Beyond make-or-buy: cross-company short-term capacity backup in semiconductor industry ecosystem

Abstract

Since the uncertainty involved in demand forecast is increasingly amplified with the forecast lead-time, high-tech companies often suffer the risks of oversupply and shortage of capacity that will affect the profitability and growth. High-tech industries including semiconductor and TFT-LCD industries are capital-intensive, in which the capacity plan and corresponding capital investment decisions are critical due to demand fluctuation. Once the capacity is planned, the company may suffer the risks of either low capital-effectiveness due to low capacity utilization and capacity oversupply, or poor customer satisfaction caused by the capacity shortage. Most of the existing studies focused on solving the long-term capacity shortage issue through optimizing the capacity investment plan, or medium-term capacity plan to allocate demands among the wafer fabrication facilities (fabs) to balance the loading and product mix. Focusing on a real setting, this study proposed a systematic decision method to analyze short-term solutions of cross-company capacity backup between the companies in the semiconductor industry ecosystem. In particular, a game theory and decision tree analysis model was developed to support this decision. A case study was conducted with real data of semiconductor manufacturing companies in Taiwan for validation. The results have demonstrated practical viability of this approach. The approach suggested has been implemented in this company.

Appendix

The objective functions and constraints of Company A & B under different capacity backup strategy are formulated as follows.

1.1 Strategy 1: non-cooperative

Company A

(13)

$$ {\text{St}}.\,\alpha Q_{a} + Q_{b} \leqq { \min }\left( {\alpha X_{a,} X_{b} } \right), $$

(14)

(Total extra output is limited by remaining capacity)

$$ P_{a} - VC_{a} - \, O_{a} > 0, \, O_{b} - OC_{a} > 0,Q_{a} , \, Q_{b} \ge 0 $$

(15)

(Backup agreement is conditioned on positive net profit)

Company B

$$ {\text{Max}}\,\pi_{b} = \left( {P_{b} - VC_{b} - O_{b} } \right) \times Q_{b} + \left( {O_{a} - OC_{b} } \right) \times \alpha Q_{a} $$

(16)

$$ {\text{St}}.\,\alpha Q_{a} + Q_{b} \leqq { \min }\left( {\alpha X_{a,} \, X_{b} } \right), $$

(17)

$$ P_{b} - VC_{b} - O_{b} > 0, \, O_{a} - OC_{b} > 0, \, Q_{a} , \, Q_{b} \ge 0 $$

(18)

Since each company would optimize its own profit, there are two individual equations, Eqs. 13–15 and 16–18. There is a special parameter α in the objective function and constraint, which represents a capacity exchange rate between company A and B. This difference comes from the product complexity of the two companies. If one set of equipment could run one piece of Company A’s product, then it could run α piece of Company B’s product. Because X _a and Q _a are measured by Company A’s product and X _b and Q _b are measured by Company B’s product, X _a and Q _a need to be multiplied by α to be compared with X _b and Q _b .

Observing that both objective function and constraint are linear combination of Q _a and Q _b in Eqs. 13 and 14 (since the parameters P _a , P _b , VC _a , VC _b , O _a , O _b , OC _a , OC _b ,…, α, X _a , X _b are all constants to Q _a and Q _b ), therefore, it is easy to find the optimal solution at the corner point of the constraint equation as shown in Fig. 10. So, the optimization happens only when Company A gets full backup from Company B (Q _b  = 0), or Company B gets full backup from Company A (Q _a  = 0). Thus we could get the equilibrium payoff in equation 1 and equation 2. Notes that in this problem the backup price P _a and P _b are independent of the backup quantity Q _a and Q _b . This is an assumption different with the famous Stackelberg model or Cournot model to deal with pricing and quantity decision on duopoly market. We made this assumption since the backup price mechanism is not the same as the product price which is impacted by demand and supply quantity in duopoly market. Indeed, the backup price is set according to the manufacturing cost and profit margin of the specific process step. Thus, it will not be impacted by the backup quantity.

Fig. 10

Equilibrium of non-cooperative capacity strategy

1.2 Strategy 2: cooperative to maximize total profit

$$ \begin{aligned} {\text{Max }}\left( {\pi_{a} + \pi_{b} } \right) & = \left( {P_{a} - VC_{a} - O_{a} } \right) \times Q_{a} + \left( {O_{b} - OC_{a} } \right) \times Q_{b} /\alpha \\ & \quad + \left( {P_{b} - VC_{b} - O_{b} } \right) \times Q_{b} + \left( {O_{a} - OC_{b} } \right) \times \alpha Q_{a} \\ & = \left( {P_{a} - VC_{a} - \alpha OC_{b} + \left( {\alpha - 1} \right)O_{a} } \right) \times Q_{a} + \left( {P_{b} - VC_{b} - OC_{a} /\alpha - \left( { 1- 1/\alpha } \right)O_{b} } \right) \times Q_{b} \\ \end{aligned} $$

