Strategies for a centralized single product multiclass M/G/1 make-to-stock queue

Make-to-stock queues are typically investigated in the M/M/1 settings. For centralized single-item systems with backlogs, the multilevel rationing (MR) policy is established as optimal and the strict priority (SP) policy is a practical compromise, balancing cost and ease of implementation. However, the optimal policy is unknown when service time is general, i.e., for M/G/1 queues. Dynamic programming, the tool commonly used to investigate the MR policy in make-to-stock queues, is less practical when service time is general. In this paper we focus on customer composition: the proportion of customers of each class to the total number of customers in the queue. We do so because the number of customers in M/G/1 queues is invariant for any nonidling and nonanticipating policy. To characterize customer composition, we consider a series of two-priority M/G/1 queues where the first service time in each busy period is different from standard service times, i.e., this first service time is exceptional. We characterize the required exceptional first service times and the exact solution of such queues. From our results, we derive the optimal cost and control for the MR and SP policies for M/G/1 make-to-stock queues

Removal Efficiency of Electrochemical Process by Iron Oxide Nanoparticles Impregnated on Rod Carbon for Arsenite Anions in a High Ionic Strength Solution

The entry of heavy metals (e.g., arsenite anions) into water sources due to industrial and mining activities is considered a serious problem for the environment. Therefore, arsenite removal from polluted water has attracted the attention of researchers due to its toxic effects on human health. In the present study, the efficiency of the electrochemical (EC) purification of arsenite anions in a high ionic strength solution was investigated using a carbon electrode impregnated with iron oxide nanoparticles (NPs). These NPs were synthesized by the co-precipitation method and immediately impregnated on the carbon rod. Experiments were performed by two electrodes (carbon and carbon impregnated with NP electrode) in a 50 mL EC reactor. The effect of different parameters such as electrical current (0.1, 0.3, 0.5, 0.7, & 0.9 A), EC time (2, 5, 10, 15, and 20 minutes), pH (3, 5, 7, 9, & 11), and the initial concentrations of arsenite anion (2, 5, 10, 15 and 20 mg/L) was investigated on the removal efficiency to achieve the highest removal of arsenite anions. Arsenite anions (10 mg/L) were completely removed from the aqueous solution with an ionic strength of 0.141 M at an electrical current of 0.7 A, a pH of 8, and an EC time of 20 minutes. In addition, pH was the most effective parameter in removing arsenite anions from aqueous solution in the EC method. According to the results, EC treatment using an electrode impregnated with iron oxide NPs is highly efficient in removing arsenite anions from the contaminated water

Managing Inventory, Transportation and Location in a Supply Chain

We consider three problems on inventory, transportation and location in a supply chain. In Chapter 2, we study Multilevel Rationing (MR) and Strict Priority (SP) stock allocation policies for a centralized single product multi-class M/G/1 make-to-stock queueing systems. To obtain the total cost of the system under these policies, we introduce a new method called “customer composition”. Using this method, we focus on the proportion of customers of each class out of the total number of customers in the queue since the number of customers in M/G/1 queues is invariant for any non-idling and non-anticipating policy. We consider a series of two-priority M/G/1 queues with an exceptional service time in each busy period to characterize the customer composition. We derive closed form expressions for the costs of SP and MR policies using these results. In Chapter 3, we consider a two-echelon inventory system with a congested centralized production facility and several Distribution Centers (DCs). We assume that the production and transportation times are stochastic that are generally distributed, and customers arrive to each DC according to an independent Poisson process. Inventory at DCs is managed using the one-for-one replenishment policy. We use the customer composition approach to characterize the total inventory carrying and backlog costs of the system under the FCFS, SP and MR allocation policies at the warehouse. For the special case of exponentially distributed production and transportation times, we use the unit-flow method and derive closed form expressions for the optimal cost and base-stock level of the DCs. We numerically demonstrate that prioritization using either the SP or the MR policy could be very beneficial in comparison with the FCFS policy. In Chapter 4, we study a two-echelon supply chain with a set of suppliers, a set of retailers and a set of capacitated cross-docks which are to be established. The demand of the retailers could be satisfied from the suppliers through the cross-docks. The objective is to determine the number and location of cross-docks, the assignment of retailers to suppliers so that the total cost of pipeline and retailers’ inventory, transportation, and facility location is minimized. We formulate the problem as a non-linear mixed integer programming and derive several structural results for special cases of the problem. To solve the general problem, we show that it can be written as a cutting stock problem and develop a column generation algorithm to solve it. We investigate the efficiency of the proposed algorithm numerically.Ph

