# American Institute of Mathematical Sciences

January  2021, 17(1): 409-426. doi: 10.3934/jimo.2019118

## Incentives for production capacity improvement in construction supplier development

 School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

* Corresponding author: Wei Zeng

Received  February 2019 Revised  April 2019 Published  September 2019

The purpose of this paper is to investigate the supplier development (SD) in construction industry. As the supplier's production capacity cannot meet the construction requirements, the owner wants to take incentives to encourage the supplier to improve its production capacity. A principal-agent model and a Stackelberg game model are proposed to study the impact of owner's incentives including cost sharing and purchase price incentive on the production capacity improvement in SD. Furthermore, we give a sensitivity analysis of the influence of supplier's internal and external parameters, i.e., purchase quantity, cost structure, market price and market demand, etc., on the production capacity improvement. The findings of this study can help the owner to make a better decision on the incentive mechanisms for SD, resulting in both better SD practices and a win-win situation.

Citation: Yanjun He, Wei Zeng, Minghui Yu, Hongtao Zhou, Delie Ming. Incentives for production capacity improvement in construction supplier development. Journal of Industrial & Management Optimization, 2021, 17 (1) : 409-426. doi: 10.3934/jimo.2019118
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##### References:
The genetic algorithm flowchart of the principal-agent model
The evolution process of the principal-agent model
The evolution process of the Stackelberg game model
Overview of differences between reactive/strategic and direct/indirect supplier development
 Characteristics Incentive mechanism Reactive Correct of the laggard supplier's deficiency and achieve short-term improvements; Problem-driven or supplier self-select through performance or capability deficiency [15]. Limited, minimal and specific investments or negative feedback to achieve short-term improvement and competitiveness [14]. Proactive Achieve continuous improvement of supply base, long-term competitive advantages; Market-oriented [14]. Significant levels of resource commitment and investment to pursuit continuous improvement and long-term competitiveness [14]. Direct Deep corporation with the supplier and commits financial and/or human capital and plays an active role; Collaborative approach based on frequent manufacturer-supplier exchanges, resulting in bilateral deployment of relationship-specific investments [15], [23], [28]. Support in equipment or capital investments; Advice on organizational procedures and training of technical staff training, furnishing temporary on-site support to enhance further interaction [23], [36]. Indirect Limited, minimal and specific investments; focus on supplier identification, targets (goals) setting, measurement of goal attainment, as well as feedback of goal attainment to suppliers [15], [36]. Evaluating the suppliers' operations, setting performance goals, providing performance feedback, instilling competitive pressure, promising future business based on goal attainment or recognizing the suppliers' progress by designating them as preferred suppliers [15], [36].
 Characteristics Incentive mechanism Reactive Correct of the laggard supplier's deficiency and achieve short-term improvements; Problem-driven or supplier self-select through performance or capability deficiency [15]. Limited, minimal and specific investments or negative feedback to achieve short-term improvement and competitiveness [14]. Proactive Achieve continuous improvement of supply base, long-term competitive advantages; Market-oriented [14]. Significant levels of resource commitment and investment to pursuit continuous improvement and long-term competitiveness [14]. Direct Deep corporation with the supplier and commits financial and/or human capital and plays an active role; Collaborative approach based on frequent manufacturer-supplier exchanges, resulting in bilateral deployment of relationship-specific investments [15], [23], [28]. Support in equipment or capital investments; Advice on organizational procedures and training of technical staff training, furnishing temporary on-site support to enhance further interaction [23], [36]. Indirect Limited, minimal and specific investments; focus on supplier identification, targets (goals) setting, measurement of goal attainment, as well as feedback of goal attainment to suppliers [15], [36]. Evaluating the suppliers' operations, setting performance goals, providing performance feedback, instilling competitive pressure, promising future business based on goal attainment or recognizing the suppliers' progress by designating them as preferred suppliers [15], [36].
