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Integration of energy aspects into the economic lot scheduling problem
Abstract
Due to the role the manufacturing sector plays in the depletion of resources and the generation of greenhouse gas emissions, the consumption of energy has more and more often made it onto research agendas in the area of production planning over the last decade. The work at hand integrates energy aspects into the well-known Economic Lot Scheduling Problem (ELSP) by taking account of the cost arising from the product-dependent energy usage of the production facility during machine startups and shutdowns as well as during tool change, idle, and production phases. To determine a cyclic production schedule that minimizes the sum of tool change, inventory holding, and energy usage costs, we use the Common-Cycle-Approach of Hanssmann (1962) and the Basic-Period-Approach of Haessler and Hogue (1976) and adjust them accordingly. Using the data sets of Bomberger and Eilon, we show that considering energy cost in the ELSP affects the resulting cyclic production schedule and significantly reduces the company's energy cost.
... The objective criteria were divided into financial criteria and non-financial criteria. Financial criteria in the papers were used to minimize the total costs [11], [17]- [19], minimize sequence-dependent setup costs [20], minimize setup cost [16], [21], [22], minimize holding costs [20]- [22], minimize backorder costs [20], minimize backlogging costs [22], minimize production/ manufacturing costs [20], [22], minimize remanufacturing cost [22], minimize energy costs [21]- [23], and maximize profit [15], [24]. Non-financial criteria were used to minimize earliness tardiness [14], minimize total tardiness [23], minimize CO2 emissions [14]- [16], [19], minimize makespan [9], [12], [13], [25], minimize total energy consumption [9], [10], [12], [13], [25], minimize delay [14], and maximize utilization of machines [13]. ...
... The objective criteria were divided into financial criteria and non-financial criteria. Financial criteria in the papers were used to minimize the total costs [11], [17]- [19], minimize sequence-dependent setup costs [20], minimize setup cost [16], [21], [22], minimize holding costs [20]- [22], minimize backorder costs [20], minimize backlogging costs [22], minimize production/ manufacturing costs [20], [22], minimize remanufacturing cost [22], minimize energy costs [21]- [23], and maximize profit [15], [24]. Non-financial criteria were used to minimize earliness tardiness [14], minimize total tardiness [23], minimize CO2 emissions [14]- [16], [19], minimize makespan [9], [12], [13], [25], minimize total energy consumption [9], [10], [12], [13], [25], minimize delay [14], and maximize utilization of machines [13]. ...
... Multi-products require more complicated and complex models and solutions. There were 2 papers that defined lot sizes and scheduling for single products, namely [16], [19] TABLE II REVIEW BASED ON MANUFACTUING SYSTEM, NUMBER OF PRODUCT, DATA TYPE, MODEL TYPE, OBJECTIVE CRITERIA, SYSTEM OF OBJECTIVES, SOLUTION METHOD, AND SUSTAINABILITY POLICY Reference [12] Reference [14] Reference [15] Reference [11] Reference [13] Reference [17] Reference [25] Reference [16] Reference [21] Reference [10] Reference [22] Reference [18] Reference [24] Reference [9] Reference [23] Reference [20] Reference [19] Mfg. System Single machine or multi-products, namely [9], [10], [21]- [25], [11]- [15], [17], [18], [20]. ...
... However, non-fossil fuels consumption is still relatively low in the Middle East and the Gulf regions and therefore has a significant impact on climate change and energy-related Carbon dioxide (CO 2 ) emissions [19]. From the literature, 23% of the increase in energy consumption between 2007 and 2012, and 3% of the increase in energy-related emissions [20] have taken place in the industry sector [21]. And, as shown in Fig. 2, this trend is projected to further increase with the industry development by 2040. ...
... Zhang, Cai [98] minimized the electricity cost of a grid-connected manufacturing process considering solar power generation. Beck, Biel [21] optimized an energy-aware PP, taking into account Turn-off/Turn-on of machines, tool change, and idle and production phases. Proposing a linear programming model, Sianaki, Masoum [99] optimized the energy-consumption, subject to the energy limit posed by production demands. ...
... The costs obtained from both the proposed SEAMPS and the conventional problems are presented in Supplementary Materials Tables 4 and 5 The conventional problem can be defined through Constraints (10)e (21) and Eq. (8) as its objective function to be minimized. ...
Considering economic and environmental concerns as well as thermal and visual comfort requirements, this paper introduces the idea of Smart Energy-Aware Manufacturing Plant Scheduling, for general manufacturing processes, especially high-value-added ones. The integrated system benefits from the use of a grid-connected Microgrid, a combined cooling, heat, and power system, and renewable power. Employing the Conditional Value-at-Risk and guaranteeing both solution and model robustness through an original multi-objective risk-based robust mixed-integer linear programming to optimally support the system make the contribution of the paper novel and unique. The main objective is to schedule manufacturing (non-shiftable) and non-manufacturing (shiftable and interruptible) loads, and distributed energy resources based on the real-time-pricing policy in an interactive decentralized operation of a capacitated multi-carrier energy production-consumption system. Compared to the conventional system, the results outline 64.63%, 1.62%, 100%, and 65.23% less Carbon dioxide emissions, net production, power exchange, and total costs, on average. The proposed framework is preferable to the framework that is based on the use of combined heat and power systems, at least in terms of a reduction in production costs. Considering both the supply- and demand-side uncertainties, the framework performs good trade-offs between solution robustness and model robustness, and environmental and economic concerns.
