Modelling of some problems on production planning and inventory management

The major issues of recent research is the products nature live when it can be deteriorated, when it can be used fully, when deterioration rate is random or when products have fixed lifetime. These problems are solved by this research studies. Along with the product’s nature, the optimal buffer inventory, replenishment rate, imperfect production, and inspection errors during the shipment of production system from in-control-state to out-of-control state are efficiently studied by this research studies. The dissertation consists of six different studies on products produced by production system. The first chapter of the thesis is devoted to discuss the background of different study, basic concepts, and terminology, historical review of the inventory model and objective and organization of the thesis. In Chapter 2, an inventory model of two-warehouse is considered with quadratically increasing demand and time-varying deterioration. Comparing to the existing literature, the model is derived with finite replenishment rate and unequal length of the time cycle. The associated cost of the system is minimized. A numerical example, the graphical representation and sensitivity analysis are provided to illustrate the model. Chapter 3 describes a deteriorating inventory model with ramp-type demand pattern under stock-dependent consumption rate. The deterioration of the product is considered as probabilistic to make the research a more realistic one. The proposed model assumes partially backorder rate, which follows a negative exponential with the waiting time. The purpose of this study is to develop an optimal replenishment policy such that the total profit is maximized. Here, it is provided a simple solution procedure to obtain the optimal solution. Chapter 4 illustrates a mathematical model to obtain an optimal replenishment policy for deteriorating items with maximum lifetime, ramp-type demand, and shortages. Holding cost and deterioration function both are linear function of time, which are treated as constants in most of the deteriorating inventory model. Numerical examples along with graphical representations are provided to illustrate the model. In Chapter 5, a two-echelon supply chain model with variable setup cost and deterioration cost are analyzed. It is assumed that the setup cost is directly proportional and the deterioration rate is inversely proportional to reliability. Basic algebraical procedure is used to obtain the optimal closed-form solution of this model. The objective is to minimize the total cost of the entire system by considering reliability as a decision variable. In Chapter 6, an effort has been made to obtain an optimal buffer inventory and inspection policy with preventive maintenance and two types of inspection errors. This model considerers a production system that is subject to a random deterioration from an incontrol state to an out-of-control state with a specific distribution. An on-line inspection is started after some time to inspect products. To detect the defective items another human inspection policy is considered at the end of production cycle. Chapter 7 deals with the problem of determining the optimal production run time for an imperfect production system with inspection policy. This model considerers that product inspection perform at any arbitrary time of the production cycle. Two types of inspection errors (Type I and Type II) are considered to make the model more realistic rather than the existing models. Defective items are salvaged at some cost before being shipped. Non-inspected defective items are passed to customers with free minimal repair warranty. Lastly, Chapter 8 concludes the thesis and discusses its achievements. It also suggests further studies in this area.