Economic Lot Scheduling Problem Research Articles

Integration of power energy aspects into the Economic Lot Scheduling Problem

Beck et al. [2019. Integration of energy aspects into the economic lot scheduling problem. International Journal of Production Economics 209, 399–410] extended the Economic Lot Scheduling Problem (ELSP) to account for energy costs as well as tool change and inventory holding costs. In particular, the authors considered 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. This note extends the model proposed by Beck et al. (2019) in two ways: it 1) considers variable production rates and 2) includes power-demand costs, i.e. the energy cost component that depends on the maximum power demand required, thus taking account of a more realistic representation of energy costs in the model.The resulting problem is solved using the common cycle policy, and a numerical experiment is performed to investigate the behaviour of the proposed model. The experiment illustrates that the modified model leads to significant cost savings as compared to the traditional ELSP or the model proposed by Beck et al. (2019), which illustrates the potential usefulness of the proposed approach in practice for reducing energy costs.

Hybrid bi-objective economic lot scheduling problem with feasible production plan equipped with an efficient adjunct search technique

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.

A dynamic programming approach for solving the economic lot scheduling problem with batch shipments

This note investigates the economic lot scheduling problem (ELSP) with batch shipments. It first modifies an existing formulation of the ELSP to account both for the cases of equal-sized and geometrically increasing batch shipments, and it then adapts the popular dynamic programming approach of Bomberger to the new planning situation. In addition, the paper specifies some steps of Bomberger's solution procedure that had been formulated imprecisely in the original publication of the author. The paper compares the solution approach proposed in this note to the popular methods of Hanssmann as well as Haessler and Hogue in a numerical experiment and highlights the influence of the batch shipments on the relative performance of the solution procedures. Our results show that the proposed modification reduces the performance disadvantage of Bomberger's basic period approach, which may be interesting especially for practitioners that are interested in an easy-to-apply procedure for solving the ELSP in practice. Our changes to Bomberger's solution procedure support finding the lowest total cost solution that had not always been obtained in earlier publications.

A dynamic programming approach for solving the economic lot scheduling problem with batch shipments

This note investigates the economic lot scheduling problem (ELSP) with batch shipments. It first modifies an existing formulation of the ELSP to account both for the cases of equal-sized and geometrically increasing batch shipments, and it then adapts the popular dynamic programming approach of Bomberger to the new planning situation. In addition, the paper specifies some steps of Bomberger's solution procedure that had been formulated imprecisely in the original publication of the author. The paper compares the solution approach proposed in this note to the popular methods of Hanssmann as well as Haessler and Hogue in a numerical experiment and highlights the influence of the batch shipments on the relative performance of the solution procedures. Our results show that the proposed modification reduces the performance disadvantage of Bomberger's basic period approach, which may be interesting especially for practitioners that are interested in an easy-to-apply procedure for solving the ELSP in practice. Our changes to Bomberger's solution procedure support finding the lowest total cost solution that had not always been obtained in earlier publications.

Matheuristics for the lot sizing problem with back-ordering, setup carry-overs, and non-identical machines

Abstract In this study, the capacitated lot-sizing problem (CLSP) with back-ordering, setup carry-overs between periods, and non-identical parallel machines (CLSP-BOPM) is considered. The problem is one of the most general extensions of the well-known economic lot scheduling problems (ELSPs). Three matheuristics are designed and implemented starting from the ideas of variable neighborhood local search, local branching, and feasibility pump (FP), adapted and improved by considering the specific characteristics of the problem. Algorithms are tested on a set of medium to large problem instances. The FP algorithm outperforms all other algorithms and two different mixed-integer programming solvers as it requires a shorter computational time. To test the robustness of the algorithm, tests on three particular cases of the general problem, belonging to the family of discrete ELSPs, have been performed. Results from the proposed solver and a known specific state-of-the-art algorithm demonstrate substantial improvements.

Integration of energy aspects into the economic lot scheduling problem

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.

Planning of multi-product pipelines by economic lot scheduling models

In chemical and petroleum industry pipelines are one of the most important means of transportation. However, flexibility of pipeline transport systems is limited by many restrictions. Therefore, the planning of pipeline operations is a crucial part of logistics management in these industries. A particularly challenging problem is the pipeline scheduling which is concerned with finding the sequences, times, and sizes of batch injections in pipeline systems. This paper specifically studies the underlying core scheduling problem by assuming a simple multi-product pipeline system. It is shown that finding a sequence of batches which minimizes stock holding and setup costs in the long run is an NP-hard scheduling problem, namely a variant of the economic lot scheduling problem (ELSP) with additional constraints. Therefore, a powerful heuristic for the sequence-dependent ELSP is adapted and extended to meet the requirements of the outlined pipeline scheduling problem. The application of the heuristic is illustrated by case studies from chemical and petroleum industry.

