Basic Period Approach Research Articles

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.

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.

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.

Solving the Economic Lot and Inspection Scheduling Problem using the Extended Basic Period approach under Power-of-Two policy

The focus of this study is to solve the Economic Lot and Inspection Scheduling Problem (ELISP) using the Extended Basic Period (EBP) approach under Power-of-Two (PoT) policy. The objective of the ELISP is to determine an optimal cycle time and an optimal production and inspection schedule so as to minimize the total cost per unit time. Under PoT policy, we formulate a mathematical model by taking into account the constraints for both production and inspection capacities. Also, we propose a Hybrid Genetic Algorithm (HGA) which is equipped with a search algorithm that not only seeks to improve solution quality, but also assures a feasible solution for each chromosome obtained from the evolutionary processes. Our numerical experiments show that the proposed HGA effectively solves the ELISP using the EBP approach, and its solutions outperform the solutions from the ELISP using the Common Cycle approach.

Solving the economic lot scheduling problem with deteriorating items using genetic algorithms

The focus of this study is to solve the Economic Lot Scheduling Problem (ELSP) with deteriorating items using the extended basic period approach under Power-of-Two (PoT) policy. The ELSP is concerned with the lot sizing and scheduling decision of n items, and, PoT policy requires the replenishment frequency of each item to be a PoT integer. Since the conventional ELSP is shown as an NP-hard problem, we propose a hybrid genetic algorithm (HGA) that is equipped with a feasibility testing procedure, namely, Proc FT, and a binary search heuristic to efficiently solve the ELSP with deteriorating items. We use Proc FT to test the feasibility of the local optimum for the set of replenishment frequencies obtained by the evolutionary process of genetic algorithm. When the local optimum for the set of replenishment frequencies is infeasible, we employ the proposed binary search heuristic to search for a feasible solution with the minimal objective value. We use six benchmark examples to evaluate the performance of the proposed hybrid GA. Our numerical results demonstrate that the proposed hybrid GA is an efficient approach in solving the ELSP with deteriorating items. Therefore, we conclude that the proposed HGA could be a favorable decision support tool for managers in the food industry to efficiently derive their production scheduling and lot-sizing strategies for deteriorating items.

A basic period approach to the economic lot scheduling problem with shelf life considerations

Almost all the research on the economic lot scheduling problem (ELSP) considering limited shelf life of products has assumed a common cycle approach and an unrealistic assumption of possibility of deliberately reducing the production rate. In many cases, like in food processing industry where limited shelf life for products is common, changing the production rates is not allowed at all because it may result in products with poor quality. In this paper, we allow products to be produced more than once in a cycle and do not allow reducing production rates. We present a modification to the Haessler's basic period procedure to account for the shelf life. Proposed ‘branch-and-bound like’ procedure exploits these extra constraints to efficiently achieve a feasible solution. Numerical examples are presented to show that our approach outperforms common cycle approach with shelf life considerations.

The peak load minimization problem in cyclic production

The objective of this study is to determine a production schedule for a set of jobs so as to minimize the peak load for the entire planning horizon given the production duration and the cyclic frequencies of the jobs. We refer to this problem as the peak load minimization problem (PLMP). An efficient heuristic, viz. Proc. PLMP, is proposed to solve such class of problems. There are two parts for the Proc. PLMP: a greedy procedure that secures an initial production schedule and a schedule smoothing procedure that performs a local search to reduce the maximal load. Numerical experiments verify that Proc. PLMP is efficient, since its run time is of cubic order of the problem size, i.e., it is approximately an O( n 3) algorithm. A major application of Proc. PLMP is to test the feasibility of a given set of a solution for the Economic Lot Scheduling Problem using the extended basic period approach. Scope and purpose The most prominent model for cyclic production is the economic lot scheduling problem (ELSP) in which n products are produced in lots of different sizes and, thereby, require different cyclical patterns. Under the extended period approach for the ELSP, there are two major problems in its cyclic production schedules. First, feasibility test of a given set of multipliers for a specified length of the basic period is a very hard problem, and second, the basic periods are typically unevenly loaded. Cost optimization, feasibility test as well as good shop practice, require the balancing of the loads on the basic periods. This can be achieved by minimizing the maximal load, which gives rise to the peak load minimization problem (PLMP) treated here. The problem is shown more complex than NP-hard. In order to solve the PLMP, we propose an efficient heuristic, Proc. PLMP. Proc. PLMP has been tested on problems of up to n=80 products, and it runs in cubic order of the problem size. Proc. PLMP also demonstrates its successful application to solve the feasibility test problem for the ELSP.

An optimal algorithm for the basic period approach to the economic lot scheduling problem

This paper develops a global optimum solution to the Economic Lot Scheduling Problem (ELSP) using the restrictions of the basic period approach as originally formulated by Bomberger. The ELSP is a classic problem in production which involves scheduling multiple products on a single facility, with the restriction that no two products may be produced at the same time. Ideally, a manufacturer could generate a schedule which would minimize the sum of setup and holding costs, but the complexities involved have so far precluded the attainment of such an ideal. This article presents a real time solution method for practical sized problems using the basic period version of the ELSP. The authors believe this is the first global optimal algorithm for the basic period ELSP to be presented in the literature. It is anticipated that future research will extend the idea presented in this article to cover more general approaches to the ELSP.

Application of ELSP solution techniques to the deterministic robotic scheduling problem

This paper studies the flexible deterministic robotic scheduling problem (FDRSP) where one tool changer (robot) is in charge of several machining operations and overlapping tool changes are not allowed. The relationship between the FDRSP and the economic lot scheduling problem (ELSP) is explored. The most promising solution techniques for the ELSP guaranteeing feasibility in advance are modified and applied to the FDRSP. It is concluded that the basic period approach performs the best in small problems, while the rounding to powers of two approach is superior for medium to large problems.

An extension of the extended basic period approach for economic lot scheduling problems

This paper addresses the problem of choosing cyclical production patterns for several products which are produced on a common production facility. The extended basic period approach of Elmaghraby is extended by allowing more than two basic periods. The problem of dimensionality of the dynamic programming formulation is dealt with by aggregating the capacity data in different basic periods.

An Improved Extended Basic Period Procedure for Solving the Economic Lot Scheduling Problem

Abstract This paper describes an easily programmable procedure for solving the problem of determining lot sizes for n products to be produced on a single machine. The procedure is based upon the extended basic period approach of Elmagrahby. Feasible solutions are obtained by restricting the number of periods between runs for each product to the powers of 2. The effectiveness of the procedure is demonstrated by solving six problems originally solved by Fujita. Significantly better answers were found for five of the six while in one case the procedure generated a solution that was only slightly inferior.