Detection of an appropriate pharmaceutical company to get a suitable vaccine against COVID‐19 with minimum cost under the quality control process

Abstract

Some international pharmaceutical companies have succeeded in producing vaccines against COVID-19. Countries all over the world have aimed to obtain these vaccines with minimum cost. We consider a set of K-independent Markovian waiting lists. Each list contains a set of countries, where each one of them has an exponential service time and a Poisson arrival process. These companies differ in some characteristics such as the vaccine production cost and the speed of the required quantity delivery. We present a new detection model that helps in providing an appropriate decision to choose a suitable company. Moreover, the concept of balking and the retention of reneged countries is taken into consideration under the quality control process of each waiting list. Under steady state, we face an interesting and difficult discrete stochastic optimization problem. Its solution gives an optimal distribution of the searching effort, which is bounded by a known probability distribution. A simulation study has been derived to get the minimum value of the paid cost random values. The highest service rate, the total expected profit of each queuing system, and the optimum performance measures, which depend on this cost, have been obtained to show the effectiveness of this model.

Detection Model With a Maximum Discounted Effort Reward Search to Maintenance a Best Decision Under the Quality Control Process

“…[1] solved a difficult optimization problem under the steady-state situation to get a suitable company with the highest service rate. The search models for the lost targets vary according to the circumstances in which the searching process takes place, for example, [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]. The main purpose of these models is to find these targets with minimum cost and maximum probability.…”

Traffic Flow Optimization: Modeling the Inter-Arrival Times for Simulation Model

“…There are many types of modern optimization approaches, but simulation is widely used and seems reliable to cater traffic management problem. Generally, in the traffic engineering and queuing analysis field, the randomness of vehicle time between arrivals is considered exponentially distributed (Adam, 1950;El-Hadidy et al, 2021;Jose, 2021;Kumar, 2022;Meng et al, 2009;Saritha et al, 2022;Sumaryo et al, 2015;Wang et al, 2021). Sumaryo et al (2015) used queuing models M/M/1 and M/G/1 to model traffic flow circumstances.…”

“…Researchers in discrete-event simulation modelling, on the other hand, tend to use the distributions for inter-arrival and process times recommended by the built-in tools (Frough et al, 2019;El-Hadidy et al, 2021;Jose, 2021;Kumar, 2022;Meng et al, 2009;Saritha et al, 2022;Sumaryo et al, 2015;Wang et al, 2021). Arena Input Analyzer, for example, one of the most widely used tools, provides the best distribution based on the smallest mean square error value.…”

Developing a detection model for a COVID‐19 infected person based on a probabilistic dynamical system

“…Previous works 20–32 presented more useful search models in many real life situations to detect the lost target with minimum cost and maximum probability. Recently, El‐Hadidy and Alfreedi 33 used a novel search model to discover an appropriate pharmaceutical company to get a suitable vaccine against COVID‐19 with minimum cost under the quality control policy. The minimum values of the detection cost and the searching effort are obtained from solving an interesting stochastic optimization problem.…”