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Journal Articles by W. Benton

European Journal of Operational Research, 2003

In this paper we consider the purchasing decisions facing a buying firm which receives incrementa... more In this paper we consider the purchasing decisions facing a buying firm which receives incrementally discounted price schedules for a group of items in the presence of constraints such as budgets and space limitations. The constraints take the form of upper bounds on positively weighted linear combinations of order size, dollar volume, unit price and order frequency. We adapt the solution procedures from an earlier paper [Naval Res. Logis. 40 (2) (1993) 255] to treat this case. The results show that simultaneous order quantities for multiple items, offered with separate incremental discounts and subject to joint resource constraints, can be calculated efficiently using a combination of Lagrangean relaxation and, as needed, partial enumeration. This problem proved to be no more and no less tractable than its counterpart with all units discounts.

European Journal of Operational Research, 2003

The ability to determine the optimal frequencies and offsets for independent and unrestricted ord... more The ability to determine the optimal frequencies and offsets for independent and unrestricted ordering cycles for multiple items can be very valuable for managing storage capacity constrained facilities in a supply chain. The complexity of this problem has resulted in researchers focusing on more tractable surrogate problems that are special cases of the base problem. This research has focused on developing fundamental properties of the original problem. We exploit the problem structure and present a heuristic for offsetting independent and unrestricted ordering cycles for items to minimize their joint storage requirements. Heuristics of this type may prove useful in solving the more general problem of selecting order quantities to minimize combined holding, ordering, and storage costs.

The ability to determine the optimal frequencies and offsets for independent and unrestricted ord... more The ability to determine the optimal frequencies and offsets for independent and unrestricted ordering cycles for multiple items can be very valuable for managing storage capacity constrained facilities in a supply chain. The complexity of this problem has resulted in researchers focusing on more tractable surrogate problems that are special cases of the base problem. This research has focused on developing fundamental properties of the original problem.

Papers by W. Benton

European Journal of Operational Research, 2003

In this paper we consider the purchasing decisions facing a buying firm which receives incrementa... more In this paper we consider the purchasing decisions facing a buying firm which receives incrementally discounted price schedules for a group of items in the presence of constraints such as budgets and space limitations. The constraints take the form of upper bounds on positively weighted linear combinations of order size, dollar volume, unit price and order frequency. We adapt the solution procedures from an earlier paper [Naval Res. Logis. 40 (2)(1993) 255] to treat this case. The results show that simultaneous order quantities for ...

European Journal of Operational Research, 2003

In this paper we consider the purchasing decisions facing a buying firm which receives incrementa... more In this paper we consider the purchasing decisions facing a buying firm which receives incrementally discounted price schedules for a group of items in the presence of constraints such as budgets and space limitations. The constraints take the form of upper bounds on positively weighted linear combinations of order size, dollar volume, unit price and order frequency. We adapt the solution procedures from an earlier paper [Naval Res. Logis. 40 (2)(1993) 255] to treat this case. The results show that simultaneous order quantities for ...

Naval Research Logistics, 1993

In this article we investigate situations where the buyer is offered discounted price schedules f... more In this article we investigate situations where the buyer is offered discounted price schedules from alternative vendors. Given various discount schedules, the buyer must make the best buying decision under a variety of constraints, such as limited storage space and restricted inventory budgets. Solutions to this problem can be utilized by the buyer to improve profitability. EOQ models for multiple products with all-units discounts are readily solvable in the absence of constraints spanning the products. However, constrained discounted EOQ models lack convenient mathematical properties. Relaxing the product-spanning constraints produces a dual problem that is separable, but lack of convexity and smoothness opens the door for duality gaps. In this research we present a set of algorithms that collectively find the optimal order vector. Finally, we present numerical examples using actual data, to illustrate the application of the algorithms.