... Thus, developing new types of clean and sustainable energy, such as wind as a very valuable Renewable Energy Resource (RER), has become more and more crucial for industries and businesses. This is due to the increasing responsibility of the industries for primary energy consumption from 31% in 200731% in (IEA, 2007 to 39.4% in 2010 (Biel and Glock, 2016), and further to 54% in 2012 (Beck et al., 2018). This is well in line with the increasing share of the industry sector on energy-related CO 2 emissions from 28% of the overall energy-related CO 2 emissions in 2012 to 31% in 2040 . ...
... This is well in line with the increasing share of the industry sector on energy-related CO 2 emissions from 28% of the overall energy-related CO 2 emissions in 2012 to 31% in 2040 . Among industries, the manufacturing sector is responsible for at least 65% of the energy usage in 2012, and this share is expected to increase until 2040 (Beck et al., 2018). Therefore, it is clear that promoting Energy Efficiency (EE) in manufacturing is a great potential for energy consumption reduction as well as energy-related CO 2 emissions and that this approach will not lose its relevance in the decades to come. ...
... Their model integrated the Turn off/ Turn on of machines with scheduling to obtain the EEPP. Beck et al. (2018) integrated energy aspects into the PP considering the cost arising from the energy-oriented production during Turn off/Turn on of the machines as well as during tool change, idle, and production phases. Giglio et al. (2017) designed a system to produce multi-class single-level products through both manufacturing of raw materials and remanufacturing of return products aiming to define and solve an integrated LS and EEPP problem in a JSMS. ...
This paper is the first to introduce the concept of Smart Energy-Efficient Production-Planning (SEEPP) for a general Job-Shop manufacturing system in the presence of Grid-connected Microgrid with wind power generation. To cope with the unpredictability of wind speed and the uncertainties of demands, a novel risk-based Robust Mixed Integer Linear Programming (RMILP) model is mathematically formulated. The last aim of the model is to minimize the total day-ahead cost of the system considering peak demand charge. The results show the capability of the proposed integrated framework to obtain a constructive trade-off between scenario-based cost deviations, and heat and power imbalances considering the attitude of Decision Makers (DMs) toward risk. The results further indicate that the proposed SEEPP concept is able to produce products with at least 1.95% less cost than conventional manufacturing systems, although it supports a much wider range of demands for products. The performance of the model is analyzed and evaluated in terms of accuracy, robustness, and computational efficiency.
... Compared to studies on ELSP (e.g., [4,9,31,45,48,65]), ELDSP has been much less investigated. Torabi et al. [50] formulated ELDSP over a finite planning horizon and under the CC approach, for a two-level supply chain, featuring a supplier operating a flexible flow line (FFL) production system and a single AF. ...
This paper addresses the economic lot and delivery scheduling problem (ELDSP) within three-echelon supply chains, focusing on the complexities of demand uncertainty, limited shelf-life of products, and sequence-dependency of setups. We develop a novel mixed-integer non-linear programming (MINLP) model for a supply chain comprising one supplier, multiple manufacturers with flexible flow shop (FFS) production systems, and multiple retailers, all operating over a finite planning horizon. The common cycle (CC) strategy is adopted as the synchronization policy. Our model employs fuzzy set theory, particularly the “ Me measure,” to effectively handle the retailers’ demand uncertainty. Our findings indicate that total supply chain costs escalate with an increase in demand, final components’ holding costs, and sequence-dependent setup costs, but decrease with increasing production rates. Furthermore, while total costs are significantly sensitive to changes in demand, they are relatively insensitive to fluctuations in sequence-dependent setup times. The models developed offer valuable managerial insights for optimizing costs in synchronized multi-stage supply chains, aiding managers in making informed decisions about production lot sizes and delivery schedules under both deterministic and fuzzy demand scenarios. Additionally, the proposed models bridge key research gaps and provide robust decision-making tools for cost optimization, enhancing supply chain synchronization in practical settings.
... According to the International Energy Agency (EIA 2013), the industry sector consumes 42% of the total energy worldwide. Approximately 65% of the energy used in the industrial sector was contributed by manufacturing firms in 2012 which is deemed to rapidly increase by 2040 (Beck et al. 2019). Also, the governments that are providing subsidized energy are withdrawing their support due to unstable economic conditions (Modarres and Izadpanahi 2016). ...
There is an increasing concern about incorporating green criteria into production planning approaches. Production planning models that ignore green parameters may generate outcomes that are unfriendly to the environment. The relevant literature has suggested a flourishing trend towards the integration of green parameters into production planning approaches. The earlier reviews have most commonly analyzed the green production planning approaches from an “energy efficiency” perspective. Literature on the integration of other green criteria is also available. However, such studies are rarely reviewed. Along with “energy efficiency,” the study in hand reviews the production planning strategies from another green perspective which is “low-carbon emissions.” The first objective of this study is to review the medium and short-term production planning approaches from the aforementioned green criteria and provide a classification scheme. Second, new research avenues are identified to facilitate researchers in incorporating green schemes in production planning approaches. This study explored various databases for articles published on green production planning approaches. Consequently, 84 articles published between 2011 and 2022 were considered for the review. This review pointed out that most of the studies on green production planning considered “energy efficiency” and studies on “carbon emissions” were overlooked. Furthermore, green concepts were mostly integrated into the short-term production planning level and comparatively few studies were found for the medium-term. This study will help researchers to analyze green production planning in terms of modeling approaches, objective functions, uncertainties, solution approaches, etc.
