Heuristic for integrated purchasing and production planning

In manufacturing industries, production planning and scheduling strategy usually flow in a hierarchical direction. In this direction, the production planning problem is solved first; then the scheduling problem is solved to meet the production targets. This often generates an infeasible production plan because of not considering the details of scheduling. Therefore, it is necessary to develop models that can integrate production planning and scheduling. For manufacturing companies that have identical units of single products and are often grouped in production batches (lots), lot streaming can be used as a scheduling technique. However, there has been no model to integrate production planning (lot sizing) and scheduling, using lot streaming technique which can accelerate production. The main objective of this research is to develop mixedinteger mathematical models for integration of lot sizing and flowshop lot streaming problems such as variable sublots, consistent and equal sublots, scheduling with learning effects and the possibility of preventive maintenance tasks. The objective of these mathematical models is minimization of total costs and also, five goals of problem can simultaneously be solved, namely: determining the sequence among sublots, optimal number of sublots for each lot, size of each lot, inventory levels and size of individual sublots. The second objective of this research is to propose a solution procedure for problems when data are fuzzy. Finally, the third research objective is to validate the proposed model through a case study. Three software are used to extract the results of mathematical models and validate the solution procedure. The name of these software are: LINGO, MINITAB and MATLAB. In this research, the author proposes the first mixed-integer mathematical models for integration of lot sizing and lot streaming problems. By these proposed models, not only sequencing and timing decisions of multiple products are calculated but also lot size of each product, work-in-process and inventory levels of finished products are calculated when lots can be split into smaller sublots. To get the results of mathematical models, in three examples, 70 randomlygenerated problems are solved by LINGO solver. Moreover, a two-way ANOVA test as a statistical method is applied to validate the mathematical model, using four examples consisting sixteen problems, by MINITAB software. The NDM Company is used as a case study. The mathematical models are used to solve NDM company’s problems by LINGO solver. The results showed 32 percent (77.66 hours) reduction in makespan compared to non-integrated mathematical model. Validation of the proposed solution procedure is achieved by comparison of results with max-min method results,using Shahab Shishe company data. The results of using the proposed mathematical models in this research are first to reduce cost by using these proposed models. Secondly is greater marginal benefits were obtained by intermingled sublot cases than non-intermingled sublot cases. It is concluded that better makespans were obtained by intermingled sublot cases than non-intermingled sublot case.

Course scheduling and classroom assignment problem is a common problem for all educational fields. It is an NP Hard problem. Especially, universities should handle this problem while preparing course timetabling for each level due to elective courses and students taking upper/lower-level courses. There is a vast literature on this problem both for modelling and solution approaches. Although the essence of the problems is similar for the most, each problem has some unique restriction and/or parameters. We study the timetabling of the courses of Industrial Engineering program at Yaşar University. We develop a mathematical model to maximize the minimum lecturer satisfaction. Due to the computational complexity of the problem, we proposed a heuristic solution method, namely the Genetic Algorithm. Gene structure we use ensures the feasibility of many constraints of the mathematical model. Computational results of optimal and heuristic method are compared. As a real-life implementation, a university in Turkey Industrial Engineering Department data is used and results were reported. KeywordsCourse schedulingMathematical modelling0–1 Integer modellingTimetablingGenetic algorithm

Finding solutions for the p-median problem is one of the primary research issues in the field of location theory. Since the p-median problem has proved to be a NP-hard problem, several heuristic and approximation methods have been proposed to find near optimal solutions with acceptable computational time. This study introduces a computationally efficient and deterministic algorithm whose objective is to return a near optimal solution for the p-median problem. The merit of the proposed approach, called Relocation Median (RLM), lies in solving the p-median problem in superior computational time with a tiny percentage deviation from the optimal solution. This approach is especially relevant when the problem is enormous where, even when a heuristic method is applied, the computational time is quite high. RLM consists of two parts: The first part uses a greedy search method to find an initial solution; the second part sequentially substitutes medians in the initial solution with additional vertices to reduce the total travel cost. Experiments show that to solve the same p-median problem, the RLM approach can significantly shorten the computational time needed by a genetic algorithm based approach to obtain solutions with similar quality.

