Nonstationary stochastic periodic review inventory problems with proportional costs occur in a nu... more Nonstationary stochastic periodic review inventory problems with proportional costs occur in a number of industrial settings with seasonal patterns, trends, business cycles, and limited life items. Myopic policies for such problems order as if the salvage value in the current period for ending inventory were the full purchase price, so that information about the future would not be needed. They
By R. Anupindi, T. Morton and D. Pentico; The Non-Stationary Stochastic Lead-Time Inventory Probl... more By R. Anupindi, T. Morton and D. Pentico; The Non-Stationary Stochastic Lead-Time Inventory Problem: Near-Myopic Bounds, Heuristics, and Testing.
If some, but not all, customers are willing to wait for an out-of-stock product to become availab... more If some, but not all, customers are willing to wait for an out-of-stock product to become available, sellers may be able to increase their profits by offering a price discount to backorder demands rather than losing those sales. We modify an existing model for the deterministic EOQ with partial backordering by making the backordering percentage a function of the size
International Journal of Production Economics, 2015
ABSTRACT A significant extension of the classic EOQ model is the assumption that realized demand ... more ABSTRACT A significant extension of the classic EOQ model is the assumption that realized demand decreases if customers are forced to backorder. To capture the way this decrease depends on the waiting time, different functional forms have been proposed, ranging from the simple (e.g., constant or linear forms) to the complex (e.g., exponential or rational forms.) This paper explores the question of whether the computationally more tractable simple forms can give high quality approximations to the complex ones. We calculated average and worst case performance on a representative suite of test problems, each characterized by a “backorder resistance” parameter. We show that for low values of this parameter, results from the approximating functions are virtually as good as those from the correct ones, and for high values of the parameter, very good results can be achieved by using an iterative technique.
ABSTRACT The classic Economic Order Quantity model assumes that an order is paid for at the time ... more ABSTRACT The classic Economic Order Quantity model assumes that an order is paid for at the time of its receipt. In practice, suppliers may require purchasers to pay a fraction of the order’s cost in advance and sometimes allow them to divide the prepayment into multiple equal-sized parts to be paid during a fixed lead time. In this paper, an EOQ model with multiple prepayments under three different conditions: (a) no shortage, (b) full backordering and (c) partial backordering, are developed. Numerical examples illustrate the proposed models and solution method.
ABSTRACT In many transactions concerning selling and buying, a specified delay of payment is offe... more ABSTRACT In many transactions concerning selling and buying, a specified delay of payment is offered or accepted by the seller. This can be regarded as a kind of discount and has potential consequences for the order size. These kinds of effects are not explicitly incorporated in the classical formulas for economic order quantities (EOQ). In this research we consider an EOQ problem under partial delayed payment. A fraction of the purchasing cost must be paid at the beginning of the period and the remaining amount can be paid later. Shortages are permitted and occur as a combination of backorders and lost sales. The aim of this paper is to determine the order and shortage quantities.
Determining an order quantity when quantity discounts are available is a major interest of materi... more Determining an order quantity when quantity discounts are available is a major interest of material managers. A supplier offering quantity discounts is a common strategy to entice the buyers to purchase more. In this paper, EOQ models with incremental discounts and either full or partial backordering are developed for the first time. Numerical examples illustrate the proposed models and solution methods.
While there has been considerable work over the years on multistage lot-sizing models, particular... more While there has been considerable work over the years on multistage lot-sizing models, particularly in an MRP environment, there has been relatively little work on systems recognizing the WIP effects when there is gradual conversion of the components into the final product, as in production planning using the EPQ model for planning the final product. Here we consider lot-sizing planning for a two-stage system in which the final product is planned using an EPQ model with partial backordering and the production of the components is controlled using basic EPQ models without backordering.
While there has been considerable work over the years on multistage lot-sizing models, particular... more While there has been considerable work over the years on multistage lot-sizing models, particularly in an MRP environment, there has been relatively little work on systems recognizing the WIP effects when there is gradual, rather than batch, conversion of the components into the final product. We consider lot-sizing planning for a two-stage system in which the final product is planned using an EPQ model with partial backordering and the production of the components is controlled using basic EPQ models without backordering.
In previous work we established a closed-form optimal stocking strategy for an EPQ model with par... more In previous work we established a closed-form optimal stocking strategy for an EPQ model with partial backordering at a constant rate β. Here we extend this work to allow for the possibility that the percentage of demand backordered will increase when production starts again. We show how our previous model can be adapted to find the optimal decision variable values for this new assumption and develop the condition that the initial value of β must meet for partial backordering to be optimal.
