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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.
THE OPTIMAL PRODUCTION PLAN UNDER LIMITED PRODUCTION CAPACITY AT ANY POINT IN TIME
, 2006
"... Abstract For the production planning decision maker needing to fit new orders into a preexisting production plan with limited production capacity, he must estimate how much unused capacity exists at any given point in time in the prearranged production plan. In this study, we assume that the avail ..."
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Abstract For the production planning decision maker needing to fit new orders into a preexisting production plan with limited production capacity, he must estimate how much unused capacity exists at any given point in time in the prearranged production plan. In this study, we assume that the available production capacity at each point in time is estimated and known, and it is intended to build this issue into a mathematical model that is concrete for discussion with the purpose of minimizing total costs, where the total costs is the sum of production operating costs and inventory costs at any given point in time during the production process. Seeking an optimal solution and a sensitivity analysis of optimal solutions are the main parts of this study. From the results of this study, we can provide a decision procedure for an optimal production control plan for a new order for the production planners as a decision reference.
1 Project Description
"... This project will examine the problem of controlling the inventory of an product with partially observed, nonstationary, random demand. The probability distribution for the demand process is not known with certainty at any point in time, and this distribution may randomly change from one period to ..."
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This project will examine the problem of controlling the inventory of an product with partially observed, nonstationary, random demand. The probability distribution for the demand process is not known with certainty at any point in time, and this distribution may randomly change from one period to the next. The underlying demand process is partially observed through the previous demand observations which are themselves random. Because the control decisions are made with only partial information about the demand process, the level of uncertainty and the cost of suboptimal decisions is much higher than for most problems considered in the research literature. The nonstationary aspect of the demand process further increases the uncertainty because older observations of demand are less valuable in identifying the current state than more recent observations. This problem is an accurate representation of the inventory control problems faced by many organizations. However, it has not been directly addressed in the inventory literature or by existing decision support systems � therefore, inventory managers are forced to make potentially costly simplifying assumptions when addressing this challenging problem. The primary objectives of this project are to 1. Develop a modeling framework that adequately captures the important aspects of the problem,
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.