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The stochastic economic lot scheduling problem: heavy traffic analysis of dynamic cyclic policies
, 2000
"... We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: A single server processes N customer classes, and completed units enter a finished goods inventory that services exogenous customer demand. Unsatisfied demand is backordered, and each class ..."
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We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: A single server processes N customer classes, and completed units enter a finished goods inventory that services exogenous customer demand. Unsatisfied demand is backordered, and each class has its own general service time distribution, renewal demand process, and holding and backordering cost rates. In the first problem, a setup cost is incurred when the server switches class, and the setup cost is replaced by a setup time in the second problem. In both problems we employ a longrun average cost criterion and restrict ourselves to a class of dynamic cyclic policies, where idle periods and lot sizes are statedependent, but the N classes must be served in a fixed sequence. Motivated by existing heavy traffic limit theorems, we make a time scale decomposition assumption that allows us to approximate these scheduling problems by diffusion control problems. Our analysis of the approximating setup cost problem yields a closedform dynamic lotsizing policy and a computational procedure for an idling threshold. We derive structural results and an algorithmic procedure for the setup time problem. A computational study compares the proposed policy and several alternative policies to the numerically computed optimal policy.
Some complexity results in cyclic scheduling
 Mathematical and Computer Modelling
, 1994
"... precedence constraints graph In this paper we investigate the complexity of various cyclic scheduling problems in flowshop, jobshop and other environments. We review existing results and provide proofs for two new complexity results: We show that maximizing throughput in a flexible assembly line ..."
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precedence constraints graph In this paper we investigate the complexity of various cyclic scheduling problems in flowshop, jobshop and other environments. We review existing results and provide proofs for two new complexity results: We show that maximizing throughput in a flexible assembly line is NPhard, and in the process we give a polynomial transformation of generic makespan minimization problems in static scheduling to cycle time minimization in cyclic scheduling problems. Secondly, we show that when we try to schedule a single job type in a cyclic, reentrant flow shop, even if we are given the sequence of operations on each machine, it is still NPhard to figure out how to place the operations onto cycles of a given length so as to minimize flow time (or, equivalently, work in process). This paper can also be viewed as a classification of cyclic scheduling research from the perspective of computational complexity. 1
A unifying approximate dynamic programming model
, 2008
"... for the economic lot scheduling problem ..."
On the Economic Lot Scheduling Problem with Fuzzy Demands
"... Abstract⎯In this paper, we investigate the economic lot scheduling problem (ELSP) with fuzzy demands. We assume that the demand for each product i can be approximated using some triangular membership functions. In this study, we solve the fuzzy ELSP using two basic solution approaches, namely, the I ..."
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Abstract⎯In this paper, we investigate the economic lot scheduling problem (ELSP) with fuzzy demands. We assume that the demand for each product i can be approximated using some triangular membership functions. In this study, we solve the fuzzy ELSP using two basic solution approaches, namely, the Independent Solution (IS) and the Common Cycle (CC) approach. For both approaches, we derive the optimal fuzzy replenishment cycles and secure closedform formula for their crisp figures in fuzzy sense, respectively. Also, we derive the conditions that assert the CC approach to secure the optimal solution for the fuzzy ELSP in many realistic situations. For the cases that deviate from those optimalsituations, we give an upper bound for the maximum error of the solution of the CC approach from optimality. A 10product example demonstrates how to secure the solutions for the IS and the CC approach for the fuzzy ELSP, and illustrates the error bound of the CC approach.
Scheduling economic lot sizes in deteriorating production systems
 Naval Research Logistics
, 2003
"... Abstract: The paper considers the economic lot scheduling problem (ELSP) where production facility is assumed to deteriorate, owing to aging, with an increasing failure rate. The time to shift from an “incontrol ” state to an “outofcontrol ” state is assumed to be normally distributed. The system ..."