By R. Anupindi, T. Morton and D. Pentico; The Non-Stationary Stochastic Lead-Time Inventory Probl... more By R. Anupindi, T. Morton and D. Pentico; The Non-Stationary Stochastic Lead-Time Inventory Problem: Near-Myopic Bounds, Heuristics, and Testing.
Nonstationary stochastic periodic review inventory problems with proportional costs occur in a nu... more Nonstationary stochastic periodic review inventory problems with proportional costs occur in a number of industrial settings with seasonal patterns, trends, business cycles, and limited life items. Myopic policies for such problems order as if the salvage value in the current period for ending inventory were the full purchase price, so that information about the future would not be needed. They
International Transactions in Operational Research, 2011
If some, but not all, customers are willing to wait for an out-of-stock product to become availab... more If some, but not all, customers are willing to wait for an out-of-stock product to become available, sellers may be able to increase their profits by offering a price discount to increase the number of backordered demands rather than losing those sales. We modify an existing model for the deterministic EOQ with partial backordering by making the backordering percentage a function of the size of the discount. We combine results about the optimal solution for a partial backordering model with a fixed backorder percentage and a search procedure to determine whether offering a discount is optimal and, if so, how large the discount should be to maximize profit.
International Journal of Production Economics, 2011
Our original models for the EOQ and EPQ with partial backordering assumed that the backordering r... more Our original models for the EOQ and EPQ with partial backordering assumed that the backordering rate, b, is a constant. In this paper we extend those models to allow b to increase linearly as the time until delivery decreases. We show how those previous models can be adapted to find the optimal decision variable values for this new assumption and develop, for each model type, a condition that the initial value of b must meet for partial backordering to be optimal.
International Journal of Production Economics, 2014
ABSTRACT The classic Economic Order Quantity model assumes that the unit purchasing cost is not b... more ABSTRACT The classic Economic Order Quantity model assumes that the unit purchasing cost is not based on the order quantity. In practice, a supplier may offer purchasers an all-units discount. We develop a model and solution procedure for the EOQ with all-unit discounts and partial backordering at a constant rate. We show, and illustrate with a numerical example, how that model can be used to find the solution for the EOQ with discount and full backordering. A multi-factor experiment is used to gain insights into the improvement in performance of the proposed procedure relative to using the basic EOQ or the EOQ with full backordering and to identify the model parameters that have the greatest impact on the model's performance.
International Journal of Logistics Research and Applications, 2003
... et al., 2000). The requirements for firms doing business in the EU are clear, and these regul... more ... et al., 2000). The requirements for firms doing business in the EU are clear, and these regulations may also act as entry barriers for firms not aware of the changes required for reverse logistics activities. Legislation in the USA ...
International Journal of Industrial Organization, 1994
Page 1. Discrete Choice Theory of Product Differentiation Simon P. Anderson André de Palma Jacque... more Page 1. Discrete Choice Theory of Product Differentiation Simon P. Anderson André de Palma Jacques-François Thisse Page 2. Page 3. ...
ABSTRACT A constant unit purchase cost is one of the main assumptions in the classic Economic Ord... more ABSTRACT A constant unit purchase cost is one of the main assumptions in the classic Economic Order Quantity model. In practice, suppliers sometimes face a known price increase. In this paper, we develop EOQ models with a known price increase and partial backordering under two different assumptions about when the increase will occur. We prove the concavity of the extra profit functions for both scenarios if a special order is placed just before the price increases. A solution method is proposed and numerical examples are presented.
ABSTRACT A constant unit purchase cost is one of the main assumptions in the classic economic ord... more ABSTRACT A constant unit purchase cost is one of the main assumptions in the classic economic order quantity model. In practice, suppliers sometimes offer special sale prices to stimulate sales or decrease inventories of certain items. In this paper we develop an EOQ model with a special sale price and partial backordering. We prove the convexity of the cost-reduction function if a special order is placed at the special sale price. A solution method is proposed and numerical examples are presented. (c) 2012 Elsevier B.V. All rights reserved.
Models for the basic deterministic EOQ or EPQ problem with partial backordering or backlogging ma... more Models for the basic deterministic EOQ or EPQ problem with partial backordering or backlogging make all the assumptions of the classic EOQ or EPQ model with full backordering except that only a fraction of the demand during the stockout period is backordered. In this survey we review deterministic models that have been developed over the past 40 years that address the basic models and extensions that add other considerations, such as pricing, perishable or deteriorating inventory, time-varying or stock-dependent demand, quantity discounts, or multiple-warehouses.
