Optimal and Heuristic Resource Allocation Policies in Serial Production Systems

We have studied the optimal server allocation policies for a tandem queueing system under different system settings. Motivated by an industry project, we have studied a two stage tandem queueing system with arrival to the system and having two flexible servers capable of working at either of the stations. In our research, we studied the system under two different circumstances: modeling the system to maximize throughput without cost considerations, modeling the system to include switching and holding costs along with revenue for finished goods. In the maximizing throughput scenario, we considered two different types of server allocations: collaborative and non-collaborative. For the collaborative case, we identified the optimal server allocation policies for the servers and have proved the structure of the optimal server allocation policy using mathematical iteration techniques. Moreover, we found that, it is optimal to allocate both the servers together all the time to get maximum throughput. In the non-collaborative case, we have identified the optimal server allocation policies and found that it is not always optimal to allocate both the servers together. With the inclusion of costs, we studied the system under two different scenarios: system with switching costs only and system having both switching and holding costs. In both the cases, we have studied the optimal server allocation policies for the servers. Due to the complicated structure of the optimal server allocation policy, we have studied three different heuristics to approximate the results of the optimal policy. We found that the performance of one of the heuristics is very close to the optimal policy values

A hybrid meta-heuristic approach for buffer allocation in remanufacturing environment

Remanufacturing system is complicated due to its stochastic nature. Random customer demand, return product rate and system unreliability contribute to this complexity. Remanufacturing systems with unreliable machines usually contain intermediate buffers which are used to decouple the machines, thereby, reducing mutual interference due to machine breakdowns. Intermediate buffers should be optimized to eliminate waste of resources and avoid loss of throughput. The Buffer Allocation Problem (BAP) deals with allocating optimally fixed amount of available buffers to workstations located in manufacturing or remanufacturing systems to achieve specific objectives. Optimal buffer allocation in manufacturing and remanufacturing systems not only minimizes holding cost and stock space, but also makes facilities planning and remanufacturing decisions to be effectively coordinated. BAP in a non-deterministic environment is certainly one of the most difficult optimization problems. Therefore, a mathematical framework is provided to model the dependence of throughput on buffer capacities. Obviously, based on the survey undertaken, not only there exists no algebraic relation between the objective function and buffer size but the current literature does not offer analytical results for buffer capacity design in remanufacturing environment. Decomposition principle, expansion method for evaluating system performance and an efficient hybrid Meta-heuristic search algorithm are implemented to find an optimal buffer allocation for remanufacturing system. The proposed hybrid Simulated Annealing (SA) with Genetic Algorithm (GA) is compared to pure SA and GA. The computational experiments show better quality, more accurate, efficient and reliable solutions obtained by the proposed hybrid algorithm. The improvement obtained is more than 4.18 %. Finally, the proposed method is applied on toner cartridge remanufacturing company as a case study, and the numerical results from hybrid algorithm are presented and compared with results from SA and GA

Comparison of agent-based scheduling to look-ahead heuristics for real-time transportation problems

We consider the real-time scheduling of full truckload transportation orders with time windows that arrive during schedule execution. Because a fast scheduling method is required, look-ahead heuristics are traditionally used to solve these kinds of problems. As an alternative, we introduce an agent-based approach where intelligent vehicle agents schedule their own routes. They interact with job agents, who strive for minimum transportation costs, using a Vickrey auction for each incoming order. This approach offers several advantages: it is fast, requires relatively little information and facilitates easy schedule adjustments in reaction to information updates. We compare the agent-based approach to more traditional hierarchical heuristics in an extensive simulation experiment. We find that a properly designed multiagent approach performs as good as or even better than traditional methods. Particularly, the multi-agent approach yields less empty miles and a more stable service level

Analysis of delayed product differentiation under pull type policies

Delayed product differentiation (DPD) increases manufacturers\u27 competitiveness in the market by enabling them to more quickly respond to changes in customers\u27 demands. DPD has also been shown to require less Work-in-Process (WIP) than a non-DPD setup in some cases. Previous research was mainly focused on the level of semi-finished and/or finished good inventory under a base-stock policy. The control of WIP inventory was not considered. DPD may also improve response times under pull inventory control schemes, in which the amount of WIP is controlled directly. These systems can be modeled as closed queueing networks in which a fixed number of kanbans circulate as customers among each set of one or more processing stages.;In this study, we first developed models to analyze the performance of simple kanban and CONstant-WIP (CONWIP) controlled systems and set the number of kanbans to achieve a specified performance level. The models help us better understand the behavior of pull systems. The performance evaluation method uses nonlinear programming (NLP) models to bound the throughput for fixed number of kanbans or minimize the number of kanbans necessary to achieve a specified throughput. The model shows how random supplies and demands prevent equilibrium from occurring in a single-stage kanbans system.;We studied a model for a system of two products with unlimited supply and demand using three CONWIP loops to represent the common processes and the differentiated processes for each product. The same system after DPD has more common processes and fewer differentiated processes. The NLP model can determine numbers of kanbans for each loop to achieve specified throughput targets. Because the throughput bounds are not as tight as desired, we developed a heuristic algorithm that starts from the NLP solution and adjusts the kanbans using simulation to evaluate the performance. A comparison of the result of the heuristic algorithm for the systems with and without DPD indicates that DPD reduces the amount of WIP necessary to achieve a specified throughput. Furthermore, we show how models of systems with similar structure can be generalized