... As in the previous contribution, the focus is on the definition of an energy-efficient schedule and not on the evaluation of the power requirements of the system under consideration. Beck et al, (2019) integrate energy assessments to the economic lot scheduling problem (ELSP). Idle, production, and tool-change phases are considered in the model in order to minimize energy consumption, tool changes, and holding costs. ...
The attention paid to energy consumption is growing steadily due to the costs associated with energy usage as well as the resulting environmental impacts. This work proposes an analytical method to assess the energy consumption and the power requirements of a productive system. By exploiting queuing theory, it is possible to achieve a probabilistic view of energy consumption. This method is useful to define the contractual power level and calculate the service level associated with it, so it is applicable as a decision-support tool during the design of productive systems when it is not possible to obtain field data (green-field design). Three different models characterised by an increasing degree of complexity were exploited. The three models share the feature of an infinite number of servers, while the increasing complexity is due to the introduction of batch arrivals and the variability of the size of the arrival lot. A connection is made between production variables and power used by machines to consider energy consumption. A numerical example shows the applicability of the method and highlights the different results obtained through the three models. In addition, analytical formulations are available for all three proposed models; thus, no simulation process is needed.
... As in the previous contribution, the focus is on the definition of an energy-efficient schedule and not on the evaluation of the power requirements of the system under consideration. Beck et al, (2019) integrate energy assessments to the economic lot scheduling problem (ELSP). Idle, production, and tool-change phases are considered in the model in order to minimize energy consumption, tool changes, and holding costs. ...
... Huang, Yao [4], Ouenniche, and Boctor [5], each proposed two new heuristics approaches to solve the mathematical model for the ELSP with a flow shop system as a multi-product, multi-stage, economic lot-sizing problem. Recently, ELSP has been extended to sustainability challenges, Beck et al. [6] studied the effects of energy usage on ELSP with different approaches. Ferretti [7] considers ELSP with returns and sorting line regarding environmental legislations. ...
Supply chain management intends to integrate supply chains' activities such as material flow, information flow and financial issues. Material flow management is the most significant issue since the inventory level in the whole supply chain could be optimized by an integrated plan. In other words, when one member of the supply chain plans to reduce its inventory level solely, despite reducing inventory in this node the inventory will be stocked in other partners' warehouses. Therefore, in this paper a new mathematical model has been developed to facilitate the process of finding the optimum solution in economic production, purchase and delivery lots and their schedules in a three-echelon supply chain environment; including raw material in suppliers, manufacturer and assembly facility as a customer. The manufacturer with a flow shop system provides its requirements from supplier, assemble multiple products, and delivers products to the customer (automotive OEM alike) on an optimum multiple delivery points. The delivery cycles would be identified through the production common cycle regarding the supply chain flexibility. Finally, a modified real-valued Genetic Algorithm (MRGA), and an Optimal Enumeration Method (OEM) are developed, and some numerical experiments have been done and compared as well.
... We simplify the ELSP by focusing on a well-known particular class: the common cycle approach which is often considered in the literature (see e.g., Beck et al., 2019;Zhang and Rajaram, 2017;Taleizadeh et al., 2015). With a common cycle, all products are manufactured once in some sequence, before any product is produced twice. ...
Managers are often inclined to maximize the utilization of production plants to compensate for the high fixed costs. Therefore, when marketing conditions justify higher variety and manufacturers have excess capacity, they tend to introduce new variants. By studying product proliferation in the context of the economic lot sizing problem, we show that the mindset of adding new products as long as the utilization is “low” can cause unbearable cash flow issues and profit losses. Instead of capacity utilization, we propose manufacturers to pay attention to the idle fraction of non-productive time (IFNPT); when IFNPT drops to zero (i.e., absence of idleness), managers should first increase capacity and then consider introducing new products. Since managers cannot observe the net profit contribution of a product, IFNPT constitutes a pragmatic indicator for deciding when to stop product proliferation. We also show that firms can afford a larger product portfolio with lower setup times and higher sale heterogeneity across the products. We gain additional insights by proving useful properties of the profit function that allow the study of product portfolio growth through time. We provide analytical justifications to support our main insights.
... For example, Rapine et al. (2018) tackles a single-item lot-sizing problem in a production system with identical, capacitated parallel machines, with a set of constraints limiting the energy consumption in each period. Similarly, Masmoudi et al. (2017) proposes a lot-sizing problem in a flow-shop system with energy consideration and Beck et al. (2019) addresses an extended economic lot scheduling problem. Finally, problems arise at operational level since electricity prices vary according to short periods and specific power limits are imposed by energy providers. ...
In this research, the economic lot scheduling problem (ELSP), as an NP-hard problem in terms of a bi-objective approach considering deteriorating items and shortage, is studied. The goal is to simultaneously minimise ‘setup and inventory holding costs, comprising deterioration’, and ‘total amount of units facing shortage throughout every period. Two policies besides a heuristic method are employed simultaneously, named extended basic period and Power-of-Two (PoT), to make sure of having feasible replenishment cycles. For handling the considered problem, three multi-objective techniques are employed: non-dominated sorting genetic algorithm II (NSGAII), non-dominated ranking genetic algorithm (NRGA), and a multi-objective procedure hybridized of NSGAII and particle swarm optimization (PSO), called PSNSGAII. Also, three metrics are used to assess the quality of the algorithms’ outputs, including spacing, mean ideal distance, and spread. Experimental results, including extensive conducted parametric and non-parametric statistical analyses, prove that the proposed hybrid PSNSGAII algorithm can well meet discussed criteria compared to other employed algorithms in both ‘quality of solutions’ and ‘diversity’ in almost all small, medium and large test instances. Finally, some useful managerial and practical insights are presented.