This paper delves into a two-agent scheduling problem in which two agents are competing for a single resource. Each agent has a set of jobs to be processed by a single machine. The processing time, release time, weight, and the due dates of each job are known in advance. Both agents have their objectives, which are conflicting in nature. The first agent tries to minimize the total completion time, while the second agent tries to minimize the number of tardy jobs. The two agents’ scheduling problem, an NP-hard problem, has a wide variety of applications ranging from the manufacturing industry to the cloud computing service provider. Due to the wide applicability, each variation of the problem requires a different algorithm, adapted according to the user’s requirements. This paper provides mathematical models, heuristic algorithms, and two nature-based metaheuristic algorithms to solve the problem. The algorithm’s performance was gauged against the optimal solution obtained from the AMPL-CPLEX solver for both solution quality and computational time. The outlined metaheuristics produce a solution that is comparable with a short computational time. The proposed metaheuristics even have a better solution than the CPLEX solver for medium-size problems, whereas the computation times are much less than the CPLEX solvers.

Develops a linear programming model for integrated production planning based on the practice of a major Canadian steel making company. Considers the entire planning activity in the company as an integrated process involving a number of closely related sub‐functions, such as raw material purchasing, semi‐finished product purchasing and production, and capacity allocation, as well as finished product production and distribution. The mathematical programming model takes into account production costs, product throughput rates, customer demands, sales prices and facility capacities for optimal production planning. Presents a numerical example based on realistic system structure and practical planning data to illustrate the model. Computation results and analysis show that the integrated methodology is a feasible and practical approach for steel production planning.

A new heuristic method is presented for the resolution of multiresource constrained conflicts in project scheduling. In attempting to find a minimal makespan solution, the algorithm employs a simple procedure to generate a feasible solution with no backtracking. A postanalysis phase then applies a hill-climbing search. The solution method is different from existing heuristic methods in that it repairs resource conflicts rather than constructs detailed schedules by dispatching activities. Resource-violating sets of activities are identified which must be prevented from concurrent execution because this would violate resource constraints. Repairs are made by imposing an arc to sequence two activities in such a resource violating set. Computational results are compared with those of existing heuristics for the minimal makespan problem.

In real world manufacturing systems there are many combinatorial optimization problems (COP) imposing on more complex issues, such as complex structure, nonlinear constraints, and multiple objectives to be handled simultaneously. Manufacturing scheduling is one of the important and complex COP models, where it can have a major impact on the productivity of a production process. Moreover, the COP models make the problem intractable to the traditional optimization techniques because most of scheduling problems fall into the class of NP-hard combinatorial problems. In order to develop effective and efficient solution algorithms that are in a sense good, i.e., whose computational time is small as within 3 min, or at least reasonable for NP-hard combinatorial problems met in practice, we have to consider: quality of solution, computational time and effectiveness of the nondominated solutions for multiobjective optimization problem (MOP). When solving any NP-hard problem, a genetic algorithm (GA) based on principles from evolution theory is most powerful metaheuristics. In this paper, we concern with the design of hybrid genetic algorithms (HGA) and multiobjective HGA (Mo-HGA) to solve manufacturing scheduling problems. Firstly we introduce typical models in manufacturing scheduling systems such as parallel machines scheduling (PMS), flexible job-shop scheduling problem (FJSP) and assembly line balancing (ALB) problem. Secondly to solve NP-hard COP models, we introduce design scheme of HGA combined with fuzzy logic controller (FLC) and multiobjective HGA (Mo-HGA) with several fitness assignment mechanisms. For demonstrating computational experiments by HGA and Mo-HGA, the effectiveness of the HGA for the HDD (hard disc device) and Mo-HGA for TFT-LCD (thin-film transistor-liquid crystal display) module assembly problems as a practical manufacturing model, respectively is demonstrated in the concatenated paper Part II.

00/01553 Thermodynamics of TiO x in blast furnace-type slags

Vehicle routing problem (VRP) is about finding optimal routes for a fleet of vehicles so that they can meet the demands for a set of given customers by traveling through those paths. This problem is one of the most important and most applicable problems of transportation and logistics scope. In this paper, green vehicle routing and scheduling problem with a heterogeneous fleet, including reverse logistics in the form of collecting returned goods along with weighted earliness and tardiness costs considering multiple time windows, is studied to establish a trade-off between operational and environmental costs. In this regard, a mixed-integer non-linear programming (MINLP) model is proposed at the first stage; then its accuracy and correct functioning are evaluated by solving some examples. Demand is considered uncertain based on fuzzy numbers that robust possibilistic programming is employed regarding the other parameters uncertainty. Since this problem is categorized as an NP-hard problem, a genetic algorithm (GA) is suggested to find near-optimal solutions for large instances in a rational computational time. Eventually, the GA’s performance is evaluated compared to solving the mathematical model for small-sized problems. Analysis of the results considering two criteria, solutions quality and computational times, indicates the satisfactory operation of the proposed algorithm in a proper computational time.