Integrated multiproduct batch production and truck shipment scheduling under different shipping policies

The classical economic lot-scheduling problem (ELSP) involves the batch sizing and scheduling of multiple products in a single facility under deterministic conditions over an infinite planning horizon. It is assumed that the products are delivered to customers at continuous rates. In today's supply chains, however, often employing complex delivery networks, the finished goods are usually transported in discrete lots to succeeding stages along the distribution process, in order to take advantage of economies of scale in transportation. In this paper, we formulate mathematical models that attempt to integrate the production lot scheduling problem with outbound shipment decisions. The optimization objective is to minimize the total relevant costs of a manufacturer, which distributes a set of products to multiple retailers. In making the production/distribution decisions, the common cycle approach is employed to solve the ELSP, for simplicity. Two different shipping scenarios, i.e. periodic full truckload (TL) peddling shipments and less than truckload (LTL) direct shipping, are integrated with and linked to the multiproduct batching decisions. We consider these two shipment policies for both coordinated and uncoordinated scenarios. The resulting mixed-integer, non-linear programming models (MINLPs) are solved by the BONMIN solver. Finally, a set of numerical examples illustrate and evaluate the relative efficacies of these policies.

Integrated Multiproduct Batch Production and Truck Shipment Scheduling under Different Shipping Policies

The classical economic lot-scheduling problem (ELSP) involves the batch sizing and scheduling of multiple products in a single facility under deterministic conditions over an infinite planning horizon. It is assumed that the products are delivered to customers at continuous rates. In today’s supply chains, however, often employing complex delivery networks, the finished goods are usually transported in discrete lots to succeeding stages along the distribution process, in order to take advantage of economies of scale in transportation. In this paper, we formulate mathematical models that attempt to integrate the production lot scheduling problem with outbound shipment decisions. The optimization objective is to minimize the total relevant costs of a manufacturer, which distributes a set of products to multiple retailers. In making the production/distribution decisions, the common cycle approach is employed to solve the ELSP, for simplicity. Two different shipping scenarios, i.e. periodic full truckload (TL) peddling shipments and less than truckload (LTL) direct shipping, are integrated with and linked to the multiproduct batching decisions. We consider these two shipment policies for both coordinated and uncoordinated scenarios. The resulting mixed-integer, non-linear programming models (MINLPs) are solved by the BONMIN solver. Finally, a set of numerical examples illustrate and evaluate the relative efficacies of these policies.

The impact of batch shipments on the Economic Lot Scheduling Problem

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.

Economic Lot Scheduling Problem with two Imperfect Key Modules

This paper considers an Economic Lot Scheduling Problem (ELSP) with two imperfect Key Modules (KMs), in which extending similar work on the Economic Production Quantity scope. It is assumed that each KM has its own probability to shift from in-control state to out-of-control state. When the production shifts to out-of-control state, it starts to produce defected items. The problem in this paper is defined as finding the cycle times for several items under ELSP with two KMs context in order to minimize the total cost covering holding cost, setup cost and quality-related cost. A series of modelling was done in order to develop the formula and algorithms to solve the cycle time T under the Independent Solution (IS) and Common Cycle (CC) approach. A numerical illustration is given based on the modified Bomberger (1966) stamping problem.

A price-directed heuristic for the economic lot scheduling problem

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.

An Algorithm for Economic Lot Scheduling Problem

The Economic Lot Scheduling Problem (ELSP) has been well-researched for over half a century. This paper, by using extended basic period approach, offers a new algorithm which differs from previous algorithms in that every item is of different importance. Such an item, whose daily cost is very high, is considered to be of greater importance and is called “key item”; and such an item, whose total production time per times is long, is considered to be of greater importance and is called “obstacle item”. By making key items’ multipliers to be of good compatibility and loading obstacle items preferentially, new algorithm can offer good solution.

