Mohsen Elhafsi - Academia.edu (original) (raw)
Papers by Mohsen Elhafsi
We consider the optimal control of an assemble-to-order (ATO) system with m components, a single ... more We consider the optimal control of an assemble-to-order (ATO) system with m components, a single end-product, and n customer classes. Demand from each class occurs continuously over time according to a Poisson process. Components are produced in separate production facilities, each with a finite production rate and exponentially distributed production times. Components can be stocked ahead of demand but incur
We consider an assembly system with multiple stages, multiple items, and multiple customer classe... more We consider an assembly system with multiple stages, multiple items, and multiple customer classes. The system consists of m production facilities, each producing a different item. Items are produced in variable batch sizes, one batch at a time, with exponentially distributed batch production times. Demand from each class takes place continuously over time according to a compound Poisson process. At
We consider an assembly system with multiple stages, multiple items, and multiple customer classe... more We consider an assembly system with multiple stages, multiple items, and multiple customer classes. The system consists of m production facilities, each producing a different item. Items are produced one unit at a time. To produce one unit of an item, one unit from each of its predecessor items is needed. Upon production completion, items are placed in inventory. At
OR Spektrum, 1996
In this paper, we study a manufacturing system consisting of two machines separated by two interm... more In this paper, we study a manufacturing system consisting of two machines separated by two intermediate buffers, and capable of producing two different products. Each product requires a constant processing time on each of the machines. Each machine requires a constant non-negligible setup change time from one product to the other. The demand rate for each product is considered to be piecewise constant. Each machine undergoes failure and repair. The time-to-failure and time-to-repair are exponentially distributed random variables. The setup change and processing operations are resumable. We model our system as a continuous time, continuous flow process. An optimal control problem is formulated for the system to minimize the total expected discounted cost over an infinite horizon. To determine the optimal control policy structure, a discrete version of the problem is solved numerically using a dynamic programming formulation with a piecewise linear penalty function. A real-time control algorithm is then developed with the objective of maintaining low work-in-process inventory and keeping the production close to the demand. The algorithm uses a hierarchical control structure to generate the loading times for each product on each machine in real time and to respond to random disruptions in the system. The system is simulated using this algorithm to study its performance. The performance of the algorithm is also compared to alternative policies.
Proceedings of the Fourth International Conference on Computer Integrated Manufacturing and Automation Technology, 1994
In this paper, we study the scheduling of a deterministic one-machine two-part-type setup system ... more In this paper, we study the scheduling of a deterministic one-machine two-part-type setup system under steady and transient conditions. The optimal solution, expressed as an optimal feedback control, provides the optimal production rates and setup switching epochs as a function of the state of the system. For the steady state, the optimal cyclic schedule is determined. For the transient case,
International Journal of Production Research, 2014
ABSTRACT This paper studies a single end product assemble-to-order system serving both the demand... more ABSTRACT This paper studies a single end product assemble-to-order system serving both the demand of the end product and the individual components. Demands are assumed to form independent Poisson streams with different rates. Unsatisfied demand, both for the end product and for components, is assumed lost and thus incurs a per unit lost sale penalty. The end product is assembled from K distinct components each produced on a different production facility (or procured from independent suppliers). Production lead times are non-identical and are assumed to be independent and exponentially distributed. Produced components are held in stock in anticipation of future demands. The goal is to determine the optimal component production and inventory allocation policy. The optimal policy is characterised using a Markov Decision Process model. It is shown that, in addition to the state-dependent threshold type, the optimal policy exhibits counter-intuitive features which have not been observed in systems without components demand. In particular, for certain combinations of system parameters, the optimal inventory allocation policy switches priority as the inventory level of components changes. Furthermore, for a particular component k, as the inventory level of other components increases, the desirability of satisfying Component k demand decreases. Finally, because in general the optimal policy is fairly complicated and is difficult to obtain numerically, due to the curse of dimensionality of dynamic programming, three heuristic policies are proposed. Extensive numerical experiments indicate that the three heuristics perform very well compared to the optimal policy.