Nonstationary stochastic periodic review inventory problems with proportional costs occur in a nu... more Nonstationary stochastic periodic review inventory problems with proportional costs occur in a number of industrial settings with seasonal patterns, trends, business cycles, and limited life items. Myopic policies for such problems order as if the salvage value in the current period for ending inventory were the full purchase price, so that information about the future would not be needed. They
By R. Anupindi, T. Morton and D. Pentico; The Non-Stationary Stochastic Lead-Time Inventory Probl... more By R. Anupindi, T. Morton and D. Pentico; The Non-Stationary Stochastic Lead-Time Inventory Problem: Near-Myopic Bounds, Heuristics, and Testing.
If some, but not all, customers are willing to wait for an out-of-stock product to become availab... more If some, but not all, customers are willing to wait for an out-of-stock product to become available, sellers may be able to increase their profits by offering a price discount to backorder demands rather than losing those sales. We modify an existing model for the deterministic EOQ with partial backordering by making the backordering percentage a function of the size
International Journal of Production Economics, 2015
ABSTRACT A significant extension of the classic EOQ model is the assumption that realized demand ... more ABSTRACT A significant extension of the classic EOQ model is the assumption that realized demand decreases if customers are forced to backorder. To capture the way this decrease depends on the waiting time, different functional forms have been proposed, ranging from the simple (e.g., constant or linear forms) to the complex (e.g., exponential or rational forms.) This paper explores the question of whether the computationally more tractable simple forms can give high quality approximations to the complex ones. We calculated average and worst case performance on a representative suite of test problems, each characterized by a “backorder resistance” parameter. We show that for low values of this parameter, results from the approximating functions are virtually as good as those from the correct ones, and for high values of the parameter, very good results can be achieved by using an iterative technique.
ABSTRACT The classic Economic Order Quantity model assumes that an order is paid for at the time ... more ABSTRACT The classic Economic Order Quantity model assumes that an order is paid for at the time of its receipt. In practice, suppliers may require purchasers to pay a fraction of the order’s cost in advance and sometimes allow them to divide the prepayment into multiple equal-sized parts to be paid during a fixed lead time. In this paper, an EOQ model with multiple prepayments under three different conditions: (a) no shortage, (b) full backordering and (c) partial backordering, are developed. Numerical examples illustrate the proposed models and solution method.
ABSTRACT In many transactions concerning selling and buying, a specified delay of payment is offe... more ABSTRACT In many transactions concerning selling and buying, a specified delay of payment is offered or accepted by the seller. This can be regarded as a kind of discount and has potential consequences for the order size. These kinds of effects are not explicitly incorporated in the classical formulas for economic order quantities (EOQ). In this research we consider an EOQ problem under partial delayed payment. A fraction of the purchasing cost must be paid at the beginning of the period and the remaining amount can be paid later. Shortages are permitted and occur as a combination of backorders and lost sales. The aim of this paper is to determine the order and shortage quantities.
Determining an order quantity when quantity discounts are available is a major interest of materi... more Determining an order quantity when quantity discounts are available is a major interest of material managers. A supplier offering quantity discounts is a common strategy to entice the buyers to purchase more. In this paper, EOQ models with incremental discounts and either full or partial backordering are developed for the first time. Numerical examples illustrate the proposed models and solution methods.
While there has been considerable work over the years on multistage lot-sizing models, particular... more While there has been considerable work over the years on multistage lot-sizing models, particularly in an MRP environment, there has been relatively little work on systems recognizing the WIP effects when there is gradual conversion of the components into the final product, as in production planning using the EPQ model for planning the final product. Here we consider lot-sizing planning for a two-stage system in which the final product is planned using an EPQ model with partial backordering and the production of the components is controlled using basic EPQ models without backordering.
While there has been considerable work over the years on multistage lot-sizing models, particular... more While there has been considerable work over the years on multistage lot-sizing models, particularly in an MRP environment, there has been relatively little work on systems recognizing the WIP effects when there is gradual, rather than batch, conversion of the components into the final product. We consider lot-sizing planning for a two-stage system in which the final product is planned using an EPQ model with partial backordering and the production of the components is controlled using basic EPQ models without backordering.
In previous work we established a closed-form optimal stocking strategy for an EPQ model with par... more In previous work we established a closed-form optimal stocking strategy for an EPQ model with partial backordering at a constant rate β. Here we extend this work to allow for the possibility that the percentage of demand backordered will increase when production starts again. We show how our previous model can be adapted to find the optimal decision variable values for this new assumption and develop the condition that the initial value of β must meet for partial backordering to be optimal.
