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

Due to their importance in industry and mathematical complexity, dynamic demand lot-sizing problems are frequently studied. In this article, we consider coordinated lot-size problems, their variants and exact and heuristic solutions approaches. The problem class provides a comprehensive approach for representing single and multiple items, coordinated and uncoordinated setup cost structures, and capacitated and uncapacitated problem characteristics. While efficient solution approaches have eluded researchers, recent advances in problem formulation and algorithms are enabling large-scale problems to be effectively solved. This paper updates a 1988 review of the coordinated lot-sizing problem and complements recent reviews on the single-item lot-sizing problem and the capacitated lot-sizing problem. It provides a state-of-the-art review of the research and future research projections. It is a starting point for anyone conducting research in the deterministic dynamic demand lot-sizing field.     

Integrative Cycle Scheduling Approach for a Capacitated Flexible Assembly System*

This study revisits the traditional single stage, multi-item, capacitated lot-sizing problem (CLSP) with a new integrative focus on problem structuring. Unlike past research, we develop integrative cycle scheduling approaches which simultaneously address lot-sizing, capacity, and sequencing issues. Our purposes are to (1) explore the effect of sequencing on inventory levels, (2) examine the problem of infeasibility in the economic lot scheduling problem (ELSP), and (3) provide a simple methodology of generating low-cost cycle schedules in an environment with discrete shipping, dynamic demands, limited capacity, zero setup cost, and sequence-independent setup times. Our procedures are compared to benchmark cycle scheduling approaches in terms of both inventory cost and computation time under different demand scenarios, using the operating data from a flexible assembly system (FAS) at the Ford Motor Company's Sandusky, Ohio plant.     

Discrete parallel machine makespan ScheLoc problem

Scheduling–Location (ScheLoc) problems integrate the separate fields of scheduling and location problems. In ScheLoc problems the objective is to find locations for the machines and a schedule for each machine subject to some production and location constraints such that some scheduling objective is minimized. In this paper we consider the discrete parallel machine makespan ScheLoc problem where the set of possible machine locations is discrete and a set of n jobs has to be taken to the machines and processed such that the makespan is minimized. Since the separate location and scheduling problem are both \(\mathcal {NP}\)-hard, so is the corresponding ScheLoc problem. Therefore, we propose an integer programming formulation and different versions of clustering heuristics, where jobs are split into clusters and each cluster is assigned to one of the possible machine locations. Since the IP formulation can only be solved for small scale instances we propose several lower bounds to measure the quality of the clustering heuristics. Extensive computational tests show the efficiency of the heuristics.     

An Efficient Zero-One Formulation of the Multilevel Lot-Sizing Problem

This paper presents a zero-one linear formulation of the multilevel lot-sizing problem for materials requirement planning systems without capacity constraints. The model is an efficient statement of the problem and has a structure that is particularly convenient for research work. In addition, it is demonstrated that the relaxed linear programming solution to this formulation will always be integer. The results of a rather large computational history are reported along with a variable reduction methodology that allows for the solution of reasonably sized research problems.     

A BRANCH AND BOUND PROCEDURE FOR SETUP PROBLEMS IN FLEXIBLE MANUFACTURING SYSTEMS

We address a medium- to short-term production planning problem in a flexible manufacturing environment. First we present a single-machine, mixed integer programming model for part type selection and lot-sizing problems over a T-period planning horizon. Demand for part types changes dynamically through the periods. The objective is to meet the demand for part types during the periods they are demanded. Available machine time and tool magazine capacities are the system constraints in our models. We next extend on the single- machine model to include multiple machines. In addition to part type selection and lotsizing decisions, the extended model also addresses the machine-loading decision. We present exact branch and bound procedures based on linear programming relaxations for the two models. We also report the results of our computational experiments.     

Education: MRP/GT: A FRAMEWORK FOR PRODUCTION PLANNING AND CONTROL OF CELLULAR MANUFACTURING

American industry typically uses material requirements planning (MRP) for manufacturing control. This paper presents production planning and control procedures based on group technology (GT), which is used in British manufacturing. A translation between these ideas and the American approach is made, and it is suggested that a combination of MRP and GT is viable. The problems that arise, especially in the areas of lot-sizing and sequencing/scheduling, and their possible solutions are discussed. Since increased adoption of GT is expected within the next decade, an intensified research effort is warranted in these and other areas so that existing MRP systems can be modified or extended to handle cellular manufacturing control problems. Subject Areas: Material Requirements Planning and Production/Operations Management.     

