Modeling the Capacitated Multi-Level Lot-Sizing Problem under Time-Varying Environments and a Fix-and-Optimize Solution Approach.

Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms

In this paper we give an overview of recent developments in the field of modeling deterministic single-level dynamic lot sizing problems. The focus of this paper is on the modeling of various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production–distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research.

The aim of this work is to propose a solution approach for a capacitated lot sizing and scheduling real problem with parallel machines and shared buffers, arising in a packaging company producing yoghurt. The problem has been formulated as a hybrid Continuous Set-up and Capacitated Lot Sizing Problem (CSLP–CLSP). A new effective two stage optimisation heuristic based on the decomposition of the problem into a lot sizing problem and a scheduling problem has been developed. An assignment of mixture to buffers is made in the first stage, and therefore the corresponding orders are scheduled on the production lines by performing a local search. Computational tests have been performed on the real data provided by the company. The heuristic exhibits near-optimal solutions, all obtained in a very short computational time.

Integrated lot sizing and energy-efficient job shop scheduling problem in manufacturing/remanufacturing systems

The determination of lot sizes and production schedules of multiple products in multiple periods is difficult when sequence-dependent set-up costs are present. By using an initial set-up cost estimator (ISCE) the joint problem can be divided and solved sequentially. A search of the literature reveals that, while there is considerable research on the individual problems of lot sizing and scheduling, there is a dearth of study on either the joint problem or on the effect of ISCE selection on the total cost solution. Using a variety of data sets, this paper evaluates the sensitivity of ISCE selection on the solution to the joint problem. Results of the study demonstrate that the choice of an ISCE can have a significant effect on the final lot sizes and schedules. Additionally, the research shows that ‘common sense’ a priori assumptions about ISCE performance may lead to the selection of an inappropriate ISCE.

Hybrid proactive approach for solving maintenance and planning problems in the scenario of Industry 4.0

A lot-sizing problem is considered for a group of items with a common manufacturing setup. These items are aggregated in a group by a technique of group technology. The common setup cost for the group is generally less than the sum of each item's setup costs. The cost reduction is expected when lot-sizing is carried out for the group of items rather than for each item independently. The determination of the lot-size for a group of items sharing a common setup is called "group lot-sizing". It is shown by simulation that the percentage of the total cost reduction (PCR) is different due to the dispersion of time between orders (TBO) and the group setup ratio (GSR), the ratio of the group to the sum of each item's setup costs. A small dispersion of TBO or small GSR brings about an increase of PCR. Lastly, the optimal grouping method using dynamic programming and a numerical example is shown.

An integrated approach for lot-sizing and storage assignment

Visionary leaders are leaders who shape the future in the direction of their goals and realize their attitudes and actions in this direction. In this situation visionary leaders struggle to obtain positive outputs from the internal and external environment of the organization, especially in a framework required by continuous change, which is a necessity of the time. One of these positive outcomes is organizational agility. The aim of this study is to illuminate the effect of visionary leadership behavior, one of the modern leadership theories that emerged together with the necessities of the time, on organizational agility. The research was performed on 308 non-managerial white-collar employees working in aircraft leasing companies operating within the structure of general aviation organizations throughout Turkey. Questionnaires were conducted by face-to-face interview method. In the study firstly, the “Visionary Leadership Scale” measured by Sashkin (1996) and transformed into Turkish scale by Tanrıbil (2015), and also, “Organizational Agility Scale” measured by Sharifi and Zhang (1999) and transformed into Turkish scale by Akkaya and Tabak (2018) were used. Analysis results were created using SPSS 23 and Amos 24 applications. In this context in the study, frequency analysis, factor analysis, and reliability analysis, descriptive statistics, and correlation analysis were applied. Additionally, Structural Equation Models (SEMs) analysis was used to test the confirmatory factor analysis, goodness of fit values and coefficients values related to the variables. The research findings showed that visionary leadership and organizational agility has a positive and significant relationship. In addition, a partial effect of visionary leadership on organizational agility was found. Regarding the sub-dimensions, it was determined that communication and risk have effects on flexibility; communication, risk, respect, and focus have effects on response; reliability, respect, and focus have effects on competence; and risk and focus have effects on speed.

Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches

For capacitated multi-item lot sizing problems, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework. Advanced analytics can predict the probability that an event will happen and has been applied to pressing industry issues, such as credit scoring, risk management, and default management. Although little research has applied such technique for lot sizing problems, we observe that advanced analytics can uncover optimal patterns of setup variables given properties associated with the problems, such as problem attributes, and solution values yielded by linear programming relaxation, column generation, and Lagrangian relaxation. We, therefore, build advanced analytics models that yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to partition the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. The discussion is followed by computational tests, where comparisons with other methods indicate that our approach can obtain better results for the benchmark problems than other state-of-the-art methods. Summary of Contribution: In this study, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems. The advanced analytics models are used to yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to divide the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. Through computational tests based on benchmark problems, we observe that the proposed approach can obtain better results than other state-of-the-art methods.

Pricing, relaxing and fixing under lot sizing and scheduling

A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

The lot‐sizing problem in capacitated multi‐stage systems with a serial product structure is addressed. This is a complex optimization problem that is part of the decision set in material requirements planning (MRP) systems. The mathematical model that describes the problem uses the concept of echelon stock and includes lead times. Setup times are taken into account, which implies that the problem of finding a feasible solution is NP‐Complete. This paper proposes a heuristic method that provides a production plan in order to minimize inventory, production, and setup costs. The heuristic starts from a solution for the uncapacitated problem, which is given by the sequential application of the Wagner‐Whitin algorithm. Feasibility is then attempted by shifting production amounts between periods. Computational tests conducted in 1,800 instances with up to 40 components and 18 periods have shown that feasible solutions were obtained in 83.7% of the instances. For the infeasible instances, on average, the heuristic is able to find solutions with very low capacity excess. The solutions' quality is evaluated through a lower bound provided by Lagrangean relaxation and on average the gap is less than 10%.

The aim of this work was to study a distribution and lot-sizing problem that considers costs with transportation to a company warehouse as well as, inventory, production and setup costs. The logistic costs are associated with necessary containers to pack produced items. The company negotiates a long-term contract in which a fixed cost per period is associated with the transportation of the items. On the other hand, a limited number of containers are available with a lower cost than the average cost. If an occasional demand increase occurs, other containers can be utilized; however, their costs are higher. A mathematical model was proposed in the literature and solved using the Lagrangian heuristic. Here, the use of the Lagrangian/surrogate heuristic to solve the problem is evaluated. Moreover, an extension of the literature model is considered adding capacity constraints and allowing backlogging. Computational tests show that Lagrangian/surrogate heuristics are competitive, especially when the capacity constraints are tight.