Purpose
This paper aims to present a novel bi-objective mathematical model for a production-inventory system under uncertainty.
Design/methodology/approach
This paper addresses agile and lean manufacturing concepts alongside with green production methods to design an integrated capacitated lot sizing problem (CLSP). From a methodological perspective, the problem is solved in three phases. In the first step, an FM/M/C queuing system is used to minimize the number of customers waited to receive their orders. In the second step, an effective approach is applied to deal with the fuzzy bi-objective model and finally, a hybrid metaheuristic algorithm is used to solve the problem.
Findings
Some numerical test problems and sensitivity analyzes are conducted to measure the efficiency of the proposed model and the solution method. The results validate the model and the performance of the solution method compared to Gams results in small size test problems and prove the superiority of the hybrid algorithm in comparison with the other well-known metaheuristic algorithms in large size test problems.
Originality/value
This paper presents a novel bi-objective mathematical model for a CLSP under uncertainty. The proposed model is conducted on a practical case and several sensitivity analysis are conducted to assess the behavior of the model. Using a queue system, this problem aims to reduce the items waited in the queue to receive service. Two objective functions are considered to maximize the profit and minimize the negative environmental effects. In this regard, the second objective function aims to reduce the amount of emitted carbon.
Following the scarcity of resources, rising energy prices, and an increasing awareness of the role manufacturing plays in the generation of greenhouse gas emissions, the usage of energy has more and more been considered in research on production planning and scheduling in recent years. Time-varying energy prices, which have been introduced to penalize energy usage during peak-demand periods and which are supposed to smooth energy demand, have added a new aspect to this stream of research. This article studies how the integration of a waste heat recovery system, which can convert industrial waste heat into electrical energy, along with an electrical energy storage system can balance the positive and negative effects of energy peak prices on the production plan in a serial multi-stage production system. After developing an appropriate model, we investigate how the use of the waste heat recovery system and the electrical energy storage system impact production planning. In a numerical analysis, we investigate under which conditions the recovery of waste heat combined with the opportunity to store energy provides practitioners with an efficient tool to lower total energy usage and to better react to time-varying energy prices, and thus to reduce total energy cost.
A new 'econological scheduling' model combining the economic and ecological aspects of a multi-part multi-machine setup operating under a time-of-use tariff is presented. The operating speed of the machines and the frequency of operating speed change are allowed to vary, and the peak load and energy consumption during a shift is estimated using discrete event simulation. The electricity cost and environmental impact for a target production quota are simultaneously minimized using a multi-criterion meta-heuristic optimization. The proposed model is demonstrated via a case study on a manufacturing unit producing parts using machining and welding operations. A comparison among econological, economic, and ecological approaches and the underlying dynamics of scheduling under a time-varying electricity tariff are presented as one of several strategies for enabling a manufacturing system to be more eco-friendly without substantially increasing the electricity cost.
The paper investigates the effects of production scheduling policies aimed towards improving productive and environmental performances in a job shop system. A green genetic algorithm allows the assessment of multi-objective problems related to sustainability. Two main considerations have emerged from the application of the algorithm. First, the algorithm is able to achieve a semi-optimal makespan similar to that obtained by the best of other methods but with a significantly lower total energy consumption. Second, the study demonstrated that the worthless energy consumption can be reduced significantly by employing complex energy-efficient machine behaviour policies.
Many countries are actively trying to cope with recent effects of climate change and the energy crisis. At the same time, efficient energy use and the reduction of greenhouse gas emissions are very important, not only to reduce energy costs but also to contribute to an environment-friendly, sustainable lifestyle. Currently, manufacturing industries in some countries pay stratified electricity rates that depend on the time of the day (i.e. peak load, mid-load and off-peak load). Hence, the production scheduling process, which considers time-dependent and machine-dependent electricity costs, enables these industries to minimise energy expenses. Additionally, the emerging Smart Grid is supposed to require industries to pay real-time hourly electricity costs. More energy-efficient, intelligent production scheduling is thus a major goal. This paper deals with minimising the total production cost of the flexible job-shop scheduling problem. Our method allows each decision-maker in the manufacturing industry to seek a compromise solution for total production costs, by considering electricity costs with distributed energy resources and energy storage. We use constraint programming and mixed-integer programming approaches to solve this problem, and compare our proposed models with the classical computational method.
Manufacturing enterprises nowadays face the challenge of increasing energy prices and requirements to reduce their emissions. Most reported work on reducing manufacturing energy consumption today focuses on the need to improve the efficiency of resources (machines) largely ignoring the potential for energy reducing on the system-level where the operational method can be employed as the energy saving approach. The advantage is clearly that the scheduling and planning approach can also be applied across existing legacy systems and does not require large investment. Therefore, a multi-objective scheduling method is developed in this paper with reducing energy consumption as one of the objectives. This research focuses on classical job shop environment which is widely used in the manufacturing industry. A model for the bi-objectives problem that minimises total electricity consumption and total weighted tardiness is developed and the Non-dominant Sorting Genetic Algorithm is employed as the solution to obtain the Pareto front. A case study based on a modified 10×10 job shop is presented to show the effectiveness of the algorithm and to prove the feasibility of the model.