(19)

$$ {\text{St}}.\,\alpha Q_{a} + Q_{b} \leqq { \min }\left( {\alpha X_{a,} \, X_{b} } \right) $$

(20)

$$ Q_{a} , \, Q_{b} \geqq 0 $$

(21)

Strategy 2 is a true cooperative strategy, which assumes that the two parties have consensus to take the overall system as a profit center. And they share the total profit by a certain allocation ratio. Therefore, it has a unique profit function as shown in Eq. 19. The capacity constraint in Eq. 20 is exactly the same as Eqs. 2 and 5 of non-cooperative strategy, but the profit constraint in Eq. 21 has removed the backup agreement for individual profit that P _a  − VC _a  − O _a  > 0, O _b  − OC _a  > 0, in Eq. 15 and P _b  − VC _b  − O _b  > 0, O _a  − OC _b  > 0 in Eq. 18. Except for the change in these parameters, we could see the objective function and constraint structures are very like those in Eqs. 13–15 or 16–18. In another word, both the objective function and constraint function are also a linear combination of Q _a and Q _b , and the optimal solution would happens at the corner points either Q _a  = 0 or Q _b  = 0. If we assume that company A share β of the total profit, then B company share (1 – β) of total profit, and the payoff for Strategy 2 could be derived as shown in Eqs. 3 and 4.

As for the profit allocation ratio, it must be negotiated before the capacity backup. A simple allocation rule may depend on their capacity or equipment contribution. However, sometimes it may be not easy to have a consensus about the allocation ratio in practice. Compared with non-cooperative strategy, this cooperative strategy is easier to get a stable equilibrium since both parties would not insist to get profit from get physical wafer backup, but from a profit sharing mechanism. The pitfall of this mechanism is on the mutual trust (to share information) and profit allocation rule.

1.3 Strategy 3: cooperative to ensure equal profit

$$ \begin{aligned} {\text{Max }}\left( {\pi_{a} + \pi_{b} } \right) & = \left( {P_{a} - VC_{a} - O_{a} } \right) \times Q_{a} + \left( {O_{b} - OC_{a} } \right) \times Q_{b} /\alpha \\ & \quad + \left( {P_{b} - VC_{b} - O_{b} } \right) \times Q_{b} + \left( {O_{a} - OC_{b} } \right) \times \alpha Q_{a} \\ & = \left( {P_{a} - VC_{a} - \alpha OC_{b} + \left( {\alpha - 1} \right)O_{a} } \right) \times Q_{a} + \left( {P_{b} - VC_{b} - OC_{a} /\alpha - \left( { 1- 1/\alpha } \right)O_{b} } \right) \times Q_{b} \\ \end{aligned} $$

(22)

$$ {\text{St}}.\,\alpha Q_{a} + Q_{b} \leqq { \min }\left( {\alpha X_{a} ,X_{b} } \right) $$

(23)

$$ \pi_{a} = \pi_{b} , $$

(24)

where

$$ \begin{aligned} \pi_{a} & = \left( {P_{a} - VC_{a} - O_{a} } \right) \times Q_{a} + \left( {O_{b} - OC_{a} } \right) \times Q_{b} /\alpha \\ \pi_{b} & = \left( {P_{b} - VC_{b} - O_{b} } \right) \times Q_{b} + \left( {O_{a} - OC_{b} } \right) \times \alpha Q_{a} \\ & \quad P_{a} - VC_{a} - O_{a} > 0, \, P_{b} - VC_{b} - O_{b} > 0,Q_{a} ,Q_{b} > 0 \\ \end{aligned} $$

(25)

Strategy 3 is also a cooperative strategy, but it assumes that each party wants to get physical wafer backup and get equal profit. Compared to Strategy 2, its objective function (22) is exactly the same as Eq. 19, capacity constraint Eq. 23 is the same as Eq. 20, but it adds an extra constraint π _a  = π _b in Eq. 24 and the equations of π _a and π _b is the same as that in Eqs. 13 and 14 Furthermore, the decision variable Q _a and Q _b in this model is limited to be non-zero value in Eq. 25 so that both company A and B could get extra capacity after backup (on the same time, each of them need to provide some surplus capacity). Another feature in Eq. 25 add back the individual company’s backup profit condition that P _a  − VC _a  − O _a  > 0 and P _b  − VC _b  − O _b  > 0. This is for the purpose to coherent with the condition that each company must get some physical wafer backup. After adding the constraint of equal profit and non-zero backup quantity, the optimal solution may shift from original corner point to somewhere in between the original corner points. It takes some algebra to derive the optimal solution. Notating Q* _a and Q* _b as the optimal level of Q _a and Q _b , and (π*_a3, π*_b3) as the payoff, the equilibrium quantity and payoff can be derived.