Economic Lot Scheduling Problem Research Articles

Integrative Cycle Scheduling Approach for a Capacitated Flexible Assembly System*

ABSTRACTThis study revisits the traditional single stage, multi‐item, capacitated lot‐sizing problem (CLSP) with a new integrative focus on problem structuring. Unlike past research, we develop integrative cycle scheduling approaches which simultaneously address lot‐sizing, capacity, and sequencing issues. Our purposes are to (1) explore the effect of sequencing on inventory levels, (2) examine the problem of infeasibility in the economic lot scheduling problem (ELSP), and (3) provide a simple methodology of generating low‐cost cycle schedules in an environment with discrete shipping, dynamic demands, limited capacity, zero setup cost, and sequence‐independent setup times. Our procedures are compared to benchmark cycle scheduling approaches in terms of both inventory cost and computation time under different demand scenarios, using the operating data from a flexible assembly system (FAS) at the Ford Motor Company's Sandusky, Ohio plant.

Single facility, multi-item lot sizing under just-in-time and “cyclic scheduling for improvement”

In recent years some of the models for Economic Lot Scheduling Problem (ELSP) have been extended to incorporate Just-in-Time (JIT) concepts, by allowing setup costs, setup times and capacity, to be decision variables. All these models result in some forms of cyclic schedules. Hall (1988) proposes “cyclic scheduling for improvement” as a central theme under Just-in-Time and recommends a continual “cycle time analysis for improvement”. This paper presents expanded economic lot scheduling models based on Common Cycle Policy under the framework of “cycle time analysis for improvement”, and proposes a step-by-step procedure for such an analysis, using the various models. The procedure is illustrated with a numerical example.

Controllable production rates in a family production context

We consider a single facility dedicated to the production of a family of items where the policy used is to cycle production through the items every T units of time. This is known as the Common Cycle or Rotation Schedule and is a special case of the Economic Lot Scheduling Problem (ELSP). We consider the case in which the production rates can be reduced from known maximum rates. Moreover, we assume that production rates can be changed during the production runs. We optimally partition the items into those with high and low holding costs. The former are initially produced to meet demand while the latter are always produced at their maximum rates. Numerical examples indicate savings almost twice as large as those reported in the literature.

Economic lot scheduling of fully loaded processes with external setups

Without restricting the class of permissible schedules, we derive optimal schedules for economic lot scheduling problems that are fully loaded, have external setups, and have only two products. The fully loaded condition accurately represents certain types of bottlenecks. We show that the optimal schedule must have the Wagner-Whitin property. We also develop a measure of aggregate inventory, derive an optimal steady-state aggregate inventory policy, and provide conditions under which the aggregate inventory level of an optimal schedule must approach a steady state. By restricting the class of permissible schedules to rotation cycle schedules, we extend these results to more than two products.

Computing Optimal Lot Sizes in the Economic Lot Scheduling Problem

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 in 1987 by G. Dobson. The two algorithms together comprise a simple, plausible heuristic for the ELSP as a whole.

Coordination of replenishment activities†

SUMMARY Extensive research on the Economic Lot Scheduling Problem (ELSP), and on related topics, has produced powerful techniques originally designed to solve quite specific (coordination) problems. This paper emphasizes the omni-presence of coordination issues in multi-item inventories, characterizes them as problems of staggering and/or clustering replenishment activities or events, and shows how ELSP techniques combine to form a pertinent and fairly comprehensive methodology. A numerical example illustrates the use of one particularly powerful tool (powers of two) in stabilizing replenishment workloads.

An Extension to the Class of Easy Economic Lot Scheduling Problems

Abstract We extend known conditions under which a rotation schedule is optimal in the Economic Lot Scheduling Problem by using a tighter lower bound that explicitly considers machine capacity. We also show how these results can be used when backorders are allowed.