On cutting stock with due dates

Classical stock cutting calls for fulfilling a given demand of parts, minimizing raw material needs. With the production of each part type regarded as a job due within a specific date, a problem arises of scheduling cutting operations. We here propose an exact integer linear programming formulation, and develop primal heuristics, upper bounds and an implicit enumeration scheme. A computational experience carried out for the one-dimensional problem shows that our primal heuristics outperform known ones, and that the formulation has good features for finding exact solutions of non-trivial instances.     

Tactical production and distribution planning with dependency issues on the production process

Tactical production-distribution planning models have attracted a great deal of attention in the past decades. In these models, production and distribution decisions are considered simultaneously such that the combined plans are more advantageous than the plans resolved in a hierarchical planning process. We consider a two-stage production process, where in the first stage raw materials are transformed into continuous resources that feed the discrete production of end products in the second stage. Moreover, the setup times and costs of resources depend on the sequence in which they are processed in the first stage. The minimum scheduling unit is the product family which consists of products sharing common resources and manufacturing processes. Based on different mathematical modelling approaches to the production in the first stage, we develop a sequence-oriented formulation and a product-oriented formulation, and propose decomposition-based heuristics to solve this problem efficiently. By considering these dependencies arising in practical production processes, our model can be applied to various industrial cases, such as the beverage industry or the steel industry. Computation tests on instances from an industrial application are provided at the end of the paper.     

Tabu search for the real-world carpooling problem

Carpooling is a flexible shared transportation system which can effectively reduce the vehicle numbers and fuel consumption. Although many carpooling systems have been proposed, most of them lack practicality, veracity, and efficiency. In this paper, we propose a new useful variant model of the long-term carpooling problem which involves multiple origins and one destination. Such problems commonly occur in a wide number of carpooling situations in real-world scenarios. Our work is motivated by the practical needs to solve environmental pollution, parking problems, traffic jams and low utilization of resources. A Tabu search algorithm is proposed in this paper to solve the carpooling problem. The proposed algorithm aims at a wide range of passenger distribution and routing problems. The computational results based on real world user data show the effectiveness of the proposed algorithm. Moreover, we developed a mobile application based on our carpooling model.     

A MARKET UTILITY‐BASED MODEL FOR CAPACITY SCHEDULING IN MASS SERVICES

Only a small set of employee scheduling articles have considered an objective of profit or contribution maximization, as opposed to the traditional objective of cost (including opportunity costs) minimization. In this article, we present one such formulation that is a market utility‐based model for planning and scheduling in mass services (MUMS). MUMS is a holistic approach to market‐based service capacity scheduling. The MUMS framework provides the structure for modeling the consequences of aligning competitive priorities and service attributes with an element of the firm's service infrastructure. We developed a new linear programming formulation for the shift‐scheduling problem that uses market share information generated by customer preferences for service attributes. The shift‐scheduling formulation within the framework of MUMS provides a business‐level model that predicts the economic impact of the employee schedule. We illustrated the shift‐scheduling model with empirical data, and then compared its results with models using service standard and productivity standard approaches. The result of the empirical analysis provides further justification for the development of the market‐based approach. Last, we discuss implications of this methodology for future research.     

Scheduling and the problem of computational complexity

Why is it that the problem of scheduling is so computationally difficult to solve? At last recent developments in modern mathematical complexity theory are providing some insights. The paper describes in essentially non-mathematical terms the computational technique known as the ‘Branch and Bound Method’. This, the best general optimising technique available for scheduling, is also shown to have its limitations. It now appears that efficient computational and optimising algorithms are unlikely ever to be found for all except special cases of the general industrial scheduling problem. It seems that heuristic (rule-of-thumb) methods leading to approximate solutions are likely to offer the only real promise for the future.     