Computers & Operations Research, 1992

The vehicle scheduling problem (VSP) is a problem of interest to many researchers and practitione... more The vehicle scheduling problem (VSP) is a problem of interest to many researchers and practitioners. The general VSP is concerned with minimizing the total distance associated with a fixed set of vehicle routes by determining which vehicles will satisfy the demands at various customer locations. The design of most general distribution systems usually involves the assignment of permanent customer routes even though customer demand patterns are often stochastic in nature. The traditional routing designs implicitly assume that each customer will be visited each period for each route. In reality, a certain number of customers may not require a delivery for a particular period. In this research, we consider three alternative approaches for modelling the VSP with uncertain customer demands. Our solution methodology is a simple but practical heuristic which captures the best of all three approaches in order to handle the dynamic nature of vehicle scheduling under uncertain demand. An experimental design was also implemented to show the sensitivity of the proposed solution methodology to various realistic scheduling situations.

Computers & Operations Research, 1992

The vehicle scheduling problem (VSP) is a problem of interest to many researchers and practitione... more The vehicle scheduling problem (VSP) is a problem of interest to many researchers and practitioners. The general VSP is concerned with minimizing the total distance associated with a fixed set of vehicle routes by determining which vehicles will satisfy the demands at various customer locations. The design of most general distribution systems usually involves the assignment of permanent customer routes even though customer demand patterns are often stochastic in nature. The traditional routing designs implicitly assume that each customer will be visited each period for each route. In reality, a certain number of customers may not require a delivery for a particular period. In this research, we consider three alternative approaches for modelling the VSP with uncertain customer demands. Our solution methodology is a simple but practical heuristic which captures the best of all three approaches in order to handle the dynamic nature of vehicle scheduling under uncertain demand. An experimental design was also implemented to show the sensitivity of the proposed solution methodology to various realistic scheduling situations.

European Journal of Operational Research, 1997

... source of research. As can be seen from the above discussion, there has been very little rigo... more ... source of research. As can be seen from the above discussion, there has been very little rigorous operations research based quantitative measurement of supply chain partner-ship interaction. The application of operations ...

Journal of Operations Management, 2002

... Ling X. Li Corresponding Author Contact Information , a , WC Benton b and G. KeongLeong c. ..... more ... Ling X. Li Corresponding Author Contact Information , a , WC Benton b and G. KeongLeong c. ... The detailed elements in the category of long-term and intermediate operations decisions may vary a little, but the major concept is consistent. ...

European Journal of Operational Research, 2003

In this paper we consider the purchasing decisions facing a buying firm which receives incrementa... more In this paper we consider the purchasing decisions facing a buying firm which receives incrementally discounted price schedules for a group of items in the presence of constraints such as budgets and space limitations. The constraints take the form of upper bounds on positively weighted linear combinations of order size, dollar volume, unit price and order frequency. We adapt the solution procedures from an earlier paper [Naval Res. Logis. 40 (2) (1993) 255] to treat this case. The results show that simultaneous order quantities for multiple items, offered with separate incremental discounts and subject to joint resource constraints, can be calculated efficiently using a combination of Lagrangean relaxation and, as needed, partial enumeration. This problem proved to be no more and no less tractable than its counterpart with all units discounts.

European Journal of Operational Research, 2003

The ability to determine the optimal frequencies and offsets for independent and unrestricted ord... more The ability to determine the optimal frequencies and offsets for independent and unrestricted ordering cycles for multiple items can be very valuable for managing storage capacity constrained facilities in a supply chain. The complexity of this problem has resulted in researchers focusing on more tractable surrogate problems that are special cases of the base problem. This research has focused on developing fundamental properties of the original problem. We exploit the problem structure and present a heuristic for offsetting independent and unrestricted ordering cycles for items to minimize their joint storage requirements. Heuristics of this type may prove useful in solving the more general problem of selecting order quantities to minimize combined holding, ordering, and storage costs.

The ability to determine the optimal frequencies and offsets for independent and unrestricted ord... more The ability to determine the optimal frequencies and offsets for independent and unrestricted ordering cycles for multiple items can be very valuable for managing storage capacity constrained facilities in a supply chain. The complexity of this problem has resulted in researchers focusing on more tractable surrogate problems that are special cases of the base problem. This research has focused on developing fundamental properties of the original problem.