Journal of Global Optimization, 1996
This paper deals with the optimal scheduling of a one-machine two-product manufacturing system wi... more This paper deals with the optimal scheduling of a one-machine two-product manufacturing system with setup, operating in a continuous time dynamic environment. The machine is reliable. A known constant setup time is incurred when switching over from a part to the other. Each part has specified constant processing time and constant demand rate, as well as an infinite supply of
Management Science, 2004
We consider the problem of allocating demand arising from N products to M production facilities w... more We consider the problem of allocating demand arising from N products to M production facilities with finite capacity and load-dependent manufacturing lead-times. Production facilities can choose to manufacture items either to-stock or to-order. If items are stocked, demand is satisfied immediately if there is on-hand inventory. Otherwise, demand is backlogged with the production facility to which it is assigned. Products
Production and Operations Management, 2009
This paper deals with a manufacturing system consisting of a single machine subject to random fai... more This paper deals with a manufacturing system consisting of a single machine subject to random failures and repairs. The machine can produce two types of parts. When the production is switched from one part type to the other a random setup time is incurred at a constant cost rate. The objective is to track the demand, while keeping the work-in-process as close as possible to zero, for both products. The problem is formulated as an optimal stochastic control. The optimal policy is obtained numerically by descretizing the continuous time continuous state optimality conditions using a Markov chain approximation technique. The discretized optimality conditions are shown to correspond to an infinite horizon, discrete time, discrete state dynamic programming problem. The optimal setup policy is shown to have two different structures depending on the parameters of the system. A heuristic policy is proposed to approximate the optimal setup policy. Simulation results show that the heuristic policy is a very good approximation for sufficiently reliable systems.
Operations Research, 2011
We consider an assembly system with multiple stages, multiple items, and multiple customer classe... more We consider an assembly system with multiple stages, multiple items, and multiple customer classes. The system consists of m production facilities, each producing a different item. Items are produced in variable batch sizes, one batch at a time, with exponentially distributed batch production times. Demand from each class takes place continuously over time according to a compound Poisson process. At each decision epoch, we must determine whether or not to produce an item and should demand from a particular class arise whether or not to satisfy it from existing inventory, if any is available. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. In contrast to systems with exogenous and deterministic production leadtimes, we show that the optimal production policy for each item is a state-dependent base-stock policy with the base-stock level non-increasing in the inventory level of items that are downstream and non-decreasing in the inventory level of all other items. For inventory allocation, we show that the optimal policy is a multi-level state-dependent rationing policy with the rationing level for each demand class non-increasing in the inventory level of all non-end items. We also show how the optimal control problem can be reformulated in terms of echelon inventory and how the essential features of the optimal policy can be reinterpreted in terms of echelon inventory.
Management Science, 2006
We consider the optimal production and inventory control of an assemble-to-order (ATO) system wit... more We consider the optimal production and inventory control of an assemble-to-order (ATO) system with m components, one end-product, and n customer classes. Demand from each class occurs continuously over time according to a Poisson process. Components are produced one unit at a time in separate production facilities, each with a finite production rate and exponentially distributed production times. Components can be stocked ahead of demand but incur a holding cost. When an order arises, it can be either satisfied if all m components are available in stock, rejected, or backordered if backordering is allowed. A rejected or backordered demand incurs a shortage cost (a lost sale or a backorder cost), which may vary by demand class. The system manager must decide when to produce each component and, whenever an order is placed, whether or not to satisfy it from on-hand inventory. We formulate the problem as a Markov decision process and characterize the structure of the optimal policy. We show that an optimal production policy for each component is a state-dependent base-stock policy, where the basestock level for each component is non-decreasing in the inventory level of other components. We show that an optimal inventory allocation is a state-dependent multi-level rationing policy where the component rationing level for each class is non-increasing in the inventory level of other components. Using numerical results, we compare the performance of the optimal policy to simple heuristics.