Departure Time Choice Models in Urban Transportation Systems Based on Mean Field Games

Departure time choice models play a crucial role in determining the traffic load in transportation systems. Most studies that consider departure time user equilibrium (DTUE) problems make assumptions on the user characteristics (e.g., distribution of desired arrival time and trip length) or dynamic traffic model (e.g., classic bathtub or point queue models) in order to analyze the problem. This paper relaxes these assumptions and introduces a new framework to model and analyze the DTUE problem based on the so-called mean field games (MFGs) theory. MFGs allow us to define players at the microscopic level similar to classical game theory models, translating the effect of players' decisions to macroscopic models. In this paper, we first present a continuous departure time choice model and investigate the equilibria of the system. Specifically, we demonstrate the existence of the equilibrium and characterize the DTUE. Then, a discrete approximation of the system is provided based on deterministic differential game models to numerically obtain the equilibrium of the system. To examine the efficiency of the proposed model, we compare it with the departure time choice models in the literature. We apply our framework to a standard test case and observe that the solutions obtained based on our model are 5.6% better in terms of relative cost compared with the solutions determined based on previous studies. Moreover, our proposed model converges with fewer iterations than the reference solution method in the literature. Finally, the model is scaled up to the real test case corresponding to the whole Lyon metropolis with a real demand pattern. The results show that the proposed framework is able to tackle a much larger test case than usual to include multiple preferred travel times and heterogeneous trip lengths more accurately than existing models

The effect of land use configurations on concentration, spatial distribution, and ecological risk of heavy metals in coastal sediments of northern part along the Persian Gulf

In the present study, a total of 41 sediment samples were collected from the areas with different land uses: industrial (IS), urban (US), agricultural (AGS), and natural field (NS) in the northern coasts along the Persian Gulf from November 2016 to January 2017. Samples were analyzed to determine the concentration of heavy metals (Zn, Cu, Pb, Cd, Cr, and Ni). The mean concentration of Ʃ6 heavy metals in the samples taken from IS, US, AGS, NS were 2300.24, 251.02, 553.21, and 40.93 mg/kg, respectively. The predominant metals were Zn, Cu, and Pb and the mean concentrations of Ʃ3 metals (Zn, Cu, and Pb) in IS, US, AGS, NS areas were 2245.6, 241.44, 529.61, and 36.98 mg/kg, respectively. The results indicated that the mean concentrations of Ʃ6Metals/Ʃ3 metals in the IS and AGS samples were significantly higher than US and NS samples (p Cu (465.00) > Zn (427.16) > Cr (34.20) > Cd (19.45) > Ni (7.09); urban region: Zn (97.45) > Cu (79.90) > Pb (64.09) > Cr (5.30) > Ni (2.55) > Cd (1.73); agricultural region: Zn (247.88) > Pb (164.89) > Cu (116.84) > Cr (11.09) > Ni (7.45) > Cd (5.06); and natural fields: Zn (27.43) > Cu (6.34) > Pb (3.18) > Cr (1.94) > Ni (1.18) > Cd (0.83). According to geo-accumulation index (I-geo), the IS, US, and AGS were classified into “highly-extremely polluted”, “unpolluted-moderately polluted” and “highly polluted”, respectively. Similarly, in accordance with the ecological risk index (ERI), the IS and AGS fell into the very high and considerable categories, respectively, while US land uses area was categorized as low risk. Based on the results obtained from the present study, it can be concluded that the sediments of Asalouyeh coasts in the northern part of the Persian Gulf are heavily contaminated with heavy metals, causing serious negative effects on both the human being and environment