We consider two interrelated problems that occurred in disassembly systems: disassembly leveling and lot sizing. Disassembly leveling, one of disassembly process planning decisions, is to determine disassembly structures that specify parts and/or subassemblies to be obtained from disassembling used/end-of-life products, and disassembly lot sizing is the problem of determining the amounts of disassembly operations required to satisfy the demands of their parts and/or subassemblies. Unlike the existing studies, this study considers the two problems at the same time for the objective of minimizing the sum of disassembly setup and operation costs. In particular, we consider a generalized version in which disassembly levels may be different even for products of the same type. Two types of the problem are considered in this study. The first one is the basic problem without parts commonality, i.e., products do not share their parts or subassemblies, for which a polynomial time optimal algorithm is suggested after developing a mathematical programming model. The second one is an extended problem with parts commonality. After developing another mathematical programming model for the extension, we prove that it is NP hard. Then, a heuristic algorithm is suggested together with its computational results.

Finding optimal solutions to NP-Hard problems requires exponential time with respect to the size of the problem. Consequently, heuristic methods are usually utilized to obtain approximate solutions to problems of such difficulty. In this paper, a novel swarm-based nature-inspired metaheuristic algorithm for optimization is proposed. Inspired by human collective intelligence, Wisdom of Artificial Crowds (WoAC) algorithm relies on a group of simulated intelligent agents to arrive at independent solutions aggregated to produce a solution which in many cases is superior to individual solutions of all participating agents. We illustrate superior performance of WoAC by comparing it against another bio-inspired approach, the Genetic Algorithm, on one of the classical NP-Hard problems, the Travelling Salesperson Problem. On average a 3% - 10% improvement in quality of solutions is observed with little computational overhead.

Landing aircraft safely is an important operation that air traffic controllers have to deal with on a daily basis. For each arriving aircraft a runway and a landing time must be allocated. If these allocations can be done in an efficient way, it could give the airport a competitive advantage. The Aircraft Landing Problem (ALP) aims to minimize the deviation from a preferred target time of each aircraft. It is an NP-hard problem, meaning that we may have to resort to heuristic methods as exact methods may not be suitable, especially as the problem size increases. This paper proposes an iterated local search (ILS) algorithm for the ALP. ILS is a single solution based search methodology that successively invokes a local search procedure to find a local optimum solution. A perturbation operator is used to modify the current solution in order to escape from the local optimum and to provide a new solution for the local search procedure. As different problems and/or instances have different characteristics, the success of the ILS is highly dependent on the local search, the perturbation operator(s) and the perturbation strength. To address these issues, we utilize four perturbation operators and a time varying perturbation strength which changes as the algorithm progresses. A variable neighborhood descent algorithm is used as our local search. The proposed ILS generates high quality solutions for the ALP benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both solution quality and computational time. Moreover, the proposed ILS produces new best results for some instances.

Conventional approach for solving replenishment lot size problem is by using the differential calculus with the need of applying the first-order and second-order differentiations to the long-run average production-inventory cost. A recent published paper used conventional method to determine optimal lot size for an integrated production-delivery system with scrap and cost lessening distribution policy. This paper uses an alternative algebraic approach to reexamine the aforementioned problem without referring to derivatives. As a result, optimal lot size and a simpler expression for the long-run average cost are derived, and they are identical to what were obtained by using the conventional method. Key words: Lot size, optimization, scrap, multiple distribution policy, algebraic approach, production planning.

Lot sizes and setup frequency with learning in setups and process quality

This research aims to optimize the yield for hard disk drive component problem using heuristic methods. This problem is constrained by the limited budget and the requirement on the suppliers rating of the components. Because of complexity of the problem, it is considered as a NP-Hard problem which can be formulated as a nonlinear integer programming problem. Three heuristics, Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Bee Algorithm (BA), are proposed to solve this problem and compare heuristic performance from getting optimum percentage and computation time. Using the actual data from undisclosed HDD manufacturer, computational experiments are conducted under many budget constraints. The results from the experiments show that they can solve the problem with the same condition under reasonable time. Using accuracy, robustness and computation effort, it reveals that BA can solve the case study more efficient than ACO and GA.KeywordsHard Disk DriveCrossover RateHeuristic InformationBudget SettingState Transition RuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.