Journal of Global Optimization, 1997
In this paper, we deal with the production scheduling ofseveral products that are produced period... more In this paper, we deal with the production scheduling ofseveral products that are produced periodically, in a fixed sequence, ona single machine. In the literature, this problem is usually referred to asthe Common Cycle Economic Lot Scheduling Problem. We extend thelatter to allow the production rates to be controllable at the beginningof as well as during each production run of a product. Also, we assumethat unsatisfied demand is completely backordered. The objective is todetermine the optimal schedule that satisfies the demand for all theproducts and that realizes the minimum average setup, inventoryholding and backlog cost per unit time. Comparison with previousresults (when production rates are fixed) reveals that averagecosts can be reduced up to 66% by allowing controllable productionrates.
Journal of Global Optimization, 1996
This paper deals with the optimal control of a one-machine two-product manufacturing system with ... more This paper deals with the optimal control of a one-machine two-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as
International Journal of Production Research, 2008
In this paper, we study an assemble-to-order system consisting of n products assembled from a sub... more In this paper, we study an assemble-to-order system consisting of n products assembled from a subset of m distinct components where the products have a modular nested design. i.e., product i has only one additional component more than product i−1. In particular, we study the optimal production and inventory allocation policies of such systems. Components are produced on independent production facilities one unit at a time, each with a finite production rate and exponentially distributed production times. The components are stocked ahead of demand and therefore incur a holding cost per unit per unit of time. Demand from each product occurs continuously over time according to a Poisson process. The demand for a particular product can be either satisfied (provided all its components are available in stock) or rejected. In the latter case, a product-dependent lost sale cost is incurred. In this situation, a manager is confronted with two decisions: when to produce a component and whether or not to satisfy an incoming product order from on-hand inventory. We show that, for the production of a component, the optimal policy is a base-stock type where the base-stock level depends on all other components' inventory. We also show that, for inventory allocation, the optimal policy is a multi-level rationing policy where the rationing levels depend on all other components' inventory. We propose a simple heuristic that we numerically compare against the optimal policy and show that, when carefully designed, it can be very effective.
IIE Transactions, 2000
Flexible manufacturing systems are often designed as ßowshops supported by automated material han... more Flexible manufacturing systems are often designed as ßowshops supported by automated material handling devices that facilitate routing among any two processors of adjacent stages. This routing structure is complex, and results in excessive capital investment and costs of management. In this paper we propose a decomposition of two stage ßowshops into smaller independent ßowlines that allow for unidirectional routing only. We solve optimally the problem of minimizing makespan on 2 parallel ßowlines, by means of a dynamic programming algorithm (DP). Based on DP we develop lower bounds on the throughput performance of environments that consist of more than two ßowlines. We present several heuristic algorithms and report their optimality gaps. Using these algorithms, we show that the decomposition of two stage ßowshops with complicated routing into ßowline-like designs with unidirectional routing is associated with minor losses in throughput performance, and hence signiÞcant savings in material handling costs.
IIE Transactions, 1999
We study a make-to-order manufacturing system consisting of several processing centers that are s... more We study a make-to-order manufacturing system consisting of several processing centers that are subject to failures and repairs. Our objective is to build a model that can be used as a tool for negotiating the delivery date and the price of a certain upcoming order. The model takes into account the congestion level of the shop floor at the time the order is placed. Based on the workload of the processing centers, the model splits the order into lots and assigns them to the processing centers so as to determine the order completion time associated with the minimum operating cost. The efficiency of the solution method for the model allows real-time decision-making while negotiating the price and delivery date of the order to be placed. Since the decisions are made based on a snapshot of the congestion level at the shop floor, using this model will reduce the conflict between the marketing and the production activities in manufacturing organizations. ____________________________________________________________________________________________
IEEE Transactions on Automation Science and Engineering, 2000
We consider a production-inventory system with two customer classes, one patient and one impatien... more We consider a production-inventory system with two customer classes, one patient and one impatient. Orders from the patient class can be backordered if needed, while orders from the impatient class must be rejected if they cannot be fulfilled from on-hand inventory. Orders backordered incur a backorder cost, while orders rejected incur a lost sales cost. The objective is to minimize
European Journal of Operational Research, 2010
