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A dynamic programming approach for solving the economic lot scheduling problem with batch shipments
... Of late Luo et al. (2016) have utilised this approach for deriving the optimal maintenance schedule for Open Source software. Beck and Glock (2018) have used the dynamic programming approach to solve the economic lot scheduling problem and have further improved the Bomberger's method. Mandal and Venkataraman (2019) have used dynamic programming approach to determine the ordering policy and pricing policy for seasonal perishable products. ...
This paper provides a survey of literature reviews in the area of lot sizing. Its intention is to show which streams of research emerged from Harris' seminal lot size model, and which major achievements have been accomplished in the respective areas. We first develop the methodology of this review and then descriptively analyze the sample. Subsequently, a content-related classification scheme for lot sizing models is developed, and the reviews contained in our sample are discussed in light of this classification scheme. Our analysis shows that various extensions of Harris' lot size model were developed over the years, such as lot sizing models that include multi-stage inventory systems, incentives, or productivity issues. The aims of our tertiary study are the following: firstly, it helps primary researchers to position their own work in the literature, to reproduce the development of different types of lot sizing problems, and to find starting points if they intend to work in a new research direction. Secondly, the study identifies several topics that offer opportunities for future secondary research.
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.
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.
This paper considers the problem of a vendor (manufacturer) supplying a product to a buyer (customer). The vendor manufactures the product in batches at a finite rate and ships the output to the buyer. The buyer then consumes the product at a fixed rate. The objective is to minimize the mean total cost per unit time of manufacturing set-up, stock transfer and stock holding. Previously published work has concentrated on finding optimal solutions from within given classes of policy. We derive the structure of the globally-optimal solution, set out an algorithm for obtaining it and illustrate the process with two numerical examples.
The article formulates the well-known economic lot scheduling problem (ELSP) with sequence-dependent setup times and costs as a semi-Markov decision process. Using an affine approximation of the bias function, a semi-infinite linear program is obtained and a lower bound for the minimum average total cost rate is determined. The solution of this problem is directly used in a price-directed, dynamic heuristic to determine a good cyclic schedule. As the state space of the ELSP is non-trivial for the multi-product setting with setup times, the authors further illustrate how a lookahead version of the price-directed, dynamic heuristic can be used to construct and dynamically improve an approximation of the state space. Numerical results show that the resulting heuristic performs competitively with one reported in the literature.
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.
In this paper, we revisit the economic lot scheduling problem (ELSP), where a family of products is produced on a single machine, or facility, on a continual basis. Our focus is on the determination of a feasible production schedule, including the manufacturing batch size of each item. We assume that total backordering is permissible and that each of the products has a limited post-production shelf life. Several studies examining this problem have suggested a rotational common cycle approach, where each item is produced exactly once every cycle. To ensure schedule feasibility, we resort to the technique of reducing individual production rates and allow the flexibility of producing any item more than once in every cycle, in conjunction with appropriate timing adjustments. In order to solve this more generalized model, which is NP hard, we suggest a two-stage heuristic algorithm. A numerical example demonstrates our solution approach.
In this paper, economic lot scheduling problem is investigated using time-varying lot sizes approach. The process of finding the best production sequence consists of two-phase implementation of metaheuristics. In the first phase, we propose a genetic algorithm that makes use of the proposed new lower bound to arrive at the good set of production frequencies of products for ELSP without/with backorders. In the second phase, the best sequence of part production is achieved by using the above set of frequencies and employing a GA and an ant-colony algorithm. Computational experiments reveal the effectiveness of the two-phase approach over the conventional single-phase approach.
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.
In this paper, a method is given for determining the optimum production quantity for a two-stage production system. The method assumes that a lot size is manufactured through two production stages with only one set-up at each stage. A production lot is manufactured in a number of sub-batches of sizes which reduce the total manufacturing cycle time of a production lot. The production quantity is considered `optimum' when the sum of all the costs is minimized.
We show that the Economic Lot Schedule Problem (ELSP) is NP-hard in the strong sense under General Cyclic Schedules (GSC), Zero-Inventory Cyclic Schedules (ZICS), Time-Invariant Cyclic Schedules (TICS), Lot-Invariant Cyclic Schedules (LICS), and Basic Period Cyclic Schedules (BPCS).
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.
This paper presents a model which treats the manufacturing cycle time as a function of the lot size in a multi-stage production system. Using this functional relationship to determine the magnitude of the work-in-process inventory, a model is developed to calculate the economic production quantity (EPQ). The model assumes that a uniform lot size is manufactured through several operations, with only one set-up at each stage, and that transportation of sub-batches allows an overlap between operations to reduce the manufacturing cycle time. Constant fixed costs per lot, linear inventory holding costs and a constant and continuous demand of finished products are assumed over an infinite horizon. The lot size is considered "economic" when the sum of the fixed costs per lot and the inventory holding costs of both the work-in-process and finished product inventories is minimized. The model is a valid alternative to the conventional production lot size (ELQ) model which only accounts for the finished product inventory. A cost sensitivity analysis reveals the large potential savings from using the suggested EPQ model instead of the conventional ELQ model in multi-stage production systems.
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.
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 describes a model for a multi-stage production/inventory system in which a uniform lot size is produced through all stages with a single setup and without interruption at each stage. Partial lots, called batches, may be transported to the next stage upon completion. The number of the unequal sized batches may differ across stages. Considering setup costs, inventory holding costs, and transportation costs, an optimization method is developed to determine the economic lot size and the optimal batch sizes for each stage. The method is illustrated by a computational example and further numerical simulations.
An Extended Basic Period Approach of the ELSP
- S E Elmaghraby
Elmaghraby, S.E. (1977) An Extended Basic Period Approach of the ELSP. Report No. 115