Table 5: Products in departments A and B
The possible earning revenue for a different product mix is listed in Table 6. For instance, if department A makes product X1 and department B makes product Y1, the possible profit earned by A is 6.5 and the possible profit earned by B is 5. The assumption is that both departments are willing to collaborate. They are willing to communicate to achieve the entire maximum profit.

Department A

Department B

X1, Y1

4.5

3

X1, Y2

5

3.5

X2, Y1

6.5

4

X2, Y2

6

3.5

X3, Y1

7

3

X3, Y2

8

4

Table 6: Revenues for mixed product Set
So far, Company SPEC has extracted many new understanding of customers’ needs and market potential based on the gathered big data. However, managers were not able to make sure of the various bit of analysed information to make informed decisions. The CEO commented ‘the isolated information is useful but I was not able to use them to make better judgement or induce new supply chain innovation capabilities’. The comments were echoed by both factory managers. The next step of the process is to utilise the deduction graph model to create a competence network in order to better utilise the information generated from the big data analysis.
4.2 The Competence Network
A competence network can vividly express the possible means of expanding a competence set to manufacturing new products (Li, 1997). The network developed in this case contains compound nodes and considers a cyclical situation. Figure 3(a) shows the expanding process of department A to produce X1, X2, or X3, and Figure 3(b) shows the expanding process of department B to produce Y1 or Y2 based on its current skills a, b, and f.
Figure 3(a). Network of department A (existing skills are c, d, and e)
Figure 3(b). Network of department B (existing skills are a, b, and f)
Each node represents each competence set or skill. The arc shows there is a connection between the two nodes, such as, a c means skills c can be learned from skill a. As for d and m, there is no arc between these nodes, meaning that it is almost impossible to learn d from m or to learn m from d. The number on the arc means the cost spent on obtaining the skills. There are also compound nodes, such as d^e and a^b. The compound node can only be used when the decomposed nodes are obtained. In order to produce the new products, the needed skills will be obtained by learning from existing skills or by purchasing from other departments directly. For example, in Figure 3(a), the skill f can be learned from skill e, c, and d^e with the cost of 2.5, 2, and 1, respectively. But A also can purchase skill f from department B with the cost of 1.5. Also, e f g i shows the learning sequence indicating that the learning process starts from e, learns f, then learns g, then leans skill i from g. The final objective of the competence network is using optimisation software to find the best sequence with the highest profit.
Based on the developed network, the challenge faced by Company SPEC can be formulated as a linear programming problem. A deduction graph will be generated to support the model in finding the optimal solution.
According to the objective equation:
The objective equation for the eyeglasses manufacturing company should be:
The mathematic properties and constraints of the objective are listed in the Appendix.
Finally, the above objective equations and constraints were set in LINGO to obtain the optimised solution. The solution is that department A should produce X2, and department B should produce Y1. The solution result is shown in Table 7. As for department A, skill i is learning from c, skill f is bought from department B, and skill g is learning from f. And for department B, skill c is bought from department A and skill j is learning from skill c. The expanding deduction graph is shown in Figures 4(a) and 4(b).
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