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23
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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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.
Exact Computation of Optimal Inventory Policies over an Unbounded Horizon
 Mathematics of Operations Research
, 1989
"... . An inventory scheduling model with forbidden time intervals is analyzed. The objective is to minimize the longterm average cost per time unit. Unlike most of the literature on inventory theory, no restrictive assumptions are made apriori about the nature of optimal solutions. It is rather proved ..."
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. An inventory scheduling model with forbidden time intervals is analyzed. The objective is to minimize the longterm average cost per time unit. Unlike most of the literature on inventory theory, no restrictive assumptions are made apriori about the nature of optimal solutions. It is rather proved that optimal policies exist, and that some of them are cyclic with cycles of a particular structure. It is then shown that such optimal polices can be computed and an algorithm is given. 1. Introduction In the classical Economic Order Quantity (EOQ) model one seeks a policy of inventory scheduling so as to minimize the longterm average cost per time unit. Inventory is depleted at a known constant rate R and can be replenished instantaneously at any time. There is a fixed cost of C f per order, and the inventory holding cost is proportional to the amount of time and the amount of commodity held in stock: C h per time unit for each unit of commodity. Given that an order is placed at time t, i...
A unifying approximate dynamic programming model
, 2008
"... for the economic lot scheduling problem ..."
Periodic Production Scheduling at a Fastener Manufacturer
 International Journal of Production Economics
, 1996
"... We want to acknowledge the excellent contributions of one of our former MBA students, Peter Stahl, who introduced us to the problem and worked diligently with us until his graduation. We also want to thank the many people in the company who engaged in the joint endeavor which led to the results repo ..."
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We want to acknowledge the excellent contributions of one of our former MBA students, Peter Stahl, who introduced us to the problem and worked diligently with us until his graduation. We also want to thank the many people in the company who engaged in the joint endeavor which led to the results reported here. Finally, we gratefully acknowledge the helpful comments of three anonymous referees. This paper presents the application of periodic production scheduling at a metalfastener manufacturing company. The problem was initially presented as a mandate to reduce finished goods inventory by 33%. Preliminary investigations, however, revealed that any effort to reduce finished goods inventory necessarily involved two major endeavors: (1) significant improvements to forecasting and (2) a periodic production scheduling system (PPS). The forecasting system provided the input to the PPS system. The PPS required initial procedures for sorting parts into families, which, as far as possible, shared the same setup patterns, engineering specifications, raw material requirements, etc. The PPS itself was developed on a spreadsheet, and the output from this package fed into an interactive PC package. In addition to graphic presentation of production scheduling, the PC
MULTISTAGE LOT SIZING PROBLEMS VIA RANDOMIZED ROUNDING
, 1999
"... We study the classical multistage lot sizing problem that arises in distribution and inventory systems. A celebrated result in this area is the 94 % and 98 % approximation guarantee provided by poweroftwo policies. In this paper, we propose a simple randomized rounding algorithm to establish these ..."
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We study the classical multistage lot sizing problem that arises in distribution and inventory systems. A celebrated result in this area is the 94 % and 98 % approximation guarantee provided by poweroftwo policies. In this paper, we propose a simple randomized rounding algorithm to establish these performance bounds. We use this new technique to extend several results for the capacitated lot sizing problems to the case with submodular ordering cost. For the joint replenishment problem under a fixed base period model, we construct a 95.8% approximation algorithm to the (possibly dynamic) optimal lot sizing policy. The policies constructed are stationary but not necessarily of the poweroftwo type. This shows that for the fixed based planning model, the class of stationary policies is within 95.8 % of the optimum, improving on the previously best known 94 % approximation guarantee. 1.
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.
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.
Improved Randomized Approximation Algorithms for LotSizing Problems
"... We consider in this paper multiproduct, lotsizing problems that arise in manufacturing and inventory systems. We describe the problem in a manufactruring setting. There is a set N of products. For each product j E N there is a set ~j (called predecessors of product j) of products consumed in prod ..."
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We consider in this paper multiproduct, lotsizing problems that arise in manufacturing and inventory systems. We describe the problem in a manufactruring setting. There is a set N of products. For each product j E N there is a set ~j (called predecessors of product j) of products consumed in producing product