Economic lot and supply scheduling problem: a time-varying lot sizes approach

We study the economic lot and supply scheduling problem (ELSSP) that arises in the distribution and manufacturing industries. The ELSSP involves the simultaneous scheduling of end-item production and inbound transportation of input materials over an infinite time horizon to minimise the average costs of inventory, production set-up and transportation. We present a new methodology based on a time-varying lot sizes approach for the ELSSP. We also provide computational experiments showing that the developed algorithm outperforms the existing heuristic for improved integrated scheduling.     

A time-varying lot sizes approach for the economic lot scheduling problem with returns

We consider the economic lot scheduling problem with returns by assuming that each item is returned by a constant rate of demand. The goal is to find production frequencies, production sequences, production times, as well as idle times for several items subject to returns at a single facility. We propose a heu ristic algorithm based on a time-varying (TV) lot sizes approach. The problem is decomposed into two distinct portions: in the first, we find a combinatorial part (production frequencies and sequences) and in the second, we determine a continuous part (production and idle times) in a specific production sequence. We report computational results that show that, in many cases, the proposed TV lot sizes approach with consideration of returns yields a relatively minor error.     

On the feasibility of sequence-dependent economic lot scheduling problem

Most of the literature dealing with the determination of cyclic part input sequences in a flexible flow system is restricted in that it only searches for input sequences that are permutations of the minimal part set (MPS). This study is unique in that it investigates input sequences generated by integer programming (IP) formulations that balance or unbalance machine workloads to help maximize overall machine utilization (Stecke 1992). Also, this study integrates the input sequence determination decision with the part mix ratio determination, within the overall framework of a flexible approach to FMS operation over time. A simulation model of a flexible flow system was designed to study the effects on overall machine utilizations caused by utilizing alternative part mix ratios to help determine input sequences. The procedures used to determine the part mix ratios include IP formulations and those that are generated randomly, including the MPS mix ratios. Three different experimental settings are used to test these effects as well as (I) the robustness of the part input sequences that can be derived from the IP generated mix ratios, and (2) the relative importance of the part mix ratio decision in relation to the part input sequence determination. A new FMS physical design that can also be easily modelled to capture look-ahead capability proved to be simple and effective. Several significant conclusions regarding part mix ratios, pan input sequences, and look-ahead capability are revealed. These include: (1) the determination of the part mix ratios proved to be more significant in improving FMS performance than the determination of part input sequences; (2) the robust nature of the IP formulations was demonstrated; and (3) look-ahead capability provides equally high overall machine utilizations at lower levels of work-in-process. Future research areas are presented that would help validate and extend the observations found in this study.     

The economic lot scheduling problem: a survey

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.     

The economic lot scheduling problem: a content analysis

The paper at hand addresses the Economic Lot Scheduling Problem (ELSP), which is concerned with finding a feasible and cost-minimal production schedule for multiple items produced in lots on a single machine. The ELSP started to attract the attention of researchers in the 1950s, where the focus was primarily on the development of simple heuristics for solving the problem. Over the subsequent decades, this topic has frequently been addressed in the literature, with the subject of research being the development of new scheduling policies or solution procedures or extensions of the scope of the original model. To date, a large number of journal articles has been published on the ELSP and its model variants. To identify key research themes, publication patterns and opportunities for future research, the paper at hand applies a content analysis to a sample of 242 papers published on the Economic Lot Scheduling Problem. The results of the content analysis indicate that prior research on this topic had a strong focus on the development of solution methodologies, and that several aspects that are directly connected to lot sizing and scheduling have not attracted much attention in research on the ELSP yet, such as, for example, energy cost and sustainability.     

A dynamic multi-plant lot-sizing and distribution problem

In this paper, we investigate a multi-plant, production planning and distribution problem for the simultaneous optimisation of production, inventory control, demand allocation and distribution decisions. The objective of this rich problem is to satisfy the dynamic demand of customers while minimising the total cost of production, inventory and distribution. By solving the problem, we determine when the production needs to occur, how much has to be produced in each of the plants, how much has to be stored in each of the warehouses and how much needs to be delivered to each customer in each period. On a large real data-set inspired by a case obtained from an industrial partner, we show that the proposed integration is highly effective. Moreover, we study several trade-offs in a detailed sensitivity analysis. Our analyses indicate that the proposed scenarios give the company competitive advantage in terms of reduced total logistics cost, and also highlight more possibilities that become available taking advantage of an integrated approach towards logistics planning. These abundant opportunities are to be synergised and exploited in an interconnected open global logistics system.     

Solving the integrated lot-sizing and job-shop scheduling problem

Production planning and scheduling are usually performed in a sequential manner, thus generating unfeasibility conflicts. Moreover, solving these problems in complex manufacturing systems (with several products sharing different resources) is very challenging in production management. This paper addresses the solution of multi-item multi-period multi-resource single-level lot-sizing and scheduling problems in general manufacturing systems with job-shop configurations. The mathematical formulation is a generalisation of the one used for the Capacitated Lot-Sizing Problem, including detailed capacity constraints for a fixed sequence of operations. The solution method combines a Lagrangian heuristic, determining a feasible production plan for a fixed sequence of operations, with a sequence improvement method which iteratively feeds the heuristic. Numerical results demonstrate that this approach is efficient and more appropriate than a standard solver for solving complex problems, regarding solution quality and computational requirements.     