In this paper, we study a system consisting of a manufacturer or supplier serving several retaile... more In this paper, we study a system consisting of a manufacturer or supplier serving several retailers or clients. The manufacturer produces a standard product in a make-to-stock fashion in anticipation of orders emanating from n retailers with different contractual agreements hence ranked/prioritized according to their importance. Orders from the retailers are non-unitary and have sizes that follow a discrete distribution. The total production time is assumed to follow a k 0 -Erlang distribution. Order inter-arrival time for class l demand is assumed to follow a k l -Erlang distribution. Work-in-process as well as the finished product incur a, per unit per unit of time, carrying cost. Unsatisfied units from an order from a particular demand class are assumed lost and incur a class specific lost sale cost. The objective is to determine the optimal production and inventory allocation policies so as to minimize the expected total (discounted or average) cost. We formulate the problem as a Markov decision process and show that the optimal production policy is of the base-stock type with base-stock levels non-decreasing in the demand stages. We also show that the optimal inventory allocation policy is a rationing policy with rationing levels non-decreasing in the demand stages. We also study several important special cases and provide, through numerical experiments, managerial insights including the effect of the different sources of variability on the operating cost and the benefits of such contracts as Vendor Managed Inventory or Collaborative Planning, Forecasting, and Replenishment. Also, we show that a heuristic that ignores the dependence of the base-stock and rationing levels on the demands stages can perform very poorly compared to the optimal policy.
Computers & Industrial Engineering, 1997
This paper considers the scheduling of a manufacturing system with nonresumable setup changes. Th... more This paper considers the scheduling of a manufacturing system with nonresumable setup changes. The system considered involves an unreliable machine that can produce two part types. The switchover from one part type to the other incurs a given constant setup time. The setups are nonresumable, i.e. after a machine repair completion, a setup decision has to be made. The parts have specified constant processing time and constant demand rate. We give a continuous dynamic programming formulation of the problem, which is solved numerically. The optimal setup switching policies are shown to be hedging corridors. Two heuristics, for the determination of the hedging levels, are provided. We show, through simulation, that the two heuristics exhibit good performance.
We consider the optimal control of an assemble-to-order (ATO) system with m components, a single ... more We consider the optimal control of an assemble-to-order (ATO) system with m components, a single end-product, and n customer classes. Demand from each class occurs continuously over time according to a Poisson process. Components are produced in separate production facilities, each with a finite production rate and exponentially distributed production times. Components can be stocked ahead of demand but incur
We consider an assembly system with multiple stages, multiple items, and multiple customer classe... more We consider an assembly system with multiple stages, multiple items, and multiple customer classes. The system consists of m production facilities, each producing a different item. Items are produced in variable batch sizes, one batch at a time, with exponentially distributed batch production times. Demand from each class takes place continuously over time according to a compound Poisson process. At
We consider an assembly system with multiple stages, multiple items, and multiple customer classe... more We consider an assembly system with multiple stages, multiple items, and multiple customer classes. The system consists of m production facilities, each producing a different item. Items are produced one unit at a time. To produce one unit of an item, one unit from each of its predecessor items is needed. Upon production completion, items are placed in inventory. At
OR Spektrum, 1996
In this paper, we study a manufacturing system consisting of two machines separated by two interm... more In this paper, we study a manufacturing system consisting of two machines separated by two intermediate buffers, and capable of producing two different products. Each product requires a constant processing time on each of the machines. Each machine requires a constant non-negligible setup change time from one product to the other. The demand rate for each product is considered to be piecewise constant. Each machine undergoes failure and repair. The time-to-failure and time-to-repair are exponentially distributed random variables. The setup change and processing operations are resumable. We model our system as a continuous time, continuous flow process. An optimal control problem is formulated for the system to minimize the total expected discounted cost over an infinite horizon. To determine the optimal control policy structure, a discrete version of the problem is solved numerically using a dynamic programming formulation with a piecewise linear penalty function. A real-time control algorithm is then developed with the objective of maintaining low work-in-process inventory and keeping the production close to the demand. The algorithm uses a hierarchical control structure to generate the loading times for each product on each machine in real time and to respond to random disruptions in the system. The system is simulated using this algorithm to study its performance. The performance of the algorithm is also compared to alternative policies.