This paper develops operational methods for the minimization of the energy consumption of manufacturing equipment. It is observed that there can be a significant amount of energy savings when non-bottleneck (i.e. underutilized) machines/equipment are turned off when they will be idle for a certain amount of time. Using this fact, several dispatching rules are proposed. A detailed performance analysis indicates that the proposed dispatching rules are effective in decreasing the energy consumption of especially underutilized manufacturing equipment. In addition, a multi-objective mathematical programming model is proposed to minimize the energy consumption and total completion time. Using this approach, a production manager will have a set of non-dominated solutions (i.e. the set of efficient solutions) which he/she can use to determine the most efficient production sequence which will minimize the total energy consumption while optimizing the total completion time.
The economic lot-scheduling problem (ELSP) is an important production sched-uling problem that has been intensively studied over 40 years. Numerous heuristic algorithms have been developed since the problem is NP-hard. Dobson's heuristic has been regarded as the best in its performance. The present paper provides a hybrid genetic algorithm based on the time-varying lot sizes approach in the ELSP literature. Numerical experiments show that the hybrid genetic algorithm outperforms Dobson's heuristic.
The present literature survey focuses on the stochastic economic lot scheduling problem (SELSP). The SELSP deals with the make-to-stock production of multiple standardized products on a single machine with limited capacity under random demands, possibly random setup times and possibly random production times. The main task of a production manager in this setting is the construction of a production plan for the machine. Based on the critical elements of such a production plan, we present a classification and extensive overview of the research on the SELSP together with an indication of open research areas. By doing so, we intend to stimulate the discussion on the important problems concerning the SELSP both from a theoretical and a practical point of view.
In this paper, we model the effects of imperfect production processes on the economic lot scheduling problem (ELSP). It is assumed that the production facility starts in the in-control state producing items of high or perfect quality. However the facility may deteriorate with time and shifts at a random time to an out of control state and begins to produce nonconforming items. A mathematical model is developed for ELSP taking into account the effect of imperfect quality and process restoration. Numerical examples are presented to illustrate important issues related to the developed model.
Following the scarcity of resources, rising energy prices, and an increasing awareness of the role manufacturing plays in the generation of greenhouse gas emissions, the consumption of energy has more and more been the subject of research on production planning over the last decade. Even though recent years have witnessed a dramatic increase in the number of works published in this area, several related research questions have been opened up without sufficiently linking research approaches and research insights. The aim of this paper is to investigate the links between these questions and to highlight how the modeling approaches developed for different manufacturing systems, energy pricing policies, and energy efficiency criteria can benefit from each other and lead to more advanced energy-efficient production planning approaches. Therefore, this paper provides a review of the state-of-the-art of decision support models that integrate energy aspects into mid-term and short-term production planning of manufacturing companies. The paper first highlights the increasing importance of energy consumption in manufacturing and shows how considering energy consumption in production planning can contribute to more energy-efficient production processes. Subsequently, the paper outlines the review methodology used and descriptively analyzes the sampled papers. Afterwards, the selected papers are categorized according to the production planning tasks considered. From this classification, gaps in the existing literature are derived and potential areas for future research are suggested.
Industrial energy consumption accounts for approximately one third of the energy consumed by the four major end-uses of energy (i.e., residential, commercial, industrial, and transportation energy). Manufacturing is thereby responsible for the majority of energy that is consumed in industry. The scarcity of resources, rising energy prices, and an increasing awareness that lowering energy usage is a prerequisite for sustainable production processes has induced researchers to consider energy consumption in the management of production systems. This paper contributes to this emerging stream of research by studying the role of waste heat in production planning and control. More specifically, it investigates the case where industrial waste heat can be converted into electricity, which can then be used to support operating the production stages. This paper introduces the generation and transformation of waste heat into a lot size model and investigates how lot sizing policies change if waste heat is used to operate the system. Special attention is paid to the scheduling of interruptions between production runs and the determination of optimal production rates. The results of the paper indicate that using waste heat resulting from production reduces the overall energy requirements of a production system. The inventory policies developed in this paper support an efficient use of waste heat.
This paper studies the Economic Lot Scheduling Problem (ELSP) for the single-machine-multi-product case. In contrast to earlier research, it assumes that a lot may be split up into batches, which are then shipped individually to the consuming stage. Integrating batch shipments into the ELSP helps to reduce cycle times at the expense of higher transportation costs. This paper selects two popular approaches used in the literature to solve the ELSP, namely the Common-Cycle-Approach of Hanssmann and the Basic-Period-Approach of Haessler and Hogue, extends them to include both equal- and unequal-sized batch shipments, and suggests a solution procedure for each approach. Both model extensions are illustrated using the modified Bomberger and Eilon data sets, and they are compared to the special case where only complete lots are transferred to the next stage. Finally, ideas for future research are presented.
This paper aims to present a literature review and an analysis of research works in the field of economic lot scheduling problem (ELSP) based on the related articles published since 1958. Because of ELSP complexity, there are a noticeable number of studies that use algorithms based on different approaches in order to deliver a feasible solution. Therefore, the contribution of this paper is to introduce a taxonomic classification based on scheduling policies and solving methodologies proposed by authors. Also, a simple data analysis is carried out to understand the evolution of ELSP and to identify potential research areas for further studies. The results show that there is an increasing trend in this topic but there are still much needs from industrial manufacturing systems. This study is expected to provide a comprehensive list of references for other researchers, who are interested in ELSP research.
MRP concepts (materials requirement planning) are barely able to cope with today's requirements on production planning and production control. Planning and control must be improved. To achieve this, MES systems (manufacturing execution systems) are being introduced. This article presents a case from practice.