Overview of differences between reactive/strategic and direct/indirect supplier development
 Symbol Definition $q_{0}$ The production capacity of the supplier before the SD program $q^{N}$ The production capacity when not participating the SD program $q$ The production capacity after SD program $r$ The production cost of per unit $p$ The market price $k$ The cost per unit of production capacity improvement $Q$ Purchase quantity $h$ Overcapacity cost per unit $\lambda$ Purchase price incentive $\rho$ The discount rate of future market profits $\theta$ Cost sharing ratio $\omega$ Owner's utility parameter for the production capacity improvement $\delta$ The supplier's risk aversion parameter $D$ The demand in future market $\Pi_{s}^{N}$ The supplier's total profits when not participating the SD program $\Pi_{0}$ The supplier's reservation utility of future market $\Pi_{s}$ The supplier's total profits $\Pi_{sc}$ The supplier's profits of current project $\Pi_{sf}$ The supplier's profits of future market $\Pi_{b}$ The owner's profits
 Symbol Definition $q_{0}$ The production capacity of the supplier before the SD program $q^{N}$ The production capacity when not participating the SD program $q$ The production capacity after SD program $r$ The production cost of per unit $p$ The market price $k$ The cost per unit of production capacity improvement $Q$ Purchase quantity $h$ Overcapacity cost per unit $\lambda$ Purchase price incentive $\rho$ The discount rate of future market profits $\theta$ Cost sharing ratio $\omega$ Owner's utility parameter for the production capacity improvement $\delta$ The supplier's risk aversion parameter $D$ The demand in future market $\Pi_{s}^{N}$ The supplier's total profits when not participating the SD program $\Pi_{0}$ The supplier's reservation utility of future market $\Pi_{s}$ The supplier's total profits $\Pi_{sc}$ The supplier's profits of current project $\Pi_{sf}$ The supplier's profits of future market $\Pi_{b}$ The owner's profits
Summary of the sensitivity analysis in the Stackelberg game Model
 Changes in the parameter values Optimal production capacity $q^\ast=q_1$ Optimal production capacity $q^\ast=q_2$ Optimal production capacity $q^\ast=q_3$ 1.Increase in parameters related to the current project 1.1 The owner's utility parameter for the production capacity improvement $\omega$ $-$ $-$ $-$ 1.2 Purchase quantity $Q$ $-$ $-$ $\uparrow$ 2. Increase of supplier's parameters 2.1 Production cost per unit $r$ ↓ ↓ $-$ 2.2 The cost per unit of production capacity improvement $k$ ↓ $-$ $-$ 2.3 Overcapacity cost per unit $h$ $↓$ $↓$ $-$ 2.4 The supplieros risk aversion parameter $\delta$ $-$ $\uparrow$ $-$ 2.5 The supplieros reservation utility of future market $\mathrm{\Pi}_0$ $-$ $↓$ $-$ 3. Increase in market condition parameters 3.1 The market price $p$ $\uparrow$ $\uparrow$ $-$ 3.2 The discount rate of future market profits $\rho$ $\uparrow$ $-$ $-$ 4. Increase of incentive parameters 4.1 Cost sharing ratio $\theta$ $\uparrow$ $-$ $-$ 4.2 Purchase price incentive $\lambda$ $-$ $-$ $-$
 Changes in the parameter values Optimal production capacity $q^\ast=q_1$ Optimal production capacity $q^\ast=q_2$ Optimal production capacity $q^\ast=q_3$ 1.Increase in parameters related to the current project 1.1 The owner's utility parameter for the production capacity improvement $\omega$ $-$ $-$ $-$ 1.2 Purchase quantity $Q$ $-$ $-$ $\uparrow$ 2. Increase of supplier's parameters 2.1 Production cost per unit $r$ ↓ ↓ $-$ 2.2 The cost per unit of production capacity improvement $k$ ↓ $-$ $-$ 2.3 Overcapacity cost per unit $h$ $↓$ $↓$ $-$ 2.4 The supplieros risk aversion parameter $\delta$ $-$ $\uparrow$ $-$ 2.5 The supplieros reservation utility of future market $\mathrm{\Pi}_0$ $-$ $↓$ $-$ 3. Increase in market condition parameters 3.1 The market price $p$ $\uparrow$ $\uparrow$ $-$ 3.2 The discount rate of future market profits $\rho$ $\uparrow$ $-$ $-$ 4. Increase of incentive parameters 4.1 Cost sharing ratio $\theta$ $\uparrow$ $-$ $-$ 4.2 Purchase price incentive $\lambda$ $-$ $-$ $-$
Experiment Parameters
 $q_0$ p r k Q $\rho$ $\omega$ h $\Pi_0$ $\delta$ 30 100 40 20 60 0.9 20 10 300 0.1
 $q_0$ p r k Q $\rho$ $\omega$ h $\Pi_0$ $\delta$ 30 100 40 20 60 0.9 20 10 300 0.1
Parametric Analysis Results
 $\Pi_b$ $\Pi_s$ q $\lambda$ $\theta$ Principal-agent model 3803501.6 3029.1 898.4 30 0.38 Stackelberg game model 1157932.3 35456 1000 0.0011 1
 $\Pi_b$ $\Pi_s$ q $\lambda$ $\theta$ Principal-agent model 3803501.6 3029.1 898.4 30 0.38 Stackelberg game model 1157932.3 35456 1000 0.0011 1
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