Proceedings of the Fourth International Conference on Computer Integrated Manufacturing and Automation Technology, 1994
In this paper, we study the scheduling of a deterministic one-machine two-part-type setup system ... more In this paper, we study the scheduling of a deterministic one-machine two-part-type setup system under steady and transient conditions. The optimal solution, expressed as an optimal feedback control, provides the optimal production rates and setup switching epochs as a function of the state of the system. For the steady state, the optimal cyclic schedule is determined. For the transient case,
International Journal of Production Research, 2014
ABSTRACT This paper studies a single end product assemble-to-order system serving both the demand... more ABSTRACT This paper studies a single end product assemble-to-order system serving both the demand of the end product and the individual components. Demands are assumed to form independent Poisson streams with different rates. Unsatisfied demand, both for the end product and for components, is assumed lost and thus incurs a per unit lost sale penalty. The end product is assembled from K distinct components each produced on a different production facility (or procured from independent suppliers). Production lead times are non-identical and are assumed to be independent and exponentially distributed. Produced components are held in stock in anticipation of future demands. The goal is to determine the optimal component production and inventory allocation policy. The optimal policy is characterised using a Markov Decision Process model. It is shown that, in addition to the state-dependent threshold type, the optimal policy exhibits counter-intuitive features which have not been observed in systems without components demand. In particular, for certain combinations of system parameters, the optimal inventory allocation policy switches priority as the inventory level of components changes. Furthermore, for a particular component k, as the inventory level of other components increases, the desirability of satisfying Component k demand decreases. Finally, because in general the optimal policy is fairly complicated and is difficult to obtain numerically, due to the curse of dimensionality of dynamic programming, three heuristic policies are proposed. Extensive numerical experiments indicate that the three heuristics perform very well compared to the optimal policy.
Journal of Global Optimization, 1996
This paper deals with the optimal scheduling of a one-machine two-product manufacturing system wi... more This paper deals with the optimal scheduling of a one-machine two-product manufacturing system with setup, operating in a continuous time dynamic environment. The machine is reliable. A known constant setup time is incurred when switching over from a part to the other. Each part has specified constant processing time and constant demand rate, as well as an infinite supply of
Management Science, 2004
We consider the problem of allocating demand arising from N products to M production facilities w... more We consider the problem of allocating demand arising from N products to M production facilities with finite capacity and load-dependent manufacturing lead-times. Production facilities can choose to manufacture items either to-stock or to-order. If items are stocked, demand is satisfied immediately if there is on-hand inventory. Otherwise, demand is backlogged with the production facility to which it is assigned. Products
Production and Operations Management, 2009
This paper deals with a manufacturing system consisting of a single machine subject to random fai... more This paper deals with a manufacturing system consisting of a single machine subject to random failures and repairs. The machine can produce two types of parts. When the production is switched from one part type to the other a random setup time is incurred at a constant cost rate. The objective is to track the demand, while keeping the work-in-process as close as possible to zero, for both products. The problem is formulated as an optimal stochastic control. The optimal policy is obtained numerically by descretizing the continuous time continuous state optimality conditions using a Markov chain approximation technique. The discretized optimality conditions are shown to correspond to an infinite horizon, discrete time, discrete state dynamic programming problem. The optimal setup policy is shown to have two different structures depending on the parameters of the system. A heuristic policy is proposed to approximate the optimal setup policy. Simulation results show that the heuristic policy is a very good approximation for sufficiently reliable systems.