European Journal of Operational Research, 2003

In this paper we consider the purchasing decisions facing a buying firm which receives incrementa... more In this paper we consider the purchasing decisions facing a buying firm which receives incrementally discounted price schedules for a group of items in the presence of constraints such as budgets and space limitations. The constraints take the form of upper bounds on positively weighted linear combinations of order size, dollar volume, unit price and order frequency. We adapt the solution procedures from an earlier paper [Naval Res. Logis. 40 (2)(1993) 255] to treat this case. The results show that simultaneous order quantities for ...

European Journal of Operational Research, 2003

In this paper we consider the purchasing decisions facing a buying firm which receives incrementa... more In this paper we consider the purchasing decisions facing a buying firm which receives incrementally discounted price schedules for a group of items in the presence of constraints such as budgets and space limitations. The constraints take the form of upper bounds on positively weighted linear combinations of order size, dollar volume, unit price and order frequency. We adapt the solution procedures from an earlier paper [Naval Res. Logis. 40 (2)(1993) 255] to treat this case. The results show that simultaneous order quantities for ...

Naval Research Logistics, 1993

In this article we investigate situations where the buyer is offered discounted price schedules f... more In this article we investigate situations where the buyer is offered discounted price schedules from alternative vendors. Given various discount schedules, the buyer must make the best buying decision under a variety of constraints, such as limited storage space and restricted inventory budgets. Solutions to this problem can be utilized by the buyer to improve profitability. EOQ models for multiple products with all-units discounts are readily solvable in the absence of constraints spanning the products. However, constrained discounted EOQ models lack convenient mathematical properties. Relaxing the product-spanning constraints produces a dual problem that is separable, but lack of convexity and smoothness opens the door for duality gaps. In this research we present a set of algorithms that collectively find the optimal order vector. Finally, we present numerical examples using actual data, to illustrate the application of the algorithms.

Computers & Operations Research, 1992

The vehicle scheduling problem (VSP) is a problem of interest to many researchers and practitione... more The vehicle scheduling problem (VSP) is a problem of interest to many researchers and practitioners. The general VSP is concerned with minimizing the total distance associated with a fixed set of vehicle routes by determining which vehicles will satisfy the demands at various customer locations. The design of most general distribution systems usually involves the assignment of permanent customer routes even though customer demand patterns are often stochastic in nature. The traditional routing designs implicitly assume that each customer will be visited each period for each route. In reality, a certain number of customers may not require a delivery for a particular period. In this research, we consider three alternative approaches for modelling the VSP with uncertain customer demands. Our solution methodology is a simple but practical heuristic which captures the best of all three approaches in order to handle the dynamic nature of vehicle scheduling under uncertain demand. An experimental design was also implemented to show the sensitivity of the proposed solution methodology to various realistic scheduling situations.

Computers & Operations Research, 1992

The vehicle scheduling problem (VSP) is a problem of interest to many researchers and practitione... more The vehicle scheduling problem (VSP) is a problem of interest to many researchers and practitioners. The general VSP is concerned with minimizing the total distance associated with a fixed set of vehicle routes by determining which vehicles will satisfy the demands at various customer locations. The design of most general distribution systems usually involves the assignment of permanent customer routes even though customer demand patterns are often stochastic in nature. The traditional routing designs implicitly assume that each customer will be visited each period for each route. In reality, a certain number of customers may not require a delivery for a particular period. In this research, we consider three alternative approaches for modelling the VSP with uncertain customer demands. Our solution methodology is a simple but practical heuristic which captures the best of all three approaches in order to handle the dynamic nature of vehicle scheduling under uncertain demand. An experimental design was also implemented to show the sensitivity of the proposed solution methodology to various realistic scheduling situations.

European Journal of Operational Research, 1997

... source of research. As can be seen from the above discussion, there has been very little rigo... more ... source of research. As can be seen from the above discussion, there has been very little rigorous operations research based quantitative measurement of supply chain partner-ship interaction. The application of operations ...

Journal of Operations Management, 2002

... Ling X. Li Corresponding Author Contact Information , a , WC Benton b and G. KeongLeong c. ..... more ... Ling X. Li Corresponding Author Contact Information , a , WC Benton b and G. KeongLeong c. ... The detailed elements in the category of long-term and intermediate operations decisions may vary a little, but the major concept is consistent. ...