On measuring company performance within a supply chain

Emerging research strengthens the connection between supply chain performance and a company's financial performance (D’Avanzo, R., Von Lewinski, H. and Van Wassenhove, L. N., 2003. The link between supply chain and financial performance. Supply Chain Management Review, November/December, 40–47). The focus on integrating functional internal processes has expanded to include the need for integrating these with external processes of business partners (Edwards, P., Peters, M. and Sharman, G., 2001. The effectiveness of information systems in supporting the extended supply chain. Journal of Business Logistics, 22(1), 1–27). This need for enterprise efficiency is compelling companies to review, to identify, and to adopt supply chain initiatives. This research investigates the use of common measurement metrics in an attempt to determine which one(s) are most useful for measuring performance as companies implement SCM practices. For firms that were engaged in SCM we found inventory and cycle time to be the most significant metrics.     

A dynamic model for serial supply chain with periodic delivery policy

A three-echelon, dynamic lot-sizing model is presented for computing the parameters of a serial supply chain, which consists of integrated material replenishment, production at a capacity constraint, and outbound dispatching with a periodic delivery policy. The model is applicable in the general context of a three-echelon model with capacity constraint at the middle echelon of the serial supply chain which was not considered in most of the literature. This paper addresses a number of structural properties of the model and proposes a polynomial-time algorithm for deriving the optimal solution of minimising the total system costs over the planning horizon. Examples are provided to describe the algorithm.     

Dynamic co-ordinated scheduling in the supply chain under a process modernisation

A new dynamic model for co-ordinated scheduling of interlinked processes in a supply chain under a process modernisation is presented. Such a problem is vital in many of the supply chain management domains. This problem is represented as a special case of the scheduling problem with dynamically distributed jobs. The peculiarity of the proposed approach is the dynamic interpretation of scheduling based on a natural dynamic decomposition of the problem and its solution with the help of a modified form of continuous maximum principle blended with combinatorial optimisation. The special properties of the developed model allow using methods of discrete optimisation for the schedule calculation. Optimality and sufficiency conditions as well as structural properties of the model are investigated. Advantages and limitations of the proposed approach are discussed. With the developed approach, an explicit inclusion of a process modernisation in the SC co-ordinated decisions for a wide ranges of possible applications as well as a dynamic model and a tractable algorithm for optimal discrete time scheduling on the basis of continuous maximum principle have been obtained.     

Asynchronous teams for joint lot-sizing and scheduling problem in flow shops

The integrated production scheduling and lot-sizing problem in a flow shop environment consists of establishing production lot sizes and allocating machines to process them within a planning horizon in a production line with machines arranged in series. The problem considers that demands must be met without backlogging, the capacity of the machines must be respected, and machine setups are sequence-dependent and preserved between periods of the planning horizon. The objective is to determine a production schedule to minimise the setup, production and inventory costs. A mathematical model from the literature is presented, as well as procedures for obtaining feasible solutions. However, some of the procedures have difficulty in obtaining feasible solutions for large-sized problem instances. In addition, we address the problem using different versions of the Asynchronous Team (A-Team) approach. The procedures were compared with literature heuristics based on Mixed Integer Programming. The proposed A-Team procedures outperformed the literature heuristics, especially for large instances. The developed methodologies and the results obtained are presented.     

Evaluating strategic issues in supply chain scheduling using game theory

This paper deals with the problem of scheduling and batch delivery of orders in a supply chain (SC) including a supplier, a manufacturer and a final customer. First, the individual decisions of partners in the SC and their behaviours are analysed through mathematical models. Second, the best policy is obtained assuming that the SC is vertically integrated and the partners fully cooperate (this is called SC scheduling in the relevant literature). Since this strategy is usually against a partner, it might not be implemented in practice as the authors have observed this condition in real world. Hence, a fair sharing mechanism based on game theory concepts is also introduced which can motivate the partners to cooperate and adopt the best policy of the SC. The numerical examples show the superiority of integrated decisions over independent actions and also the importance of the sharing mechanism.     

A hybrid VNS-HS algorithm for a supply chain scheduling problem with deteriorating jobs

This paper investigates a coordinated scheduling problem in a two stage supply chain where parallel-batching machine, deteriorating jobs and transportation coordination are considered simultaneously. During the production stage, jobs are processed by suppliers and there exists one parallel-batching machine in each supplier. The actual processing time of a job depends on its starting time and normal processing time. The normal processing time of a batch is equal to the largest normal processing time among all jobs in its batch. During the transportation stage, the jobs are then delivered to the manufacturer. Since suppliers are distributed in different locations, the transportation time between each supplier and the manufacturer is different. Based on some structural properties of the studied problem, an optimal algorithm for minimising makespan on a single supplier is presented. This supply chain scheduling problem is proved to be NP-hard, and a hybrid VNS-HS algorithm combining variable neighbourhood search (VNS) with harmony search (HS) is proposed to find a good solution in reasonable time. Finally, some computational experiments are conducted and the results demonstrate the effectiveness and efficiency of the proposed VNS-HS.     