Operations Research, 2011
We consider an assembly system with multiple stages, multiple items, and multiple customer classe... more We consider an assembly system with multiple stages, multiple items, and multiple customer classes. The system consists of m production facilities, each producing a different item. Items are produced in variable batch sizes, one batch at a time, with exponentially distributed batch production times. Demand from each class takes place continuously over time according to a compound Poisson process. At each decision epoch, we must determine whether or not to produce an item and should demand from a particular class arise whether or not to satisfy it from existing inventory, if any is available. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. In contrast to systems with exogenous and deterministic production leadtimes, we show that the optimal production policy for each item is a state-dependent base-stock policy with the base-stock level non-increasing in the inventory level of items that are downstream and non-decreasing in the inventory level of all other items. For inventory allocation, we show that the optimal policy is a multi-level state-dependent rationing policy with the rationing level for each demand class non-increasing in the inventory level of all non-end items. We also show how the optimal control problem can be reformulated in terms of echelon inventory and how the essential features of the optimal policy can be reinterpreted in terms of echelon inventory.
Management Science, 2006
We consider the optimal production and inventory control of an assemble-to-order (ATO) system wit... more We consider the optimal production and inventory control of an assemble-to-order (ATO) system with m components, one end-product, and n customer classes. Demand from each class occurs continuously over time according to a Poisson process. Components are produced one unit at a time in separate production facilities, each with a finite production rate and exponentially distributed production times. Components can be stocked ahead of demand but incur a holding cost. When an order arises, it can be either satisfied if all m components are available in stock, rejected, or backordered if backordering is allowed. A rejected or backordered demand incurs a shortage cost (a lost sale or a backorder cost), which may vary by demand class. The system manager must decide when to produce each component and, whenever an order is placed, whether or not to satisfy it from on-hand inventory. We formulate the problem as a Markov decision process and characterize the structure of the optimal policy. We show that an optimal production policy for each component is a state-dependent base-stock policy, where the basestock level for each component is non-decreasing in the inventory level of other components. We show that an optimal inventory allocation is a state-dependent multi-level rationing policy where the component rationing level for each class is non-increasing in the inventory level of other components. Using numerical results, we compare the performance of the optimal policy to simple heuristics.
Journal of Global Optimization, 1997
In this paper, we deal with the production scheduling ofseveral products that are produced period... more In this paper, we deal with the production scheduling ofseveral products that are produced periodically, in a fixed sequence, ona single machine. In the literature, this problem is usually referred to asthe Common Cycle Economic Lot Scheduling Problem. We extend thelatter to allow the production rates to be controllable at the beginningof as well as during each production run of a product. Also, we assumethat unsatisfied demand is completely backordered. The objective is todetermine the optimal schedule that satisfies the demand for all theproducts and that realizes the minimum average setup, inventoryholding and backlog cost per unit time. Comparison with previousresults (when production rates are fixed) reveals that averagecosts can be reduced up to 66% by allowing controllable productionrates.
Journal of Global Optimization, 1996
This paper deals with the optimal control of a one-machine two-product manufacturing system with ... more This paper deals with the optimal control of a one-machine two-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as
International Journal of Production Research, 2008
In this paper, we study an assemble-to-order system consisting of n products assembled from a sub... more In this paper, we study an assemble-to-order system consisting of n products assembled from a subset of m distinct components where the products have a modular nested design. i.e., product i has only one additional component more than product i−1. In particular, we study the optimal production and inventory allocation policies of such systems. Components are produced on independent production facilities one unit at a time, each with a finite production rate and exponentially distributed production times. The components are stocked ahead of demand and therefore incur a holding cost per unit per unit of time. Demand from each product occurs continuously over time according to a Poisson process. The demand for a particular product can be either satisfied (provided all its components are available in stock) or rejected. In the latter case, a product-dependent lost sale cost is incurred. In this situation, a manager is confronted with two decisions: when to produce a component and whether or not to satisfy an incoming product order from on-hand inventory. We show that, for the production of a component, the optimal policy is a base-stock type where the base-stock level depends on all other components' inventory. We also show that, for inventory allocation, the optimal policy is a multi-level rationing policy where the rationing levels depend on all other components' inventory. We propose a simple heuristic that we numerically compare against the optimal policy and show that, when carefully designed, it can be very effective.