Solving the Economic Lot‐Scheduling Problem Using the Method of Prime Subperiods

ABSTRACTIn recent years the reported successes of Japanese production systems, particularly the just‐in‐time approach to inventory control, has caused managers to focus more of their attention on efficient decision‐making procedures for determining production schedules that minimize inventory costs. One such potential area of attention is the economic lot‐scheduling problem (ELSP), which occurs in a variety of manufacturing environments where machining operations are prevalent. The economic lot‐scheduling problem addresses the determination of lot sizes for N products with constant demand (and cycled through one machine with a given production rate) to minimize setup and inventory costs. The most successful solution approaches to the ELSP have been based on the concept of a basic period that is of sufficient length for the production of all items, even though each item might not be produced during each repetition of the basic period. This paper proposes a heuristic approach to the solution of the ELSP (referred to as the method of prime subperiods), which is an extension of the basic period approaches. The procedure is described and demonstrated via an example and then tested using a set of six example problems previously employed in the literature related to the ELSP. The results indicate as good or superior performance by the proposed method of prime subperiods.

Economic Lot Scheduling for Two-Product Problem

Abstract In this paper we propose an algorithm for the two-product single machine Economic Lot Scheduling Problem (ELSP). Past research on this problem has relied heavily on the assumption that both products are produced cyclically. In particular Boctor's algorithm provides optimal solution to the two-product problem under such assumption. We first simplify Boctor's algorithm and then propose an algorithm which allows for the unequal cycle time for the more frequently manufactured product. We show that the cost corresponding to our solution is either less than 1.015 times the cost obtained from the Independent Solution, which is a lower bound of the optimal solution, or is better than that obtained by Boctor's algorithm. An example is used to show that the difference in cost can be as much as 24%.

The Optimality of the ‘Zero-Switch’ Rule for a Class of Economic Lot-Scheduling Problems

The economic lot-scheduling problem for the single-machine, n-item scheduling problem has received attention in a number of journals. One approach is to define a sequence (called the fundamental cycle) in which every item is made at least once, and then to determine the length of production runs consistent with the aggregate inventory level which will maximize the length of the cycle duration. The assumption that production is switched from one item to the next only when the inventory level of the latter reaches zero is often used in heuristic solutions to these models. This paper illustrates the conditions in which the ‘zero-switch’ rule is a necessary condition at the optimal solution for situations in which demand is continuous and production capacity equals aggregate demand.

The Optimality of the ‘Zero-Switch’ Rule for a Class of Economic Lot-Scheduling Problems

The economic lot-scheduling problem for the single-machine, n-item scheduling problem has received attention in a number of journals. One approach is to define a sequence (called the fundamental cycle) in which every item is made at least once, and then to determine the length of production runs consistent with the aggregate inventory level which will maximize the length of the cycle duration. The assumption that production is switched from one item to the next only when the inventory level of the latter reaches zero is often used in heuristic solutions to these models. This paper illustrates the conditions in which the ‘zero-switch’ rule is a necessary condition at the optimal solution for situations in which demand is continuous and production capacity equals aggregate demand.

The Optimality of the 'Zero-Switch' Rule for a Class of Economic Lot-Scheduling Problems

The Optimality of the 'Zero-Switch' Rule for a Class of Economic Lot-Scheduling Problems

The Economic Lot-Scheduling Problem: Achieving Feasibility Using Time-Varying Lot Sizes

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.

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.

The Effect of Restricting Cycle Times in the Economic Lot Scheduling Problem

Abstract The economic lot scheduling problem (ELSP) involves specifying economic cycle times for each of several products produced by a set of machines. The extensive, usually experimentally based, literature on the ELSP indicates that it may be desirable to restrict the possible choice of cycle times for each product to a small and very structured set of possible cycle times. In this paper we examine the economic impacts of such a restriction and give evidence that is highly supportive of this type of restriction; in particular, the “powers of 2” sets of possible cycle times used in practice appear to be very desirable from an economic viewpoint.