The industrial sector is one of the largest energy consumers in the world. To alleviate the grid’s burden during peak hours, time-of-use (TOU) electricity pricing has been implemented in many countries around the globe to encourage manufacturers to shift their electricity usage from peak periods to off-peak periods. In this paper, we study the unrelated parallel machine scheduling problem under a TOU pricing scheme. The objective is to minimize the total electricity cost by appropriately scheduling the jobs such that the overall completion time does not exceed a predetermined production deadline. To solve this problem, two solution approaches are presented. The first approach models the problem with a new time-interval-based mixed integer linear programming formulation. In the second approach, we reformulate the problem using Dantzig–Wolfe decomposition and propose a column generation heuristic to solve it. Computational experiments are conducted under different TOU settings and the results confirm the effectiveness of the proposed methods. Based on the numerical results, we provide some practical suggestions for decision makers to help them in achieving a good balance between the productivity objective and the energy cost objective.
Guaranteeing environmentally conscious supply chain operations is closely linked to an organization’s sustainability and success. This paper presents two models that consider energy used for production along with the greenhouse gases (GHG) emissions from production and transportation operations in a single-vendor (manufacturer) single-buyer system under a multi-level emission-taxing scheme. The first model considers a classical coordination policy, while the second considers a vendor-managed inventory with consignment stock (VMI-CS) agreement policy. Numerical examples are provided and the two models are compared to outline managerial implications and insights. Energy usage has been found to be the main cost component for both models, thus reducing energy usage is a priority. Key results show that the VMI-CS model, over the different scenarios considered, allows the system to operate more economically.
The lack of effective process planning and scheduling solutions for the sustainable management of machining shop floors, whose manufacturing activities are usually characterized by high variety and low volume, has been crippling the implementation of sustainability in companies. To address the issue, an innovative and systematic approach for milling process planning and scheduling optimization has been developed and presented in this paper. This approach consists of a process stage and a system stage, augmented with intelligent mechanisms for enhancing the adaptability and responsiveness to job dynamics in machining shop floors. In the process stage, key operational parameters for milling a part are optimized adaptively to meet multiple objectives/constraints, i.e., energy efficiency of the milling process and productivity as objectives and surface quality as a constraint. In the consecutive system stage, to achieve higher energy efficiency and shorter makespan in the entire shop floor, sequencing/set-up planning of machining features/operations and scheduling for producing multiple parts on different machines are optimized. Artificial Neural Networks are used for establishing the complex nonlinear relationships between the key process parameters and measured datasets of energy consumption and surface quality. Several intelligent algorithms, including Pattern Search, Genetic Algorithm and Simulated Annealing, are applied and benchmarked to identify optimal solutions. Experimental tests indicate that the approach is effective and configurable to meet multiple objectives and technical constraints for sustainable process planning and scheduling. The approach, validated through industrial case studies provided by a European machining company, demonstrates significant potential of applicability in practice.
One of the primary objectives of sustainable manufacturing is to minimize energy consumption in its manufacturing processes. A strategy of energy saving is to adapt new materials or new processes; but its implementation requires radical changes of the manufacturing system and usually a heavy initial investment. The other strategy is to optimize existing manufacturing processes from the perspective of energy saving. However, an explicit relational model between machining parameters and energy cost is required; while most of the works in this field treat the manufacturing processes as black or gray boxes. In this paper, analytical energy modeling for the explicit relations of machining parameters and energy consumption is investigated, and the modeling method is based on the kinematic and dynamic behaviors of chosen machine tools. The developed model is applied to optimize the machine setup for energy saving. A new parallel kinematic machine Exechon is used to demonstrate the procedure of energy modeling. The simulation results indicate that the optimization can result in 67% energy saving for the specific drilling operation of the given machine tool. This approach can be extended and applied to other machines to establish their energy models for sustainable manufacturing.
Purpose
This research note aims to present a summary of research concerning economic‐lot scheduling problem (ELSP).
Design/methodology/approach
The paper's approach is to review over 100 selected studies published in the last 15 years (1997‐2012), which are then grouped under different research themes.
Findings
Five research themes are identified and insights for future studies are reported at the end of this paper.
Research limitations/implications
The motivation of preparing this research note is to summarize key research studies in this field since 1997, when the ELSP problems have been verified as NP‐hard.
Originality/value
ELSP is an important scheduling problem that has been studied since the 1950s. Because of its complexity in delivering a feasible analytical closed form solution, many studies in the last two decades employed heuristic algorithms in order to come up with good and acceptable solutions. As a consequence, the solution approaches are quite diversified. The major contribution of this paper is to provide researchers who are interested in this area with a quick reference guide on the reviewed studies.
The quantity of carbon dioxide (CO2) emissions is one of the most widely recognised measures of environmental sustainability. Given the mounting concern about climate change and global warming, managers are facing growing pressure to reduce CO2 emissions. In practice, other than CO2 emissions, managers may be concerned with other objectives when making a scheduling decision. This work develops the ε-archived genetic algorithm (ε-AGA) to examine two batch scheduling problems with the goal of minimising CO2 emissions and the traditional due date-based objective of minimising total weighted tardiness (TWT). Experimental results show that in terms of both quality and diversity of solutions, ε-AGA outperforms NSGA-II for same computation time limit as the stopping criteria. Several interesting observations are made. (1) These two objectives conflict with each other; (2) jobs that arrive soon after each other reduce makespan, and so reduce CO2 emissions; (3) given a set of m identical batching machines, the due dates of jobs do not seem to substantially influence CO2 emissions; and (4) in purchasing a machine, the variation in power consumption among machines is critical to reducing the TWT.