A Unifying Approximate Dynamic Programming Model for the Economic Lot Scheduling Problem

We formulate 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, we obtain a semi-infinite linear program determining a lower bound for the minimum average cost rate. Under a very mild condition, we can reduce this problem to a relatively small convex quadratically constrained linear problem by exploiting the structure of the objective function and the state space. This problem is equivalent to the lower bound problem derived by Dobson [Dobson G (1992) The cyclic lot scheduling problem with sequence-dependent setups. Oper. Res. 40:736–749] and reduces to the well-known lower bound problem introduced in Bomberger [Bomberger EE (1966) A dynamic programming approach to a lot size scheduling problem. Management Sci. 12:778–784] for sequence-dependent setups. We thus provide a framework that unifies previous work, and opens new paths for future research on tighter lower bounds and dynamic heuristics.

Economic Order Quantities in production: From Harris to Economic Lot Scheduling Problems

This article provides a short historical overview from Harris and his Economic Order Quantity (EOQ) formula to the Economic Lot Scheduling Problem (ELSP). The aim is to describe the development of the ELSP field from the EOQ formula to the advanced methods of today in a manner that suits master and graduate students. The article shows the complexities, difficulties and possibilities of scheduling and producing several different items in a single production facility with constrained capacity. The items have different demand, cost, operation time and set-up time. Set-up time consumes capacity and makes the scheduling more complicated. Idle time makes the scheduling easier but is bad from a practical point of view since it creates unnecessary costs due to low utilisation of the facility. A heuristic solution method is used on a small numerical example to illustrate different solution approaches. The solution method creates a detailed schedule and estimates the correct set-up and inventory holding cost even if the facility works close to its capacity.

A solution procedure for Economic Lot Scheduling Problems even in high utilisation facilities

Economic lot scheduling problem (ELSP) handles the problem of deciding what order quantities to use when different products/items are produced in the same capacity constrained production facility. It has previously been shown, and it is shown in this article, that it is possible to find a feasible solution fulfilling true feasibility conditions. However, if the utilisation of the production facility is high the production often has to start before the inventory reaches zero to avoid future shortages. Such ‘early starts’ creates an extra inventory holding cost that the traditional approximation for the inventory holding cost does not account for. This article presents an iterative solution procedure that computes the true inventory holding cost and minimises the total costs. Contrary to previous solution procedures, this procedure requires that the production is scheduled in detail. The heuristic solution procedure is illustrated by a numerical example, it is programmed in MATLAB and variants of the problem are presented.

Recent research trend of economic‐lot scheduling problems

PurposeThis research note aims to present a summary of research concerning economic‐lot scheduling problem (ELSP).Design/methodology/approachThe 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.FindingsFive research themes are identified and insights for future studies are reported at the end of this paper.Research limitations/implicationsThe 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/valueELSP 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.

An economic lot and delivery scheduling problem with the fuzzy shelf life in a flexible job shop with unrelated parallel machines

Article history: Received 25 March 2012 Accepted April 3 2012 Available online 5 April 2012 This paper considers an economic lot and delivery scheduling problem (ELDSP) in a fuzzy environment with the fuzzy shelf life for each product. This problem is formulated in a flexible job shop with unrelated parallel machines, when the planning horizon is finite and it determines lot sizing, scheduling and sequencing, simultaneously. The proposed model of this paper is based on the basic period (BP) approach. In this paper, a mixed-integer nonlinear programming (MINLP) model is presented and then it is changed into two models in the fuzzy shelf life. The main model is dependent to the multiple basic periods and it is difficult to solve the resulted proposed model for large-scale problems in reasonable amount of time; thus, an efficient heuristic method is proposed to solve the problem. The performance of the proposed model is demonstrated using some numerical examples. © 2012 Growing Science Ltd. All rights reserved

Multi-product lot scheduling with backordering and shelf-life constraints

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.

The economic lot scheduling problem with deteriorating items and shortage: an imperialist competitive algorithm

This paper addresses an economic lot scheduling problem (ELSP) for manufacturing environments regarding slack costs and deteriorating items using the extended basic period approach under Power-of-Two (PoT) policy. The purpose of this research is to determine an optimal batch size for a product and minimizing total related costs to such a problem. The cost function consists of three components, namely, setup cost, holding cost includes deteriorating factor, and slack cost. The ELSP is concerned with the scheduling decision of n items and lot sizing. Avoiding schedule interference is the main problem in ELSP. The used PoT policy ensures that the replenishment cycle of each item to be integer and this task reduces potential schedule interferences. Since the ELSP is shown as an NP-hard problem, an imperialist competitive algorithm is employed to provide good solutions within reasonable computational times. Computational results show that the proposed approach can efficiently solve such complicated problems.