Optimal Design and Control of Finite-Population Queueing Systems

We consider a service system with a finite population of customers (or jobs) and a service resource with finite capacity. We model this finite-population queueing system by a closed queueing network with two stages. The first stage, which represents the arrivals of customers for service, consists of an automated station with ample capacity. The second stage, which represents the service for customers, consists of multiple service stations which share the finite service resource. We consider both discrete and continuous service resources. We are interested in static or dynamic allocation of the service resource to the service stations in the second stage in order to optimize a given system measure. Specifically, a static allocation refers to a design problem, while a dynamic allocation refers to a control problem. In this thesis, we study both. For control problems, we specify a parallel-series structure for service stations. We first consider dynamically allocating a single flexible server under both preemptive and non-preemptive policies. We characterize the optimal policies of dynamically scheduling this single server in order to maximize the long-run average throughput of the system. In the special case of a series system, we show that the optimal policy is a sequential policy where each customer is served by the single server sequentially from the first station until the last one. For a parallel system, we show that there exists an optimal policy which gives the highest priority to the station that has the largest service rate. We also propose an index policy heuristic for the general parallel-series system and compare its performance as opposed to the optimal policy by a numerical study. Finally, we study dynamically allocating a finite amount of continuous service resource for the parallel system. For design problems, we consider allocating a finite amount of service resource which is continuously divisible and can be used at any of the service stations. Suppose that service times at a service station are exponentially distributed and their mean is a strictly increasing and concave function of the allocated service resource. We characterize the optimal allocation of the continuous resource in order to maximize the long-run average throughput of the system. We first show that the system throughput is non-decreasing in the number of customers. Then, we study the optimization problem in three cases depending on the population size of customers in the system. First, when there is a single customer, we show that the optimal allocation is given by a set of optimality equations. Secondly, when the number of customers approaches infinity, we show that the optimal allocation approaches to a limit. Finally, for any finite number of customers, we show that the system throughput is bounded up by a limit. Moreover, under a certain condition, we show that the system throughput function is Schur-concave.Doctor of Philosoph

Energy and performance-optimized scheduling of tasks in distributed cloud and edge computing systems

Infrastructure resources in distributed cloud data centers (CDCs) are shared by heterogeneous applications in a high-performance and cost-effective way. Edge computing has emerged as a new paradigm to provide access to computing capacities in end devices. Yet it suffers from such problems as load imbalance, long scheduling time, and limited power of its edge nodes. Therefore, intelligent task scheduling in CDCs and edge nodes is critically important to construct energy-efficient cloud and edge computing systems. Current approaches cannot smartly minimize the total cost of CDCs, maximize their profit and improve quality of service (QoS) of tasks because of aperiodic arrival and heterogeneity of tasks. This dissertation proposes a class of energy and performance-optimized scheduling algorithms built on top of several intelligent optimization algorithms. This dissertation includes two parts, including background work, i.e., Chapters 3–6, and new contributions, i.e., Chapters 7–11. 1) Background work of this dissertation. Chapter 3 proposes a spatial task scheduling and resource optimization method to minimize the total cost of CDCs where bandwidth prices of Internet service providers, power grid prices, and renewable energy all vary with locations. Chapter 4 presents a geography-aware task scheduling approach by considering spatial variations in CDCs to maximize the profit of their providers by intelligently scheduling tasks. Chapter 5 presents a spatio-temporal task scheduling algorithm to minimize energy cost by scheduling heterogeneous tasks among CDCs while meeting their delay constraints. Chapter 6 gives a temporal scheduling algorithm considering temporal variations of revenue, electricity prices, green energy and prices of public clouds. 2) Contributions of this dissertation. Chapter 7 proposes a multi-objective optimization method for CDCs to maximize their profit, and minimize the average loss possibility of tasks by determining task allocation among Internet service providers, and task service rates of each CDC. A simulated annealing-based bi-objective differential evolution algorithm is proposed to obtain an approximate Pareto optimal set. A knee solution is selected to schedule tasks in a high-profit and high-quality-of-service way. Chapter 8 formulates a bi-objective constrained optimization problem, and designs a novel optimization method to cope with energy cost reduction and QoS improvement. It jointly minimizes both energy cost of CDCs, and average response time of all tasks by intelligently allocating tasks among CDCs and changing task service rate of each CDC. Chapter 9 formulates a constrained bi-objective optimization problem for joint optimization of revenue and energy cost of CDCs. It is solved with an improved multi-objective evolutionary algorithm based on decomposition. It determines a high-quality trade-off between revenue maximization and energy cost minimization by considering CDCs’ spatial differences in energy cost while meeting tasks’ delay constraints. Chapter 10 proposes a simulated annealing-based bees algorithm to find a close-to-optimal solution. Then, a fine-grained spatial task scheduling algorithm is designed to minimize energy cost of CDCs by allocating tasks among multiple green clouds, and specifies running speeds of their servers. Chapter 11 proposes a profit-maximized collaborative computation offloading and resource allocation algorithm to maximize the profit of systems and guarantee that response time limits of tasks are met in cloud-edge computing systems. A single-objective constrained optimization problem is solved by a proposed simulated annealing-based migrating birds optimization. This dissertation evaluates these algorithms, models and software with real-life data and proves that they improve scheduling precision and cost-effectiveness of distributed cloud and edge computing systems

Mathematics in the Supply Chain

[no abstract available