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Abstract: The paper considers the economic lot scheduling problem (ELSP) where production facility is assumed to deteriorate, owing to aging, with an increasing failure rate. The time to shift from an “incontrol ” state to an “outofcontrol ” state is assumed to be normally distributed. The system is scheduled to be inspected at the end of each production lot. If the process is found to be in an “outofcontrol ” state, then corrective maintenance is performed to restore it to an “incontrol ” state before the start of the next production run. Otherwise, preventive maintenance is carried out to enhance system reliability. The ELSP is formulated under the capacity constraint taking into account the quality related cost due to possible production of nonconforming items, process inspection, and maintenance costs. In order to find a feasible production schedule, both the common cycle and timevarying lot sizes approaches are utilized. © 2003 Wiley Periodicals, Inc.
An Evolutionary Computation Approach to the Economic Lot Scheduling Problem
, 1996
"... : The economic lot scheduling problem (ELSP) addresses the problem of scheduling several items  each with its own static, deterministic demand  at a single facility, where only one item can be produced at any time. This classical production planning problem has been studied extensively over the la ..."
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: The economic lot scheduling problem (ELSP) addresses the problem of scheduling several items  each with its own static, deterministic demand  at a single facility, where only one item can be produced at any time. This classical production planning problem has been studied extensively over the last three decades and various heuristic solution methods have been proposed, most of them based on the concept of a basic period. A common drawback of the majority of the existing heuristics is the lack of explicit, algorithmic mechanisms to develop feasible schedules, and the consequent use of ad hoc procedures. We propose an efficient evolutionary computation technique for this problem. Our heuristic searches the problem domain with a population of solutions and converges very quickly to low cost, feasible schedules. We present our results in comparison to the best known heuristics. 1. Introduction The Economic Lot Scheduling Problem (ELSP) is a common production planning problem that has ...
Simulation Optimization for the Stochastic Economic Lot Scheduling Problem with SequenceDependent Setup Times
"... We consider the stochastic economic lot scheduling problem (SELSP) with lost sales and random demand, where switching between products is subject to sequencedependent setup times. We propose a solution based on simulation optimization using an iterative twostep procedure which combines global poli ..."
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We consider the stochastic economic lot scheduling problem (SELSP) with lost sales and random demand, where switching between products is subject to sequencedependent setup times. We propose a solution based on simulation optimization using an iterative twostep procedure which combines global policy search with local search heuristics for the traveling salesman sequencing subproblem. To optimize the production cycle, we compare two criteria: minimizing total setup times and evenly distributing setups to obtain a more regular production cycle. Based on a numerical study, we find that a policy with a balanced production cycle outperforms other policies with unbalanced cycles.
A genetic algorithm for lot sizing and scheduling under capacity constraints and allowing backorders
 International Journal of Production Research
, 2011
"... This paper addresses the problem of scheduling economic lots in a multiproduct singlemachine environment. A mixed integer nonlinear programming formulation is developed which finds the optimal sequence and economic lots. The model takes explicit account of initial inventories, setup times, allows ..."
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This paper addresses the problem of scheduling economic lots in a multiproduct singlemachine environment. A mixed integer nonlinear programming formulation is developed which finds the optimal sequence and economic lots. The model takes explicit account of initial inventories, setup times, allows setups to be scheduled at arbitrary epochs in continuous time and models backorders. To solve the problem we develop a hybrid approach, combining a genetic algorithm and linear programming. The approach is tested on a set of instances taken from the literature and compared with other approaches. The experimental results validate the quality of the solutions and the effectiveness of the proposed approach.
unknown title
, 2008
"... Comparison of heuristics for an economic lot scheduling problem … 437 ..."
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Lead Time Minimization of MultiProduct, SingleProcessor System: A Comparison of Cyclic Policies
, 2005
"... Lead time minimization of a multiproduct, singleprocessor system: A comparison of cyclic policies ..."
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Lead time minimization of a multiproduct, singleprocessor system: A comparison of cyclic policies