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Managing Stochastic Multiproduct Systems: Model, Measures, and Analysis
 Operations Research
, 1995
"... We consider a model for managing a single stage that produces multiple items. The production rates are finite and there are switchover times. The interarrival times and quantities of demands for the items are random, and demand may occur for a set of items. We consider order focussed measures: co ..."
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Cited by 13 (4 self)
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We consider a model for managing a single stage that produces multiple items. The production rates are finite and there are switchover times. The interarrival times and quantities of demands for the items are random, and demand may occur for a set of items. We consider order focussed measures: cost based on response times, service levels based on quoted lead times and Type1 service. We operate the stage in the following manner: (1) There is a cyclic schedule that determines the sequence of items and the number of times a particular item is produced in a cycle; (2) Given a cyclic schedule, production of each item follows a modified basestock policy or a (s,S) policy. We present a simulation based procedure to obtain good values for the base stock levels or S (for any fixed Ss) for each of the above performance measures. Numerical results indicate that good solutions can be obtained with modest computational effort. We also report on a real world implementation of this mode...
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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Cited by 13 (2 self)
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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.
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.
STOCHASTIC MODELS OF MANUFACTURING AND SERVICE OPERATIONS SMMSO 2009 The Stochastic Economic Lot Sizing Problem for Continuous MultiGrade Production
"... We study a variant of the Stochastic Economic Lot Scheduling Problem (SELSP) in which a single production facility must produce several grades to meet random stationary demand for each grade from a common finishedgoods (FG) inventory buffer with limited storage capacity. Demand that can not be sati ..."
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We study a variant of the Stochastic Economic Lot Scheduling Problem (SELSP) in which a single production facility must produce several grades to meet random stationary demand for each grade from a common finishedgoods (FG) inventory buffer with limited storage capacity. Demand that can not be satisfied directly from inventory is lost. Raw material is always available, and the production facility produces at a constant rate. When the facility is set up to produce a particular grade, the only allowable changeovers are from that grade to next lower or higher grade. All changeover times are deterministic and equal to each other. There is a changeover cost per changeover occasion, a spillover cost per unit of product in excess, whenever there is not enough space in the FG buffer to store the produced grade, and a lostsales cost per unit short, whenever there is not enough FG inventory to satisfy demand. We model the SELSP as a discretetimeMarkov Decision Process (MDP), where in each time period we must decide whether to initiate a changeover to a neighboring grade or keep the setup of the production facility unchanged, based on the current state of the system, which is determined by the current setup of the facility and the FG inventory levels of all the grades. The goal is to minimize the infinitehorizon expected average cost. For 2grade and 3grade problems we can numerically solve the exact MDP problem using successive approximation. For problems with more than 3 grades, we develop a heuristic solution which is based on approximating the original multigrade problem into many 3grade subproblems and numerically solving each subproblem using successive approximation. We present and discuss numerical results for problem incidences with 2, 4 and 5 grades, using both the exact and the heuristic procedure.
Cyclic Schedules as part of a JIT implementation at a laminate plant
"... We briefly describe a JustInTime (JIT) implementation where cyclic schedules play a critical role. Central to the implementation is a clear understanding of the interactions between scheduling, due date quotation, capacity allocation, variability in production and demand, inventory management and ..."
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We briefly describe a JustInTime (JIT) implementation where cyclic schedules play a critical role. Central to the implementation is a clear understanding of the interactions between scheduling, due date quotation, capacity allocation, variability in production and demand, inventory management and customer service. Furthermore, a novelty of this implementation is that we used the new technology of simulation based optimization to compute certain inventory levels. The goal of this paper is to communicate a successful implementation of stochastic cyclic schedules that has had a significant impact at the plant level, as well as provide details of the entire implementation (as several changes have been made at the shop floor, the plant and the supply chain levels). 1 Introduction In the summer of 1992, four employees of a laminate plant  a process engineer, a shop floor supervisor, a press operator and an assembler  asked me if I would implement a kanban system at their factory. When...
The Stochastic Economic Lot Scheduling Problem: A Survey
, 2005
"... We consider the production of multiple standardized products on a single machine with limited capacity and setup times under random demands and random production times, i.e., the socalled stochastic economic lot scheduling problem (SELSP). The main task for the production manager in this setting i ..."
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We consider the production of multiple standardized products on a single machine with limited capacity and setup times under random demands and random production times, i.e., the socalled stochastic economic lot scheduling problem (SELSP). The main task for the production manager in this setting is the construction of a production plan for the machine that minimizes the total costs, i.e., the sum of holding, backlogging and setup costs. Based on the critical elements of such a production plan, we give a classification and extensive overview of the research on the SELSP together with an indication of open research areas.
A Strong Cutting Plane Algorithm for Production Scheduling with Changeover Costs
, 1987
"... . ·r. i·: ·; i1: ·;i· · r. ..."
THE STOCHASTIC ECONOMIC LOT SCHEDULING PROBLEM: HEAVY TRAFFIC ANALYSIS OF DYNAMIC CYCLIC POLICIES
"... We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: a single server processes A ^ customer classes, and completed units enter a finished goods inventory that services exogenous customer demand. Unsatisfied demand is backordered, and each c ..."
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We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: a single server processes A ^ 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 objective is to minimize the long run e.xpected average costs of holding and backordering inventory and incurring setups. The setup cost is replaced by a setup time in the second problem, where the objective is to minimize average holding and backordering costs. In both problems we 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. Under standard heavy traffic conditions, these scheduling problems are approximated by diffusion control problems. The approximating setup cost])roblem is solved exactly, and the optimal dynamic lot sizing policy is found in closed form. Structural results and an algorithmic procedure are derived for the setup time problem. A computational study is undertaken to compare the proposed policy and several straw policies to the numerically computed optimal policy.
Unclassified SECURITY CLASSIFICATION OF THIS PAGE (~~.m. D. Ent.r.dJ
"... RODUCT RODUCTION $YCLINGJ ________________S — S.,.n,. Stephen C/Grav~~J ~~~~~~~~~~~~~~~~~ ..."
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RODUCT RODUCTION $YCLINGJ ________________S — S.,.n,. Stephen C/Grav~~J ~~~~~~~~~~~~~~~~~