Contract Design And Production Decision Models Under Uncertain Environments

In this dissertation, the supply chain pricing and warranty contract, the price re-bate and warranty contract, the warranty contract under uncertain demands, the rawmaterial pricing contract, the regulation contract and the optimal taxation contractare considered, and the corresponding second-best contract are obtained and com-pared with the first-best contract under complete information; moreover, a new classof multi-period multi-source production planning problem with service level are alsodiscussed.In Chapter2, a supply chain pricing and warranty contract problem under incom-plete information is studied, in which the supplier’s product quality is usually unob-servable to the buyer, by characterizing the subjective assessment as a fuzzy variable,a pricing and warranty contract model is developed with the purpose of maximizingthe buyer’s expected payoff. The results demonstrate that, if purchasing quantity andproduct quality are complementary, the buyer’s second-best purchasing quantity willbe less than the first-best one; if substitutable, the opposite is true.In Chapter3, a supply chain contract design problem is considered, in whichthe product quality is the supplier’s private information and the demand is uncertain.Furthermore, three strategies, named inspection, price rebate and warranty, are simul-taneously employed in the contract so as to incentivize the supplier to improve hisproduct quality. An inspection-based price rebate and warranty contract model is de-veloped with the purpose of maximizing the buyer’s expected payoff. The optimalsolution demonstrates that the second-best inspection ratio is the same as the first-bestone, and the second-best price rebate is less than the first-best one. With respect to thesupplier’s optimal warranty sharing ratio, if the supplier’s warranty sharing ratio andhis product quality are substitutable, then his second-best warranty sharing ratio willbe larger than the first-best one, while in the case of complement, it is the same as thefirst-best level.In Chapter4, a warranty contract problem is studied and a warranty contractmodel with uncertain demand is developed with the purpose of maximizing the buyer’s expected payoff by designing inspection ratio and warranty sharing ratio. The modelanalysis shows that, for the high product defective rate supplier, the optimal contract isthe same as the case of complete information, while for the low product defective ratesupplier, the optimal warranty sharing ratio is decreasing with respect to the buyer’sinspection ratio and the repair cost, and increasing with respect to his product defectiverate, the warranty cost, and the difference between the price sold to the buyer and theproduction cost.In Chapter5, an optimal nonlinear taxation problem is discussed in which theconsumer’s taste to the product is incomplete information. Since the assessment of thegovernment and the monopolist about the consumer’s taste is subjective, therefore, it isreasonable to characterize this assessment as a fuzzy variable. What’s more, a bilevelfuzzy optimal nonlinear taxation model is developed with the purpose of maximizingthe expected social welfare and the monopolist’s expected welfare under the incentivefeasible mechanism. The equivalent model for the bilevel fuzzy optimal nonlinear tax-ation model is presented and Pontryagin maximum principle is adopted to obtain thenecessary conditions of the solutions for the fuzzy optimal nonlinear taxation prob-lems. Finally, one numerical example is given to illustrate the effectiveness of theproposed model, the results demonstrate that the consumer’s purchased quantity notonly relates with the consumer’s taste, but also depends on the structure of the socialwelfare.In Chapter6, the multi-firm regulation problems with yardstick competition un-der asymmetric information are studied. A multi-firm regulation contract model is thendeveloped with the purpose of maximizing the expected social welfare. Its equivalentform is given and the sufficient and necessary conditions of the optimal regulatorypolicies are presented. Furthermore, we provide an optimal regulatory policy for aspecial case, where the output has finite first-order derivatives. An application in sup-ply chain management is given to illustrate the effectiveness of the proposed model.The results demonstrate that the firm whose marginal cost is more than the yardstickprice desires to take the yardstick price as an example.In Chapter7, a raw material pricing contract design problem is considered. Twostrategies, named wholesale price and fixed transfer are simultaneously employed in the contract. Then, a raw material pricing contract model is developed with the pur-pose of maximizing the raw material supplier’s expected payoff, and its equivalentform is obtained. The optimal contracts are obtained under the cases of completeinformation and incomplete information, respectively. The optimal contracts demon-strate that the optimal purchasing quantity under incomplete information is less thanthat of under complete information.In Chapter8, a new class of multi-product source and multi-period fuzzy randomproduction planning problems with minimum risk and service levels is studied. Be-cause the exact value of the objective function cannot be easily obtained, we adoptan approximation approach (AA) to evaluate the objective value and then discuss theconvergence of the AA, including the convergence of the objective value, the conver-gence of the optimal solutions and the convergence of the optimal value. Since theapproximating multi-product source multi-period FRPP model is neither linear norconvex, an approximation-based hybrid monkey algorithm (MA) which combines theAA, stochastic simulation (SS), neural network (NN) and MA is designed to solve theproposed model. Finally, numerical examples are provided to illustrate the effective-ness of the hybrid monkey algorithm.