Browsing by Subject "beam search"

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Open Access
Generating robust and stable machine schedules from a proactive standpoint
(2009) Gören, Selçuk
In practice, scheduling systems are subject to considerable uncertainty in highly dynamic operating environments. The ability to cope with uncertainty in the scheduling process is becoming an increasingly important issue. In this thesis we take a proactive approach to generate robust and stable schedules for the environments with two sources of uncertainty: processing time variability and machine breakdowns. The information about the uncertainty is modeled using cumulative distribution functions and probability theory is utilized to derive inferences. We first focus on the single machine environment. We define two robustness (expected total flow time and expected total tardiness) and three stability (the sum of the squared and absolute differences of the job completion times and the sum of the variances of the realized completion times) measures. We identify special cases for which the measures can be optimized without much difficulty. We develop a dominance rule and two lower bounds for one of the robustness measures, which are employed in a branch-and-bound algorithm to solve the problem exactly. We also propose a beam-search heuristic to solve large problems for all five measures. We provide extensive discussion of our numerical results. Next, we study the problem of optimizing both robustness and stability simultaneously. We generate the set of all Pareto optimal points via -constraint method. We formulate the sub-problems required by the method and establish their computational complexity status. Two variants of the method that works with only a single type of sub-problem are also considered. A dominance rule and alternative ways to enforce the rule to strengthen one of these versions are discussed. The performance of the proposed technique is evaluated with an experimental study. An approach to limit the total number of generated points while keeping their spread uniform is also proposed. Finally, we consider the problem of generating stable schedules in a job shop environment with processing time variability and random machine breakdowns. The stability measure under consideration is the sum of the variances of the realized completion times. We show that the problem is not in the class NP. Hence, a surrogate stability measure is developed to manage the problem. This version of the problem is proven to be NP-hard even without machine breakdowns. Two branchand-bound algorithms are developed for this case. A beam-search and a tabu-search based two heuristic algorithms are developed to handle realistic size problems with machine breakdowns. The results of extensive computational experiments are also provided.
Open Access
Integration of production, transportation and inventory decisions in supply chains
(2012) Koç, Utku
This dissertation studies the integration of production, transportation and inventory decisions in supply chains, while utilizing the same vehicles in the inbound and outbound. The details of integration is studied in two levels: operational and tactical. In the first part of the thesis, we provide an operational level model for coordination of production and shipment schedules in a single stage supply chain. The production scheduling problem at the facility is modelled as belonging to a single process. Jobs that are located at a distant origin are carried to this facility making use of a finite number of capacitated vehicles. These vehicles, which are initially stationed close to the origin, are also used for the return of the jobs upon completion of their processing. In the first part, a model is developed to find the schedules of the facility and the vehicles jointly, allowing effective utilization of the vehicles for both in the inbound and outbound transportation. In the second part of the dissertation, we provide a tactical level model and study a manufacturer’s production planning and outbound transportation problem with production capacities to minimize transportation and inventory holding costs. The manufacturer in this setting can use two vehicle types for outbound shipments. The first type of vehicle is available in unlimited number. The availability of the second type, which is less expensive, changes over time. For each possible combination of operating policies affecting the problem structure, we either provide a pseudo-polynomial algorithm for general cost structure or prove that no such algorithm exists even for linear cost structure. We develop general optimality properties, propose a generic model formulation that is valid for all problems and evaluate the effects of the operating policies on the system performance. The third part of the dissertation considers one of the problems defined in the second part in detail. Motivated by some industry practices, we present formulations for three different solution approaches, which we refer to as the uncoordinated solution, the hierarchically-coordinated solution and the centrallycoordinated solution. These approaches vary in how the underlying production and transportation subproblems are solved, i.e., sequentially versus jointly, or, heuristically versus optimally. We provide intractability proofs or polynomialtime exact solution procedures for the subproblems and their special cases. We also compare the three solution approaches to quantify the savings due to integration and explicit consideration of transportation availabilities.