This paper determines an optimum production schedule and raw material ordering policy for a family of products that share a common piece of production facility, and the inventory operates under a shelf life constraint. The problem of manufacturing a family of products under shelf life is addressed here mainly under three major issues: adjusted production rate, adjusted cycle time, and simultaneous adjustment of production rate and cycle time. This research addressed the issues in two major parts: the first part comprises planning an optimum production schedule and material ordering policy for a family of products with a constant production cost for operating the machines. The second part of the research considers a generalized production cost of operation where the cost of operation may increase or decrease depending on the production system. Results are demonstrated to show the computational mechanics and incremental advantages over the other models. A sensitivity analysis is performed to study the effect of variability of some parameters that play important roles in the models. An empirical test has also been conducted to show the relative performance of the models.
Nowadays, it is an essential commitment for firms to reduce energy consumption and therewith energy costs, which frequently account for a large part of the manufacturing costs. This work analyzes a system where a single product is manufactured on a machine and delivered to the subsequent production stage in batch shipments. The production rate at each stage may be varied within given limits. Energy consumption at each stage is strictly related to the production rate set according to a given function that depends on the specific characteristics of the production process. Energy consumption is assumed to occur both during production and during the idle state of the machines. The aim of this work is to propose an analytical model of this system and to minimize the total costs of producing and storing the product, including energy costs. The results of the paper indicate that energy-related costs can be reduced significantly if energy consumption is considered in planning the production process.
Hybrid flow shop (HFS) scheduling has been extensively examined and the main objective has been to improve production efficiency. However, limited attention has been paid to the consideration of energy consumption with the advent of green manufacturing. This paper proposes a new ant colony optimization (MOACO) meta-heuristic considering not only production efficiency but also electric power cost (EPC) with the presence of time-of-use (TOU) electricity prices. The solution is encoded as a permutation of jobs. A list schedule algorithm is applied to construct the sequence by artificial ants and generate a complete schedule. A right-shift procedure is then used to adjust the start time of operations aiming to minimize the EPC for the schedule. In terms of theoretical research aspect, the results from computational experiments indicate that the efficiency and effectiveness of the proposed MOACO are comparable to NSGA-II and SPEA2. In terms of practical application aspect, the guideline about how to set preference over multiple objectives has been studied. This result has significant managerial implications in real life production. The parameter analysis also shows that durations of TOU periods and processing speed of machines have great influence on scheduling results as longer off-peak period and use of faster machines provide more flexibility for shifting high-energy operations to off-peak periods.
This paper treats a version of the economic lot scheduling problem (ELSP) in which items may be produced several times in different amounts during a cycle. We show how to compute the optimal lot sizes and cycle length, given the sequence of items in a cycle. This requires solving a parametric quadratic program, plus a few EOQ calculations. Our procedure is designed to be used along with a heuristic for selecting the sequence of items in a cycle, such as the one proposed by G. Dobson [ibid. 35, No. 5, 764-771 (1987; Zbl 0636.90038)]. The two algorithms together comprise a simple, plausible heuristic for the ELSP as a whole.
This paper considers the Economic Lot Scheduling Problem; that is, the problem of scheduling several products on a single facility so as to minimize holding and setup costs. We develop a formulation that provides feasible schedules by allowing the lot sizes and thus the cycle times for each product to vary over time and by explicitly taking into account setup times. Our main results characterize when feasible schedules exist, quantify the insensitivity of the schedules; costs to minor adjustments, and thus show how close the schedules will be to ones with optimal equal cycle times. We also present a heuristic for finding good feasible schedules.
Manufacturing scheduling strategies have historically emphasized cycle time; in almost all cases, energy and environmental factors have not been considered in scheduling. This paper presents a new mathematical programming model of the flow shop scheduling problem that considers peak power load, energy consumption, and associated carbon footprint in addition to cycle time. The new model is demonstrated using a simple case study: a flow shop where two machines are employed to produce a variety of parts. In addition to the processing order of the jobs, the proposed scheduling problem considers the operation speed as an independent variable, which can be changed to affect the peak load and energy consumption. Even with a single objective, finding an optimal schedule is notoriously difficult, so directly applying commercial software to this multi-objective scheduling problem requires significant computation time. This paper calls for the development of more specialized algorithms for this new scheduling problem and examines computationally tractable approaches for finding near-optimal schedules.
The importance of material and product recovery is steadily increasing, mainly due to customer expectations and take-back obligations. Disassembly is a major operation in material and product recovery, since returned products are often disassembled to separate materials and components. The paper considers the problem of scheduling several items on a single disassembly facility. It develops a cyclic lot-scheduling heuristic for disassembly processes with sequence- dependent set-ups, resulting in disassembly frequencies for the items. Additionally, the way the problem is formulated allows calculation of the profitable use of the facility. The disassembly frequencies and the profitable use of the facility are used to create a cyclic schedule.
Motivated by a case study of a company that produces car parts, we study the multi-product economic lot scheduling problem for a hybrid production line with manufacturing of new products and remanufacturing of returned products. For this economic lot scheduling problem with returns (ELSPR), we consider policies with a common cycle time for all products, and with one manufacturing lot and one remanufacturing lot for each product during a cycle. For a given cycle time, the problem is formulated as a mixed integer linear programming (MIP) problem, which provides the basis for an exact solution. The application of this model for one of the core products of the case study company indicates a 16% reduction in cost compared to the current lot scheduling policy.