Revised GRASP with path-relinking for the linear ordering problem

The linear ordering problem (LOP) is an NP\mathcal{NP}-hard combinatorial optimization problem with a wide range of applications in economics, archaeology, the social sciences, scheduling, and biology. It has, however, drawn little attention compared to other closely related problems such as the quadratic assignment problem and the traveling salesman problem. Due to its computational complexity, it is essential in practice to develop solution approaches to rapidly search for solution of high-quality. In this paper we propose a new algorithm based on a greedy randomized adaptive search procedure (GRASP) to efficiently solve the LOP. The algorithm is integrated with a Path-Relinking (PR) procedure and a new local search scheme. We tested our implementation on the set of 49 real-world instances of input-output tables (LOLIB instances) proposed in Reinelt (Linear ordering library (LOLIB) 2002). In addition, we tested a set of 30 large randomly-generated instances proposed in Mitchell (Computational experience with an interior point cutting plane algorithm, Tech. rep., Mathematical Sciences, Rensellaer Polytechnic Institute, Troy, NY 12180-3590, USA 1997). Most of the LOLIB instances were solved to optimality within 0.87 seconds on average. The average gap for the randomly-generated instances was 0.0173% with an average running time of 21.98 seconds. The results indicate the efficiency and high-quality of the proposed heuristic procedure.     

Flexible home care scheduling

Home care services are in high demand given how they are steadily becoming the primary source of care for the elderly. Powerful decision support tools are indispensable for effectively managing available staff in the context of ever-increasing demand for care and limited caregiver availability. This paper advances home care literature by introducing flexible task durations, thereby enabling tasks to be completed faster and ultimately more care to be scheduled. This new concept, which originates from practice, introduces an additional decision to be made when creating a schedule, thereby greatly increasing the scheduling complexity. Consequently, this paper introduces a new optimization-based decision support model which allows for scheduling with flexible task duration, as well as other types of flexibility. A computational study quantifies the impact of: (i) scheduling with a finer task granularity thereby enabling accurate prioritization of high and low priority care, (ii) flexibility in task duration enabling tasks to be completed faster and more care to be scheduled, and (iii) increasing the number of different locations visited by a caregiver thereby enabling a trade-off between the number of serviced clients and caregiver workload. A new publicly available real-world data set is used, obtained directly from home care organizations operating in Flanders. Analysis of the computational results demonstrates that significant improvements in operational efficiency may be realized with minimal effort required by organizations. Furthermore, the proposed algorithm’s performance is confirmed by comparison against the bounds obtained by solving an integer programming formulation of the problem. Finally, a management policy scheme is proposed which, when gradually implemented in a home care organization, results in a more efficient and therefore cost-effective deployment of its workforce.     

Data Driven Modeling: An Application in Scheduling

This paper presents a data driven modeling (DDM) approach to certain types of optimization problems. DDM relinquishes control of the completed model to the user department rather than the operations research (OR) staff. The approach emphasizes development of models that are dependent on data maintained and understood by the users. The data base consists of coded user rules which describe when changes will occur in the problem structure and data which captures the generalization of the problem. Both the rules and data can be updated by user department personnel. These data drive a matrix generator controlled by the rules which uses the data base as input to generate the specific model formulation. This DDM system is designed by OR consultants or staff to allow independence of use along with low-cost and minimal-effort maintenance. The DDM approach is illustrated with an application to a real-world medical scheduling problem.     

Heuristic Estimation of the Efficient Frontier for a Bi-Criteria Scheduling Problem

We examine a single-machine scheduling problem where the objective is to minimize the mean and the variance of the job completion times simultaneously. We seek to identify the efficient frontier which is obtained by parametrically solving a weighted combination of the two criteria. The identification of the true efficient frontier for this problem is notoriously difficult. To estimate the frontier, we propose a heuristic procedure which is quite general and can be applied to other bi-criteria problems as well. It involves repeated applications of a relatively new technique called beam search in an adaptive manner. To evaluate the proposed procedure, we introduce two measures of performance and conduct a computational study. The results of the study indicate that the procedure is highly effective.     

Lot sizing with storage losses under demand uncertainty

We address a variant of the single item lot sizing problem affected by proportional storage (or inventory) losses and uncertainty in the product demand. The problem has applications in, among others, the energy sector, where storage losses (or storage deteriorations) are often unavoidable and, due to the need for planning ahead, the demands can be largely uncertain. We first propose a two-stage robust optimization approach with second-stage storage variables, showing how the arising robust problem can be solved as an instance of the deterministic one. We then consider a two-stage approach where not only the storage but also the production variables are determined in the second stage. After showing that, in the general case, solutions to this problem can suffer from acausality (or anticipativity), we introduce a flexible affine rule approach which, albeit restricting the solution set, allows for causal production plans. A hybrid robust-stochastic approach where the objective function is optimized in expectation, as opposed to in the worst-case, while retaining robust optimization guarantees of feasibility in the worst-case, is also discussed. We conclude with an application to heat production, in the context of which we compare the different approaches via computational experiments on real-world data.     

