Incorporating Quality Issues Into Inventory Models And Supply Chain Contract

Today, enterprises are facing increasingly competitive pressure. With buyer's power increasing, customer's requirements become more and more demanding. To maintain competitive edge, high quality is an essential factor. More and more fierce competition, rapid development of information and network technology and economic globalization, also change the enterprises'competition paradigm. Competition between single firms has been replaced by supply chains competition. Through supply chain management, information sharing and cooperation among supply chain members, the supply chain can meet customer's demanding requirement, therefore gain advantage in competition with other supply chains.Inventory model is a classic research issue in supply chain management, while supply chain contracting received extensive attention in recent years. But we notice that there are few literatures in inventory models and supply chain contracting with consideration of quality issues. With focus on these two areas, we carry out some research work.The main work and conclusions can be concluded in the following five parts:In the first part, based on Salameh and Jaber (2000), investigate the buyer's optimal ordering strategy when the defective percentage is random and inspection is imperfect. In addition to relaxing the assumption of perfect inspection, we also extend our model to considering setup cost reduction, adjustable inspection rate, shortage permission and stochastic demand.In the second part, we study buyer and vendor's integrated inventory model under the condition of random defective percentage and imperfect inspection process. Under the assumption of"lot-for-lot"production policy, we obtain the joint economic lot size to optimize the whole supply chain's benefits. Then we let the vendor's setup cost or the buyer's ordering cost be the model's decision variable, to consider the problem of setup cost or ordering cost reduction in integrated inventory model. Next, we relax the assumption of"lot-for-lot"production policy, and consider the case of vendor's lot size is an integer number times of the buyer's ordering quantity. In this case, we develop the vendor's optimal batch size and the buyer's optimal ordering quantity to minimize the whole supply chain's expected cost.In the third part, we introduce Taguchi quality cost into integrated inventory. Using Li and Maghsoodloo's asymmetrical truncated quadratic quality loss function, we develop the vendor and buyer's total expected cost function. When the process quality is given, we obtain the closed-form solution of joint economic lot size. While when the process quality is a decision variable, that is the vendor can invest in a process to decrease its variance, we can not obtain closed-form solution. Instead, we develop sufficient condition to assure the convexity of the total expected cost function, and give the condition which the optimal solution should meet.In the fourth part, we study the interaction of upstream firm's quality investment and downstream firm's inspection strategy. Traditional models focus on the manufacturer's inspection decision problem by taking quality as exogenous. Under this assumption, Deming(1982, 1986), Vander Wiel and Vardeman(1994) proved all-or-none inspection policy is optimal if the following two conditions hold: (1) the quality of units in a batch is modeled as i.i.d. random variables; (2) overall inspection cost is a sum of individually and identically determined costs for each of the items encountered. In our study, we found all-or-none inspection policy is still optimal in cooperative supply chain system even taking the quality as endogenous. But in non-cooperative supply chain system things are different. We investigate the Nash game between the manufacturer and the retailer, and found the Nash equilibrium is most related to the contract parameters: (1) ifαR < C R+Δw , there is a unique Nash equilibrium; (2) ifαR = C R+Δw , there may be a unique Nash equilibrium or infinite Nash equilibria depend on the inspection cost; (3) ifαR > C R+Δw , there may be a unique Nash equilibrium or three Nash equilibria depend on the inspection cost. Therefore in non-cooperative supply chain system, when taking the quality as endogenous, the all-or-none inspection policy is no longer optimal.In the last part, we analyze the design of optimal contract for buyer when the vendor's product quality is imperfect. Different from the past literature which focus on using supply chain contract in quality control, we study on coordinating the inventory by using supply chain contract while taking the quality as exogenous. First, as a benchmark, we investigate the buyer and vendor's integrated inventory model. Then we study the buyer's optimal ordering strategy when the buyer and vendor do not cooperate with symmetric information and asymmetric information individually. Interestingly, we found that in symmetric information case the performance of supply chain may not necessarily superior to the performance of supply chain with asymmetric information. Finally, we investigate the design of the buyer's optimal contract in symmetric and asymmetric information cases individually. The conclusions include: (1) in symmetric information case, the buyer's optimal contract can coordinate the whole channel, while the vendor can only obtain her reservation profit in this case; (2) in asymmetric information case, the buyer's optimal contract can almost achieve channel coordination, and the vendor's profit can be higher than her reservation profit if her defective percentage below the upper bound of the buyer's estimation; (3) using supply chain contract can improve the supply chain's efficiency both in symmetric and asymmetric information case.The main innovations of this study are as follows:First, in Salameh and Jaber (2000)'s model the sufficient condition to ensure that shortage will not occur in inspection period may not really prevent their occurrence. To avoid shortage occur in inspection period, in our model when finishing the inspection of the whole batch, the product in this batch can be used to meet demand. We also relax the assumption of perfect inspection process, and allow the buyer's inspection process make type I mistake, i.e. accepting an item that is defective. In the following, we extend basic model to four cases: ordering cost reduction, adjustable inspection rate, shortage permission and random demand.Second, it is generally assumed that all units produced are of perfect quality in integrated inventory models. In this dissertation we investigate the integrated model with consideration of random defective rate and imperfect inspection process. Also in our model we take the vendor's setup cost or the buyer's ordering cost as endogenous variable and analyze the joint optimal decision-making problem of setup cost, ordering cost and economic lot size.Third, using Li and Maghsoodloo's asymmetrical truncated quadratic quality loss function, we first introduce Taguchi quality loss into integrated inventory model. Also in our model, the vendor can invest in a process to decrease its variance. We analyze how the vendor and the buyer make their decisions to optimize the whole supply chain's profit.Fourth, in Deming (1982, 1986), Vander Wiel and Vardeman (1994), they take product quality as exdogenous variable. In this dissertation, we take the quality investment as endogenous variable and found all-or-none inspection policy is still optimal when the vendor and buyer cooperate. When the vendor and buyer do not cooperate, we study the Nash game between them and found there may be one unique Nash equilibrium, three Nash equilibria and infinite Nash Equilibria depends on the contract parameters and the buyer's inspection cost.Last, different from the past literatures which focus on using supply chain contract to control supplier's quality, in this dissertation by use of principle-agent theory we investigate the design of buyer's optimal contract to simulate the vendor provide true information and coordinate the inventory level to maximize the buyer's profit.To sum up, in this dissertation around quality issues we study single firm's optimal order strategy, multiple firms'integrated inventory model, the interaction between quality investment and inspection strategy and supply chain contracting with asymmetric information. Our work extends the current research in the related areas, and also provides theoretical guidance to production management decision-making.