Maintaining inventory systems with deteriorating items is one of the major problems in inventory management. This study aimed to develop an inventory model for deteriorating items with a prior focus on stochastic demand, salvage value, and shortages during which partial backlogging occurred. To achieve this, we derived an innovative approach of a single-item inventory model for deteriorating items having a time-dependent deterioration rate that follows a three-parameter Weibull distribution. While the demand pattern follows a negative exponential distribution with partial backlogging and salvage value. In a real market situation, salvage value is crucial to minimize the cost of the seller on deteriorating items. To validate our model on a real market inventory problem that incurred deteriorating items, we collected numerical data from the Ose poultry store and used the Maple mathematical software package to analyze the situation. An analytical procedure for deriving the optimal inventory solutions was provided. In addition, the necessary and sufficient conditions for the optimal policy of the inventory model were confirmed. A sensitivity analysis of the optimal solution concerning various parameters of the model was carried out to evaluate the model's responsiveness to changes in the inventory parameters. The findings from our study showed that the optimal inventory policy is best achieved when the seller places an order for 50 crates of eggs approximately every 2 weeks. In conclusion, this study can be adapted to complex situations, especially during the phase of the COVID-19 pandemic when supply chains and inventories experienced risks of disruptions.
The study of optimal queuing systems in healthcare is crucial at such a time as this to help decongest the system, and minimize financial and health-related risks associated with long waiting queues. This study examined a queuing system at an outpatient hospital clinic post intending to minimize waiting time in association with financial cost and healthcare-related risks. We observed the queuing system using the sampling survey information of 200 outpatients that visited the clinic for 4 weeks. We used the initial queuing ground truth parameters as the baseline scenario and further simulated 4 other queuing scenarios using the TORA optimization software. We calculated the total expected cost associated with the server(s) (Doctors) and the patients while in the queuing system for each scenario. We further discretize their health-related complications and calculated the incidence rate of the patients while in the queuing system to evaluate their health-related risks. The findings of our study showed that the system utilization, optimal expected total cost, health-related risks (risk of discomfort and illness/infections developed while in the queue), and waiting time are optimal at the hospital clinic with 5 severs (doctors). The contribution of this study arose from the incorporation of health-related risks incidence that patients could develop while in the queuing system.
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