In practice, the economic lot quantity problem and the scheduling problem often are treated separately in production planning. However, when a number of items must be supplied continuously and the same means of production must be employed for several of the items non-concurrently, the "economic lot scheduling problem" may have to be dealt with. Addressing itself to a reduced version of this problem, the article outlines a computational approach to finding a feasible and minimum cost (set-up plus storage) production schedule for a group of items which must be available continuously though produced consecutively in a single production center.
The ELSP is a time-honored problem that “has been around” since 1915. It is the problem of accommodating cyclical production patterns when several products are made on a single facility. Recent contributions to its resolution resulted in either analytical approaches to a restricted problem, or heuristic approaches to the entire problem.
This paper reviews critically the various contributions to the problem, and extends the analysis in the following four directions: An improved analytical approach A test for feasibility, A systematic means for escape from infeasibility, and A procedure for the determination of a basic period for a given set of multipliers to achieve a feasible schedule.
This note develops a procedure for automatically generating feasible solutions for the single-machine multi-product lot scheduling problem.
Most of the procedures that have been developed to find solutions to the single-machine, multi-product lot scheduling problem depend on judgment to define the desirable frequencies of production for the products. In this paper we describe an iterative procedure for directly determining near optimal frequencies of production for the products and the associated fundamental cycle time which, in many cases, can be used directly for constructing production schedules. In cases where feasible schedules cannot be constructed using the values from the iterative procedure, the procedure provides a basis for changing the production frequencies and the fundamental cycle time to obtain feasible schedules.
A note on Madigan, J. G., "Scheduling a Multi-Product Single Machine System for an Infinite Planning Period," Management Science, Vol. 14, No. 11 (July 1968), pp. 753-719.
The problem considered is that of scheduling the production of several different items over the same facility on a repetitive basis. The facility is such that only one item can be produced at a time; there is a setup cost and a setup time associated with producing each item; the demand rate for each item is known and constant over an infinite planning horizon, and all demand must be met.
A dynamic programming solution is developed. This solution is applied to a sample problem, and the results are compared with pertinent bounds.
In this paper, we deal with the production scheduling ofseveral products that are produced periodically, in a fixed sequence, ona single machine. In the literature, this problem is usually referred to asthe Common Cycle Economic Lot Scheduling Problem. We extend thelatter to allow the production rates to be controllable at the beginningof as well as during each production run of a product. Also, we assumethat unsatisfied demand is completely backordered. The objective is todetermine the optimal schedule that satisfies the demand for all theproducts and that realizes the minimum average setup, inventoryholding and backlog cost per unit time. Comparison with previousresults (when production rates are fixed) reveals that averagecosts can be reduced up to 66% by allowing controllable productionrates.
This paper presents an approach based on idle time windows (ITWs) and particle swarm optimization (PSO) algorithm to solve dynamic scheduling of multi-task for hybrid flow-shop. The idea of ITW is introduced, then the dynamic updating rules of the sets of ITWs are explained in detail. With the sets of ITWs of machines as constraints, the mathematical model is presented for dynamic scheduling of multi-task for hybrid flow-shop. The PSO algorithm is proposed in order to solve this problem. The results of simulation indicate that this approach satisfies the demand of dynamic scheduling of multi-task.
The economic lot scheduling problem (ELSP) is the challenge of accommodating several products to be produced on a single machine in a cyclical pattern. A solution involves determining the repetitive production schedule for N products with a goal of minimizing the total of setup and holding costs. We develop the genetic lot scheduling (GLS) procedure. This method combines an extended solution structure with a new item scheduling approach, allowing a greater number of potential schedules to be considered while being the first to explicitly state the assignment of products to periods as part of the solution structure. We maintain efficient solution feasibility determination, a problematic part of ELSP solution generation and a weakness of several other methods, by employing simple but effective sequencing rules that create “nested” schedules. We create a binary chromosomal representation of the new problem formulation and utilize a genetic algorithm to efficiently search for low cost ELSP solutions. The procedure is applied to a benchmark problem suite from the literature, including Bomberger’s stamping problem [E. E. Bomberger, Manage. Sci., Ser. A 12, 778–784 (1966; Zbl 0139.13606)], a problem that has been under investigation since the mid 1960’s. The genetic lot scheduling procedure produces impressive results, including the best solutions obtained to date on some problems.
This paper deals with production scheduling involving energy constraints, typically electrical energy. We start by an industrial case-study for which we propose a two-step integer/constraint programming method. From the industrial problem we derive a generic problem, the Energy Scheduling Problem (EnSP). We propose an extension of specific resource constraint propagation techniques to efficiently prune the search space for EnSP solving. We also present a branching scheme to solve the problem via tree search. Finally, computational results are provided.
This paper surveys the current research literature on the stochastic lot scheduling problem which deals with scheduling production of multiple products with random demand on a single facility with limited production capacity and significant change-overs between products. The deterministic version of this problem has received significant coverage in the literature; however, the stochastic problem has been addressed only recently. Furthermore, a range of distinctly different analytical methods have been applied to this problem. This paper provides a unifying framework for discussing these approaches and offers some explanation and clarification of the different analytical methods for this problem. After discussing some of the modeling and managerial implications of this problem, a detailed review of both continuous and discrete time control strategies is given, and areas for further research are outlined.
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