Currently, the company competition is getting tighter. Distribution companies need to provide excellent service to their customers to maintain their competitiveness. Distribution service performance could be measured with lead time. However, Reducing lead times may increase costs. This problem could be solved using freight consolidation and reducing backhaul. Freight consolidation can be done by using a hub-and-spoke network with a combination of inbound and outbound distribution. This study developed a route model for hybrid hub-and-spoke with time windows. This model determined the routes for shipping goods to consumers and taking products to suppliers using the same vehicle to reduce the backhaul. This model also conducted freight consolidation at the hub. The decision variables in this model included the routes of delivery to consumers, the collection of goods at the suppliers, the number of products distributed through the hub and direct shipping, and the good distribution route. This model was implemented into the problems. Besides, sensitivity analysis of the model was carried out.

In this study, an integrated inventory model was developed among one vendor, multi buyers, and multi products. The total inventory cost to be minimized in this model is a combination of the vendor's and the buyers' total inventory costs. The total vendor inventory costs consist of setup costs and holding costs and the total inventory cost of the buyer consists of ordering costs, holding costs, stockout costs, and crashing lead time costs where the crashing lead time cost is approximated with an exponential function. Three decision variables will be calculated: the number of buyer orders, the lead time of each buyer, and the frequency of vendor shipments to all buyers in one production cycle. In this study, the optimal solution of each decision variable has been developed and applied to a case to show the use of models for finding optimal solutions. The sensitivity has also been performed to show the effects of some factors on the decision variables.

COVID-19 is a new disease that is affecting almost all of the world. Until now there has not been a single drug (vaccine) that can be used to cure it. Many attempts were made to prevent the spread of this disease but COVID-19 patients are increasing every day, although at the same time some are recovering. This study will calculate the probability of additional patients occurring over a long period of time, referred as a steady state state condition, using the Markov chain method. Nine states have been formed to represent the daily increase ranges of COVID-19 patients number. The calculation results show that the possibility of additional patient number between 1 to 91, 92 to 182, 182 to 272, 273 to 363, 364 to 454, 455 to 545, 546 to 636, 637 to 727, or greater than 728 people a day are 0.21197, 0.05644, 0.08408, 0.16337, 0.13999, 0.14512, 0.07189, 0.07695, and 0.05014, respectively.

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