This paper investigates the optimization problem of scheduling autonomous mobile robots (AMRs) in hospital settings, considering dynamic requests with different priorities. The primary objective is to minimize the daily service cost by dynamically planning routes for the limited number of available AMRs. The total cost consists of AMR's purchase cost, transportation cost, delay penalty cost, and loss of denial of service. To address this problem, we have established a two-stage mathematical programming model. In the first stage, a tabu search algorithm is employed to plan prior routes for all known medical requests. The second stage involves planning for real-time received dynamic requests using the efficient insertion algorithm with decision rules, which enables quick response based on the time window and demand constraints of the dynamic requests. One of the main contributions of this study is to make resource allocation decisions based on the present number of service AMRs for dynamic requests with different priorities. Computational experiments using Lackner instances demonstrate the efficient insertion algorithm with decision rules is very fast and robust in solving the dynamic AMR routing problem with time windows and request priority. Additionally, we provide managerial insights concerning the AMR's safety stock settings, which can aid in decision-making processes.

In this course, we'll make predictions on product usage and calculate optimal safety stock storage. We'll start with a time series of shoe sales across multiple stores on three different continents. To begin, we'll look for unique insights and other interesting things we can find in the data by performing groupings and comparing products within each store. Then, we'll use a seasonal autoregressive integrated moving average (SARIMA) model to make predictions on future sales. In addition to making predictions, we'll analyze the provided statistics (such as p-score) to judge the viability of using the SARIMA model to make predictions.

Safety stock is among the most critical elements in the pharmaceutical supply chain. Yet safety stock has also proven very difficult to manage and optimize, even as it locks down working capital and drives up inventory costs. Pharmaceutical companies typically maintain high levels of safety stock to achieve better service levels that maximize revenue of high-margin products and drive customer satisfaction. Also called buffer stock, it provides a safety net against variability such as unanticipated delays in raw materials or transportation, or unusually high demand. Stockouts that result from inadequate safety stock could be highly damaging to the business, with millions in lost revenue and potential brand damage if vital medicines are unavailable.

This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order quantity, optimum order time, and the minimum total cost of purchasing, ordering, and holding over the predefined planning horizon. This problem is known as NP-hard problem. The model was presented in an optimal software form using LINGO 13.0.