Flexible Inventory Models for Imperfect Manufacturing Systems

Abstract

The economic and production order quantity models have been commonly used in today’s industrial life for optimum lot size calculations. However, these inventory models are based on the unrealistic assumption that processes produce good quality product every time. Moreover, inventory models mainly focus finish goods and raw materials inventory whereas work-in-process inventory has been ignored, relatively. Furthermore, these models are based on the fact that inspection takes negligible time as processes are assumed perfect. However, in reality, imperfection exists in manufacturing processes due to several reasons. Therefore, the role of inspection process in imperfect production environments cannot be ignored. This thesis considers imperfect production and inspection processes into consideration to develop a mathematical model that consider rework, rejection, inspection, re-inspection of reworked products with focus on work-in-process inventory for group technology manufacturing setup. The developed inventory model, named as GTOQIR model, is based on average cost minimization. Numerical examples are used to illustrate the developed model and its comparison to the existing inventory models. Furthermore, the thesis extend the developed (GTOQIR) model by adding quality cost due to rework, rejection and inspection processes (IRR) and its ultimate impact on total average cost and lot size. Mathematical inventory lot size is defined based on average cost minimization. Numerical computation highlights the significant effect of IRR quality costs with focus on work-in-process inventory. In addition, it is observed that decisions in ultra-precise and high-tech manufacturing environments are highly challenging. High-tech and good quality measuring instruments are used for product inspection when it passes through the value-added process. Product rejection, rework, and acceptance is usually based on the measurement report. However, portability exists that the technical personnel may commit error while defining product status based on measurement report. Moreover, the role of technical personnel in decision making process for inventory models focusing group-technology manufacturing setup has been less focused. Most of the literature assume that decisions are perfect. However, in reality, human errors exist in making these decisions. The thesis incorporates human errors into the decision making process in a group-technology inventory model where high value-added machining processes are involved. Mathematical model is developed for optimal lot size considering human errors in the decision making process and process imperfection with focus on work-in-process inventory. Lot size is optimized based on average cost function by incorporating human error Type I and human error Type II. The developed model is considered more flexible as it incorporate imperfection in process with human errors in the decision making process. It is a common assumption in the literature that customer demands are fulfilled during production phase of the production order quantity model although production processes are assumed as imperfect. Furthermore, manufacturing managers prefer product qualification from inspection station especially when processes are imperfect. The thesis re-consider the concept of rework and backordering for the single-stage manufacturing setup problem. It is proposed that customer demands are not fulfilled during the production phase due to process imperfection. Customer demands are satisfied either at the end of inspection process or after reworking imperfect products. Rework operation, inspection process, and planned backordering are incorporated in the developed model. Lot size and planned backorder quantities are optimized based on the minimum average cost by using analytical approach. The inventory model is compared with the mathematical model where demand are fulfilled during the production processes. Numerical examples are used for illustration of the developed model. The proposed model is considered more flexible in comparison to the existing models as it incorporates imperfection, rework, inspection rate, and planned backorders. Furthermore, it has always been a dilemma in manufacturing companies that how much extra units to be produced as safety stock when demand is certain to some extent and company know that produced products will be consumed in the market easily. In addition to this, imperfection in processes also stress the manufacturers to produce extra units to avoid any shortages. Additionally, customer is willing to wait for demands to be backordered in case of any shortages. However, inventory carrying cost may play a vital role if products are produced in relatively large amount due to high carrying cost. Therefore, mathematical model is developed based on average cost minimization that can define the ordering quantity taking safety stock into consideration with planned backorders in an imperfect production setup. Developed inventory models is a closed form solution and is illustrated via numerical examples. Numerical examples are used to highlight its significance in daily industrial life.