Prakash Abad | McMaster University (original) (raw)
Papers by Prakash Abad
Computers & Operations Research, Feb 1, 1994
... 492506. Full Text via CrossRef. 9. E. Kalai and D. Smordinsky, Other solutions to Nash'... more ... 492506. Full Text via CrossRef. 9. E. Kalai and D. Smordinsky, Other solutions to Nash's bargaining problem. ... Prakash L. Abad is Associate Professor of Management Science at the Michael G. DeGroote School of Business, McMaster University, Hamilton, Canada. ...
International Journal of Production Economics, Mar 1, 2008
Omega, 1982
An interdependent marketing-production planning model is developed based on control theory. T he ... more An interdependent marketing-production planning model is developed based on control theory. T he overall model is a composition of the Vidale-Wolfe model relating advertising rates to sales rates, and the HMMS production/ inventory plann ing model. Using the overall model as a reference point, it is shown that in certain circllll lS tances a de�entralized (separate) marketing production planning process can yield near optimal results. A transfer pricing mechanism provides the best results and several examples are presented to illustrate the cases in which decentralized planning does and does not work well.
Decision Sciences, Jul 1, 1997
A common practice in product distribution is the case in which the supplier offers a temporary re... more A common practice in product distribution is the case in which the supplier offers a temporary reduction in price. It is suggested in the literature that in such situations, the reseller may engage in forward buying (i.e., purchasing additional stock at the reduced price offered by the supplier for later sale at the regular selling price). In this paper, a model is formulated of the reseller's response when the supplier offers a temporary reduction in price. It is assumed that the market demand for the product is elastic with respect to the selling price the reseller sets. A procedure for determining the optimal response of the reseller is developed. The model presented in this paper can easily be adapted to the case in which the reseller faces a permanent increase in the price charged by the supplier.
International Journal of Systems Science, Nov 1, 1989
A multi-product multi-market segment optimal control model for coordinating marketing and product... more A multi-product multi-market segment optimal control model for coordinating marketing and production decisions in a firm is presented. On the marketing side, the model considers pricing and the rate of advertising expenditure for each product for each market segment as decision (i.e. control) variables. On the production side, the production rate for an individual product is considered as a decision variable. The model assumes that demand for a product in each market segment is subject to seasonal and other exogenous effects. The model includes the following two special cases: (a) single-product multiple-market segments, (b) multiple products having purely exogenous, time-varying demand. The production planning subproblem in the model represents a class of partially singular optimal control problems. A solution procedure using Pontryagin's maximum principle is designed to solve the partially singular control problem. A hierarchical approach is then used in designing the solution procedure for the overall ...
Optimal Control Applications & Methods, Jul 1, 1993
Consider a production process whose performance deteriorates over time. It is assumed that the pr... more Consider a production process whose performance deteriorates over time. It is assumed that the process performance can be measured in terms of the proportion of 'good' (non-defective) units of end items produced. Preventive maintenance may be applied to the process to slow down the rate of decline of (or improve) the process performance. This paper incorporates a dynamic maintenance problem into a production control model and proposes a simultaneous determination of optimal production and maintenance policies. It focuses on the study of possible trade-offs between the cost (level) of preventive maintenance applied to the process and the output of the production process. KEY WORDS Production-maintenance models Optimal production policies Optimal maintenance policies Singular arc optimal control Decomposition of serial systems q (t) =a (t) + h (m)k (u) q (t)
European Journal of Operational Research, May 1, 1993
Three heuristic procedures for the two group discriminant problem are developed that minimize the... more Three heuristic procedures for the two group discriminant problem are developed that minimize the total expected cost of miselassification in the training sample. The approach is shown through a systematic experiment to generate near optimal solutions and to be efficient in terms of computational effort when compared to existing research.