Synchronization,cross-docking,and decoupling in supply chain networks

At any distribution centre (DC), the decision of whether to synchronise inbound and outbound flows for cross-docking, or to decouple these flows by maintaining inventory, has a significant impact on supply chain performance. Key drivers of this decision, in turn, are the sizes of the discrete lots that comprise the flows. Thus, we formulate an original optimisation model that determines order lot-sizing decisions to minimise, for given constant arc flows, the sum of ordering cost and pipeline inventory cost on arcs and buffer inventory at DCs. The model employs an average throughput as a surrogate to estimate buffer inventory at facilities at which synchronisation is not economical and therefore serves to decouple inbound and outbound flows. Perfect lot-for-lot matching of shipments would impose very restrictive constraints on supply chain operations, but equality of average throughput indicates an innovative, relaxed mode of synchronisation. This mode is practicable for cross-docking by means of bulk-breaking or consolidation of shipments. A heuristic approach based on the Lagrangian relaxation and subgradient optimisation is developed for the non-linear mixed-general integer optimisation model, which is illustrated by numerical examples and tested using a benchmark data set.     

A constrained EPSAC approach to inventory control for a benchmark supply chain system

The design of an appropriate inventory control policy for a supply chain (SC) plays an essential role in tempering inventory instability and bullwhip effect. Several constraints are commonly encountered in actual operations so managers are required to take these physical restrictions into account when designing the inventory control policy. Model predictive control (MPC) appears as a promising solution to this issue, due to its capability of finding optimal control actions for a constrained SC system. Therefore, the inventory control problem for a benchmark SC is solved using the extended prediction self-adaptive control approach to MPC. To extend methodologies in our previous work, the control framework relies on generic process model and incorporates the physical constraints arising from practical operations to form the general constrained optimisation problems. The managers can choose from decentralised and centralised control structures according to specific informational and organisational factors of their SCs. The proposed control schemes in this study may be appropriate for industrial practice because the designed policy can bring a reduction of over 30% in operating cost and a significant increase of customer satisfaction level compared with that of the conventional policy.     

A spread-sheet model for efficient production and scheduling of a manufacturing line/cell

In this paper we develop an efficient spread-sheet production planning/scheduling model for a resource-constraint production line or a manufacturing cell that produces several products but one at a time with significant changeover time and changeover cost. There are also management and physical constraints related to the operating hours, production capacity and amount of inventory allowed. The production line/cell supplies several products to customers who pull the products according to their own operating policy (working hours) that may be different from manufacture's operating hours. We also show several real-world applications and highlight the benefits and merits of the model.     

Dynamic co-ordinated scheduling in the supply chain considering flexible routes

In Supply chain (SC) environments, schedules inevitably experience various unexpected disruptions. In these cases, rescheduling is essential to minimise the negative impact on the performance of the system. In this study, a hybrid rescheduling technique is developed for solving coordinated manufacturing tasks scheduling problems with due date changes and machine breakdowns. According to the dynamic features of this problem, a strategy combined with event and periodic driven methods is proposed to improve the stability and robustness of manufacturing performance in a coordinated SC. Moreover, an application case is introduced to test and evaluate the effect of different initialisations in two types of disruption scenarios. The experimental results show that the proposed rescheduling technique has good effectiveness and efficiency in the coordinated manufacturing environment.     

A parallel machine lot-sizing and scheduling problem with a secondary resource and cumulative demand

We investigate a parallel machine multi-item lot-sizing and scheduling problem with a secondary resource, in which demands are given for the entire planning horizon rather than for every single period. All-or-nothing assumption of the discrete lot-sizing and scheduling problem is valid so that a machine is either idle or works at full capacity in a period. The objective is to minimise the number of setups and teardowns. We prove that the problem is NP-hard and present two equivalent formulations. We show some properties of the optimal objective value, give optimality conditions and suggest a heuristic algorithm. We discuss and formulate two possible extensions related to real-life applications. Finally, we carry out computational experiments to compare the two formulations, to determine the effect of our proposed modeling improvements on solution performance, and to test the quality of our heuristic.     

MIP-based fix-and-optimise algorithms for the parallel machine capacitated lot-sizing and scheduling problem

This paper examines the capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup times, time windows, machine eligibility and preference constraints. Such a problem frequently arises in the semiconductor manufacturing industry by which this paper is motivated. A mixed integer programming (MIP) model is constructed for the problem. Two MIP-based fix-and-optimise algorithms are proposed in which the binary decision variables associated with the assignment of machines are first fixed using the randomised least flexible machine (RLFM) rule and the rest of the decision variables are settled by an MIP solver. Extensive experiments show that the proposed algorithms outperform the state-of-the-art MIP-based fix-and-optimise algorithms in the literature, especially for instances with high machine flexibility and high demand variation.