IIE Transactions, 2000
Flexible manufacturing systems are often designed as ßowshops supported by automated material han... more Flexible manufacturing systems are often designed as ßowshops supported by automated material handling devices that facilitate routing among any two processors of adjacent stages. This routing structure is complex, and results in excessive capital investment and costs of management. In this paper we propose a decomposition of two stage ßowshops into smaller independent ßowlines that allow for unidirectional routing only. We solve optimally the problem of minimizing makespan on 2 parallel ßowlines, by means of a dynamic programming algorithm (DP). Based on DP we develop lower bounds on the throughput performance of environments that consist of more than two ßowlines. We present several heuristic algorithms and report their optimality gaps. Using these algorithms, we show that the decomposition of two stage ßowshops with complicated routing into ßowline-like designs with unidirectional routing is associated with minor losses in throughput performance, and hence signiÞcant savings in material handling costs.
IIE Transactions, 1999
We study a make-to-order manufacturing system consisting of several processing centers that are s... more We study a make-to-order manufacturing system consisting of several processing centers that are subject to failures and repairs. Our objective is to build a model that can be used as a tool for negotiating the delivery date and the price of a certain upcoming order. The model takes into account the congestion level of the shop floor at the time the order is placed. Based on the workload of the processing centers, the model splits the order into lots and assigns them to the processing centers so as to determine the order completion time associated with the minimum operating cost. The efficiency of the solution method for the model allows real-time decision-making while negotiating the price and delivery date of the order to be placed. Since the decisions are made based on a snapshot of the congestion level at the shop floor, using this model will reduce the conflict between the marketing and the production activities in manufacturing organizations. ____________________________________________________________________________________________
IEEE Transactions on Automation Science and Engineering, 2000
We consider a production-inventory system with two customer classes, one patient and one impatien... more We consider a production-inventory system with two customer classes, one patient and one impatient. Orders from the patient class can be backordered if needed, while orders from the impatient class must be rejected if they cannot be fulfilled from on-hand inventory. Orders backordered incur a backorder cost, while orders rejected incur a lost sales cost. The objective is to minimize
European Journal of Operational Research, 2010
In this paper, we study a system consisting of a manufacturer or supplier serving several retaile... more In this paper, we study a system consisting of a manufacturer or supplier serving several retailers or clients. The manufacturer produces a standard product in a make-to-stock fashion in anticipation of orders emanating from n retailers with different contractual agreements hence ranked/prioritized according to their importance. Orders from the retailers are non-unitary and have sizes that follow a discrete distribution. The total production time is assumed to follow a k 0 -Erlang distribution. Order inter-arrival time for class l demand is assumed to follow a k l -Erlang distribution. Work-in-process as well as the finished product incur a, per unit per unit of time, carrying cost. Unsatisfied units from an order from a particular demand class are assumed lost and incur a class specific lost sale cost. The objective is to determine the optimal production and inventory allocation policies so as to minimize the expected total (discounted or average) cost. We formulate the problem as a Markov decision process and show that the optimal production policy is of the base-stock type with base-stock levels non-decreasing in the demand stages. We also show that the optimal inventory allocation policy is a rationing policy with rationing levels non-decreasing in the demand stages. We also study several important special cases and provide, through numerical experiments, managerial insights including the effect of the different sources of variability on the operating cost and the benefits of such contracts as Vendor Managed Inventory or Collaborative Planning, Forecasting, and Replenishment. Also, we show that a heuristic that ignores the dependence of the base-stock and rationing levels on the demands stages can perform very poorly compared to the optimal policy.
Computers & Industrial Engineering, 1997
This paper considers the scheduling of a manufacturing system with nonresumable setup changes. Th... more This paper considers the scheduling of a manufacturing system with nonresumable setup changes. The system considered involves an unreliable machine that can produce two part types. The switchover from one part type to the other incurs a given constant setup time. The setups are nonresumable, i.e. after a machine repair completion, a setup decision has to be made. The parts have specified constant processing time and constant demand rate. We give a continuous dynamic programming formulation of the problem, which is solved numerically. The optimal setup switching policies are shown to be hedging corridors. Two heuristics, for the determination of the hedging levels, are provided. We show, through simulation, that the two heuristics exhibit good performance.