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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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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.
Dynamic Scheduling to Minimize Lost Sales Subject to Setup Costs
, 1998
"... We consider scheduling a shared server in a twoclass, maketostock, closed queueing network. We include server switching costs and lost sales costs (equivalently, server starvation penalties) for lost jobs. If the switching costs are zero, the optimal policy has a monotonic threshold type of sw ..."
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Cited by 5 (2 self)
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We consider scheduling a shared server in a twoclass, maketostock, closed queueing network. We include server switching costs and lost sales costs (equivalently, server starvation penalties) for lost jobs. If the switching costs are zero, the optimal policy has a monotonic threshold type of switching curve provided that the service times are identical. For completely symmetric systems without setups, it is optimal to serve the longer queue. Using simple analytical models as approximations, we derive a heuristic scheduling policy. Numerical results demonstrate the effectiveness of our heuristic, which is typically within 10% of optimal. We also develop and test a heuristic policy for a model in which the shared resource is part of a series network under a CONWIP release policy.
A unifying approximate dynamic programming model
, 2008
"... for the economic lot scheduling problem ..."
DYNAMIC SCHEDULING FOR A SINGLE MACHINE SYSTEM UNDER DIFFERENT SETUP AND BUFFER CAPACITY SCENARIOS
"... The problem of dynamic scheduling for single machine manufacturing systems has been extensively studied in the past under different setup scenarios, mainly for systems with infinite buffer capacity. This paper addresses a general framework and investigates similarities and differences between polic ..."
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Cited by 1 (1 self)
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The problem of dynamic scheduling for single machine manufacturing systems has been extensively studied in the past under different setup scenarios, mainly for systems with infinite buffer capacity. This paper addresses a general framework and investigates similarities and differences between policies optimal if setup times and costs are or are not negligible, if buffers have a finite or an infinite capacity. The cost function takes into account of backlog and surplus, but also includes a demand loss component if buffers have a finite capacity and a setup cost if not negligible. Both a steady state and a transient optimization problem are considered and already known results are compared and extended to complete the analysis.
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.
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.
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.