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43
Stable Distributed, RealTime Scheduling Of Flexible Manufacturing / Assembly / Disassembly Systems
 IEEE Transactions on Automatic Control
, 1989
"... We consider general exible manufacturing/assembly/disassembly systems with the following features: (i) there are several part types, each with given processing time requirements at a specied sequence of machines; (ii) each parttype needs to be produced at a prespecied rate; (iii) parts may incur va ..."
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Cited by 62 (11 self)
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We consider general exible manufacturing/assembly/disassembly systems with the following features: (i) there are several part types, each with given processing time requirements at a specied sequence of machines; (ii) each parttype needs to be produced at a prespecied rate; (iii) parts may incur variable transportation delays when moving from one machine to another; (iv) setup times are required whenever a machine changes from a production run of parts of one type to another; (v) some parttypes may also need assembly or disassembly; and Please address all correspondence to the second author at: Coordinated Science Laboratory, University of Illinois, 1101 W. Springeld Avenue, Urbana, Illinois 61801/USA. y The research of the authors has been supported in part by the National Science Foundation under Grant No. ECS8802576, in part by the U. S. Army Research Oce under Contract No. DAAG2985K0094, and in part by the Joint Services Electronics Program under Contract No. N000...
Dynamic Scheduling of a TwoClass Queue with Setups
, 1994
"... We analyze two scheduling problems for a queueing system with a single server and two customer classes. Each class has its own renewal arrival process, general service time distribution, and holding cost rate. In the first problem, a setup cost is incurred when the server switches from one class to ..."
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Cited by 36 (3 self)
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We analyze two scheduling problems for a queueing system with a single server and two customer classes. Each class has its own renewal arrival process, general service time distribution, and holding cost rate. In the first problem, a setup cost is incurred when the server switches from one class to the other, and the objective is to minimize the longrun expected average cost of holding customers and incurring setups. The setup cost is replaced by a setup time in the second problem, where the objective is to minimize the average holding cost. By assuming that a recently derived heavy traffic principle holds not only for the exhaustive policy but for nonexhaustive policies, we approximate (under standard heavy traffic conditions) the dynamic scheduling problems by diffusion control problems. The diffusion control problem for the setup cost problem is solved exactly, and asymptotics are used to analyze the corresponding setup time problem. Computational results show that the proposed scheduling policies are within several percent of optimal over a broad range of problem parameters. We consider two dynamic scheduling problems for a singleserver queueing system with two classes of customers. In both problems, each class possesses its own renewal arrival process, general service time distribution, and holding cost rate, and the server incurs a setup when switching from one class to the other. In the setup cost
Multiproduct systems with both setup times and costs: Fluid bounds and schedules.
 Operations Research,
, 2006
"... Abstract This paper considers a multiproduct, singleserver production system where both setup times and costs are incurred whenever the server changes product. The system is maketoorder with a per unit backlogging cost. The objective is to minimize the longrun average cost per unit time. Using ..."
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Cited by 18 (0 self)
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Abstract This paper considers a multiproduct, singleserver production system where both setup times and costs are incurred whenever the server changes product. The system is maketoorder with a per unit backlogging cost. The objective is to minimize the longrun average cost per unit time. Using a fluid model, we provide a closedform lower bound on system performance. This bound is also shown to provide a lower bound for stochastic systems when scheduling is local or static, but is only an approximation when scheduling is global or dynamic. The fluid bound suggests both local and global scheduling heuristics, which are tested for the stochastic system via a simulation study.
ReEntrant Lines
 Queueing Systems
, 1993
"... Traditionally, manufacturing systems have mainly been treated as either job shops or flow shops. In job shops, parts may arrive with random routes, with each route having a low volume. In flow shops, the routes are fixed and acyclic, as in assembly lines. With the advent of semiconductor manufacturi ..."
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Cited by 15 (1 self)
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Traditionally, manufacturing systems have mainly been treated as either job shops or flow shops. In job shops, parts may arrive with random routes, with each route having a low volume. In flow shops, the routes are fixed and acyclic, as in assembly lines. With the advent of semiconductor manufacturing plants, and more recently, thin film lines, this dichotomy needs to be expanded to consider another class of systems, which we call "reentrant lines." The distinguishing feature of these manufacturing systems is that parts visit some machines more than once at different stages of processing. Scheduling problems arise because several parts at different stages of processing may be in contention with each other for service at the same machine. There may be uncertainties in the form of random service or setup times, as well as random machine failures and repairs. The goal of scheduling is to improve performance measures such as mean sojourn time in the system, which is also known as the mea...
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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Cited by 14 (1 self)
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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...
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.
Integrated Lotsizing and Scheduling for JustInTime Production of Complex Assemblies with Finite Setups,
 International Journal of Production Research,
, 1997
"... ..."
A Coordinated Production Planning Model with Capacity Expansion and Inventory Management
 Management Science
, 2001
"... M otivated by a problem faced by a large manufacturer of a consumer product, we explore the interaction between production planning and capacity acquisition decisions in environments with demand growth. We study a firm producing multiple items in a multiperiod environment where demand for items is ..."
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Cited by 10 (1 self)
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M otivated by a problem faced by a large manufacturer of a consumer product, we explore the interaction between production planning and capacity acquisition decisions in environments with demand growth. We study a firm producing multiple items in a multiperiod environment where demand for items is known but varies over time with a longterm growth and possible shortterm fluctuations. The production equipment is characterized by significant changeover time between the production of different items. While demand growth is gradual, capacity additions are discrete. Therefore, periods immediately following a machine purchase are characterized by excess machine capacity. We develop a mathematical programming model and an effective solution approach to determine the optimal capacity acquisition, production and inventory decisions over time. Through a computational study, we show the effectiveness of the solution approach in terms of solution quality and investigate the impact of product variety, cost of capital, and other important parameters on the capacity and inventory decisions. The computational results bring out some key insightsincreasing product variety may not result in excessive inventory and even a substantial increase in setup times or holding costs may not increase the total cost over the horizon in a significant manner due to the ability to acquire additional capacity. We also provide solutions and insights to the real problem that motivated this work.
Coordinating Production and Delivery Under a (z, Z)Type Vendor Managed Inventory Contract, Working Paper
, 2000
"... This paper models a type of vendormanaged inventory (VMI) agreement that occurs in practice called a (z, Z) contract. We investigate the savings due to better coordination of production and delivery facilitated by such an agreement. The optimal behavior of both the supplier and the retailer are cha ..."
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Cited by 9 (0 self)
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This paper models a type of vendormanaged inventory (VMI) agreement that occurs in practice called a (z, Z) contract. We investigate the savings due to better coordination of production and delivery facilitated by such an agreement. The optimal behavior of both the supplier and the retailer are characterized. The optimal replenishment and production policies for a supplier are found to be upto policies, which are shown to be easily computed by decoupling the periods when the supplier outsources from those when the supplier does not outsource. A simple application of the newsvendor relation is used to define the retailerâ€™s optimal policy. Numerical analysis is conducted to compare the performance of a single supplier and a single retailer operating under a (z, Z) VMI contract with the performance of those operating under traditional retailermanaged inventory (RMI) with information sharing. Our results verify some observations made in industry about VMI and show that the (z, Z) type of VMI agreement performs significantly better than RMI in many settings, New information technologies and a continued increase in competition has led to the development of new interorganizational relationships in the supply chain. One such relationship