The two-level lot-sizing problem with outbound shipment

We consider the two-level lot-sizing problem for the integrated replenishment and dispatch plan of a third-party logistics company and distribution center. Each outbound shipment for a dispatch involves cargos that incur a stepwise transportation cost. To increase the effect of shipment consolidation, the distribution center allows backlogging. This problem has the characteristics of capacitated and uncapacitated lot-sizing. A forward dynamic program is applied to exploit the beneficial characteristic of the uncapacitated problem. The forward dynamic program is implemented using Zangwill partitions to decrease the number of computational parameters with legitimacy checks to guarantee optimality. Employing these techniques, we provide an O(T⁴) algorithm, which serves as an improvement on the O(T⁶) algorithm of previous research. Moreover, computational results from actual implementations show that our algorithm is significantly faster than that of prior research.     

Dynamic interdiction networks with applications in illicit supply chains

We study the interdiction of illegal product distribution in a network with multiple sources (origins) and sinks (destinations). This work contributes to the literature of dynamic maximum flow interdiction problems by addressing multiple commodities in a network of relationships. The related distribution network consists of (1) criminals, who are hierarchically connected, and seeking to maximize the total profit flow from origins to destinations, and (2) enforcement officers aiming to minimize criminals’ long-term success by monitoring and arresting them, using the limited resources at their disposal. Considering several real-world operational details, we first propose a mixed-integer programming model by reformulating a Min–Max bi-level mathematical model. We then propose a new formulation and discuss its efficiency compared with the traditional duality-based reformulation. This new formulation also has a higher compatibility with decomposition solution methods. Utilizing the new formulation, we design a solution method based on the Benders decomposition procedure and apply several accelerating strategies (e.g., Super Valid Inequalities) to solve larger instances for a better representation of reality. Lastly, we create a heuristic method based on real-world evidence, which is usually practiced by law enforcement officers. Our results show that the quality of the heuristic method declines quickly as the network size increases.     

Eco-friendly container transshipment route scheduling problem with repacking operations

Currently, a huge amount of cargo is transported via containers by liner shipping companies. Under stochastic demand, repacking operations and carbon reduction, which may lead to an increase in effectiveness and environmental improvement, have been rarely considered in previous literature. In this paper, we investigate a container transshipment route scheduling problem with repacking operations under stochastic demand and environmental protection. The problem is a combinatorial optimization problem. Lacking historical data, a chance-constrained programming model is proposed to minimize the total operating and environment-related costs. We choose two distribution-free approaches, i.e., approximation based in Markov’s Inequality and Mixed Integer Second-Order Conic Program to approximate the chance constraints. As the loses induced by unfulfilled demand are not taken into account in the above model, a scenario-based model is developed considering the loses. Risk-neutral model may provide solutions that perform poorly while considering uncertainty. To incorporate decision makers’ perspectives, therefore, we also propose a risk-averse model adopting a risk aversion measure called Conditional Value-at-Risk to meet different preferences. Finally, we conduct computational experiments based on real data to compare the performances of the modeling methods and illustrate the impacts by testing different risk levels and confidence levels.

     

Integration between flow scheduling and personnel allocation in a parallel line system in automotive industry

A state-of-the-art review over fifty years of flow shop scheduling research, written by Gupta and Stafford (2006), comes to the conclusion that the mathematical theory of flow shop scheduling “suffers from too much abstraction and too little application”. In this paper we will develop an extended mathematical model for flow shop scheduling with parallel lines and simultaneously a worker assignment to machines as well as a solution concept for practical use. Such production systems are realized by applying the BTO-(Build to order) concept, as can be found in the automotive or computer industry, which allows customers to make any changes to their vehicles or hardware configuration within a few days before final assembly. In these cases late configuration is an important task for the producer and a complex scheduling problem arises in this context.