine the points where slope changes, breakpoints are used. As there are 3 different line segments, there are 3 breakpoints that need to be defined for the rela-tionship between allocated capacity and improvement from an action. It can be seen that slope decreases after the second break-point. It is because a decreasing return to scale is implemented after discussing with experts at Philips to reflect the reality of implementing the actions. The capacity increase results from on-site visits must also be modeled by using the same strategy.
For modeling learning capacity increase from on-site visit, linear-piece wise functions are used with two different line segments. Figure 18 represents the effects of an on-site visit on learning capacity.
In the linear piece-wise functions, the same strategy, decreasing return to scale, implemented for on-site visits. According to experts, it is because the earlier days provide more improve-ment from later days due to diminishing marginal utility rule.
Parameters:
ai: Improvement potential for action i, ∀i ∈ I sj : Sequence number of supplier j, ∀j ∈ J
icjk(sj) : Improvement capacity in topic k for supplier j, ∀j ∈ J, ∀k ∈ K predi :Size of the set for successors of predecessor action i ∀i ∈ Ip f os : Fixed cost of conducting on site visit
5.2 Applied Model : Company Case
Figure 18: Relationship between duration of on-site visit and capacity increase
vos : Daily cost of conducting on site visit
actionsij :Binary parameter that represent if action is already implemented or not, ∀j ∈ J, ∀i ∈ I zjkl: Duration of on-site visit for supplier j in topic k in line segment l
biin(ai) : Break point of line segment n for action i for realized improvement function,
=
siin(biin, ai) : Slope of line segment n for action i for realized improvement function,
=
bosl: Break point of line segment l for on site visit increase function,
=
sosjkl(bosl, sj) : Slope of line segment l for on site visit increase function,
=
Breakpoints and slopes are required for creating piece-wise functions. Breakpoints are deter-mined by making assumptions. For example, the first break-point for improvement increase function is determined as 50% of the improvement potential comes from related action. This means that a supplier starts having improvement for a continuous action after allocating ca-pacity of more than 50% of improvement from respective action. That is why in biin(ai)is ai/2
5.2 Applied Model : Company Case for all the suppliers. The assumption is also supported by the experts, as there can be actions that are half satisfied by the suppliers.
About the slope of the line segment for the function of the on-site visit, it is dependent on breakpoints which are constant for all the suppliers, sequence numbers. As the historical data suggests that suppliers that are in their first sequence increases their sustainability score by 0.12 after having the on-site visits, the upper bound for effects of on-site visit on learning capacities is determined as 0.12. As the sequence number increases, the effects of on-site visit decreases.
It is because suppliers that have a smaller sequence number benefit more from on-site visits as they are new to supplier development. As suppliers get more experience in the program, the effect of on-site visit is also expected to decrease. Sequence 6 is used as an upper limit of the sequence number because currently, the maximum sequence number that the supplier has is 4.
The capacity increase from conducting on-site visit also decreases with the sequence number in the form of (0.04 ∗ 1 − e−sj). Constant 0.04 estimated from the historical data and 1 − e−sjis used as an approximation of decrease amount for further sequences. This means upper bound of 0.12 for suppliers that are explained previously decreases as the sequence number increases by using an exponential function. An illustration of upper bound decrease concerning the sequence can be seen in Figure 19.
Figure 19: Effects of sequence number on maximum learning capacity increase
As can be seen from the Figure 19, a total capacity increase from strategies used by the buyer decreases with the sequence number. That is because suppliers might lose their attention to the program as the sequence number increases. Therefore, buyer involvement strategies are more effective in the earlier sequences. Also, the improvement when the decisions are on breakpoints is determined. The second break-point provides 0.625 of the upper bound of the learning capacity increase whereas, the third break-point provides directly the upper bound as it is the maximum degree of buyer involvement for a supplier. As it is discussed earlier, the maximum of conducting on-site visits is determined as conducting 3 days of on-site visits for a topic.
5.2 Applied Model : Company Case
1, if continuous action i in topic k assigned for supplier j 0, otherwise
1, if binary action i in topic k is chosen for supplier j 0, otherwise
, ∀ i ∈ Ibk, ∀j ∈ J, ∀k ∈ K
mijkn=Capacity allocated to continous action i in topic k by supplier j in line segment n,
∀ i, j, k, n ∈ Ick, J, K, N
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,
=
5.2 Applied Model : Company Case
Objective function maximizes the total absolute improvement potential of all suppliers. Im-provement potential results from assigning binary and continuous actions to suppliers. If an action i is assigned to supplier j, bijk= 1. There are also continuous actions that might not be completely satisfied but provides improvement for suppliers. The decision mijknrepresents how much capacity allocated by supplier j for action i. In addition to that, as the realized improvement depending on the allocated capacity for actions is modeled as linear-piece wise function, the information how much capacity is used in which line segment is used to calcu-late realized improvement from actions. The multiplication of allocated capacity for the line segment and its slope provides the improvement from an action.
Constraint (1) ensures that the total capacity allocated by a supplier for a continuous action must be less than improvement potential from that action. Constraint (2) guarantees that if a continuous action is not assigned to a supplier, that a supplier cannot allocate any of its ca-pacity to that action. Constraint (3) ensures that caca-pacity allocated for continuous and binary actions by a supplier in a topic must be less than initial capacity estimated from historical data of average improvement for each sequence and each topic, and additional capacity results from buyer involvement strategy (on-site visits) for that topic. It should be noted that duration of on-site visit is a parameter as Philips currently conduct 3 days of on-site visit for each supplier.
Constraint (4) and (5) represent if an action is already implemented in a supplier, that action cannot be assigned to that supplier. Constraint (6) is for successor relationship. If the prede-cessor action is not implemented, then the sucprede-cessor actions of the predeprede-cessor actions cannot be assigned to that supplier. Constraints (7)-(12) is for implementing linear piece-wise func-tion for improvement potential from acfunc-tions. The idea is that a line segment cannot be used if the previous line segment is not completely utilized. In addition to that, the capacities of line segments are determined from breakpoints. The budget constraint is not implemented in the base model as the buyer only conducts on-site visit and the duration is already determined.
5.2.3 Application of The Theoretical Model: Including Learning Behaviors of Suppliers