By R. Anupindi, T. Morton and D. Pentico; The Non-Stationary Stochastic Lead-Time Inventory Probl... more By R. Anupindi, T. Morton and D. Pentico; The Non-Stationary Stochastic Lead-Time Inventory Problem: Near-Myopic Bounds, Heuristics, and Testing.
Nonstationary stochastic periodic review inventory problems with proportional costs occur in a nu... more Nonstationary stochastic periodic review inventory problems with proportional costs occur in a number of industrial settings with seasonal patterns, trends, business cycles, and limited life items. Myopic policies for such problems order as if the salvage value in the current period for ending inventory were the full purchase price, so that information about the future would not be needed. They
International Transactions in Operational Research, 2011
If some, but not all, customers are willing to wait for an out-of-stock product to become availab... more If some, but not all, customers are willing to wait for an out-of-stock product to become available, sellers may be able to increase their profits by offering a price discount to increase the number of backordered demands rather than losing those sales. We modify an existing model for the deterministic EOQ with partial backordering by making the backordering percentage a function of the size of the discount. We combine results about the optimal solution for a partial backordering model with a fixed backorder percentage and a search procedure to determine whether offering a discount is optimal and, if so, how large the discount should be to maximize profit.
International Journal of Production Economics, 2011
Our original models for the EOQ and EPQ with partial backordering assumed that the backordering r... more Our original models for the EOQ and EPQ with partial backordering assumed that the backordering rate, b, is a constant. In this paper we extend those models to allow b to increase linearly as the time until delivery decreases. We show how those previous models can be adapted to find the optimal decision variable values for this new assumption and develop, for each model type, a condition that the initial value of b must meet for partial backordering to be optimal.
International Journal of Production Economics, 2014
ABSTRACT The classic Economic Order Quantity model assumes that the unit purchasing cost is not b... more ABSTRACT The classic Economic Order Quantity model assumes that the unit purchasing cost is not based on the order quantity. In practice, a supplier may offer purchasers an all-units discount. We develop a model and solution procedure for the EOQ with all-unit discounts and partial backordering at a constant rate. We show, and illustrate with a numerical example, how that model can be used to find the solution for the EOQ with discount and full backordering. A multi-factor experiment is used to gain insights into the improvement in performance of the proposed procedure relative to using the basic EOQ or the EOQ with full backordering and to identify the model parameters that have the greatest impact on the model's performance.
International Journal of Logistics Research and Applications, 2003
... et al., 2000). The requirements for firms doing business in the EU are clear, and these regul... more ... et al., 2000). The requirements for firms doing business in the EU are clear, and these regulations may also act as entry barriers for firms not aware of the changes required for reverse logistics activities. Legislation in the USA ...
International Journal of Industrial Organization, 1994
Page 1. Discrete Choice Theory of Product Differentiation Simon P. Anderson André de Palma Jacque... more Page 1. Discrete Choice Theory of Product Differentiation Simon P. Anderson André de Palma Jacques-François Thisse Page 2. Page 3. ...
ABSTRACT A constant unit purchase cost is one of the main assumptions in the classic Economic Ord... more ABSTRACT A constant unit purchase cost is one of the main assumptions in the classic Economic Order Quantity model. In practice, suppliers sometimes face a known price increase. In this paper, we develop EOQ models with a known price increase and partial backordering under two different assumptions about when the increase will occur. We prove the concavity of the extra profit functions for both scenarios if a special order is placed just before the price increases. A solution method is proposed and numerical examples are presented.
ABSTRACT A constant unit purchase cost is one of the main assumptions in the classic economic ord... more ABSTRACT A constant unit purchase cost is one of the main assumptions in the classic economic order quantity model. In practice, suppliers sometimes offer special sale prices to stimulate sales or decrease inventories of certain items. In this paper we develop an EOQ model with a special sale price and partial backordering. We prove the convexity of the cost-reduction function if a special order is placed at the special sale price. A solution method is proposed and numerical examples are presented. (c) 2012 Elsevier B.V. All rights reserved.
Models for the basic deterministic EOQ or EPQ problem with partial backordering or backlogging ma... more Models for the basic deterministic EOQ or EPQ problem with partial backordering or backlogging make all the assumptions of the classic EOQ or EPQ model with full backordering except that only a fraction of the demand during the stockout period is backordered. In this survey we review deterministic models that have been developed over the past 40 years that address the basic models and extensions that add other considerations, such as pricing, perishable or deteriorating inventory, time-varying or stock-dependent demand, quantity discounts, or multiple-warehouses.
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Papers by David Pentico