Management Science, Aug 1, 1996
We formulate a generalized model of dynamic pricing and lot-sizing by a reseller who sells a peri... more We formulate a generalized model of dynamic pricing and lot-sizing by a reseller who sells a perishable good. We assume that when it is economic to backlog demand, the reseller can plan for periods of shortage during which demand can be partially backordered. When the good is highly perishable, the reseller may need to backlog demand in order to market the good at a reasonable price. We present a simple solution procedure for solving the optimization problem. The procedure entails solving first a single nonlinear equation and then, if required, two nonlinear equations.
An optimal control model of a marketing-production system is formulated. The Marketing subsystem ... more An optimal control model of a marketing-production system is formulated. The Marketing subsystem in the model is represented by the Nerlove-Arrow model of advertising and the production subsystem by the HMM S model of production planning. Using the proposed model as a reference point, a decentralized procedure is designed for coordinating pricing, advertising, production and workforce level related decisions in a firm. Attention is especially devoted to the case when the demand for the product is highly seasonal. An example is presented to illustrate the procedure.
International Journal of Systems Science, May 1, 1985
A two-level algorithm is presented for decentralized control of a serially connected dynamic syst... more A two-level algorithm is presented for decentralized control of a serially connected dynamic system. The algorithm exploits the special structure of serially connected systems. Convergence of the algorithm is proved for linear-quadratic systems.
European Journal of Operational Research, 1994
... pp. 422 (this issue). Eisenbeis and Avery, 1972R.A. Eisenbeis and RB Avery, Discriminant Ana... more ... pp. 422 (this issue). Eisenbeis and Avery, 1972R.A. Eisenbeis and RB Avery, Discriminant Analysis and Classification Procedures, Lexington Books, Lexington, MA (1972). Erenguc ... pp. 179188. Freed and Glover, 1981N. Freed ...
Iie Transactions, Nov 1, 1998
In this paper, we consider the inventory control problem in a periodic review returnable system. ... more In this paper, we consider the inventory control problem in a periodic review returnable system. In a returnable system, containers are returned by consumers to the manufacturer for reuse. We view the returns in a given period to be a stochastic function of the number of containers out in the field. Using dynamic programming, we derive the optimal inventory control policy for the system.
Journal of the Operational Research Society, Jun 1, 1988
This paper considers the joint pricing and the lot-size determination problem faced by a retailer... more This paper considers the joint pricing and the lot-size determination problem faced by a retailer when he purchases a product for which the supplier offers incremental quantity discounts. Two common demand functions are considered:(1) the constant price-elasticity ...
Asia-Pacific Journal of Operational Research, Mar 1, 2006
Manufacturers and suppliers offer temporary reductions (or permanent increases) in the price char... more Manufacturers and suppliers offer temporary reductions (or permanent increases) in the price charged to the resellers for a variety of reasons. The trade promotion may be offered to the reseller at a single point in time or over a finite time-span. In addition, in reselling situations, the end demand tends to be sensitive to selling price. It is commonly found that under such trade promotion (or in stockpiling to an announced price increase), not all the quantity purchased by the reseller at discount may be passed on to the final consumer at a reduced selling price. In fact, previous studies have shown that it is optimal for the reseller to carry forward some of the quantity purchased at discount and sell it later at the regular price. It has been suggested in the literature that by placing a restriction on the reseller's purchase quantity, the supplier can restrict the reseller's forward buy quantity. In this paper, we evaluate this approach. In the rest of the paper, we present alternate schemes which are easy to administer and which insure that the supplier avoids the spike in demand that occurs in the unconstrained problem.
International Journal of Systems Science, Oct 1, 1974
In this paper a solution is presented to an important marketing problem : the timing of advertisi... more In this paper a solution is presented to an important marketing problem : the timing of advertising expenditure. Using a differential equation to model the relationship between the sales and advertising rates and using profit as a criterion, a synthesis of the optimal dynamic advertising policy as a function of the current sales level and length of the campaign is derived. In addition, using profit as a criterion, the profitability under an optimal dynamic advertising policy is compared with the profits obtained using an optimal static policy. It is shown that a significant increase in profits can result from employing the optimal dynamic policy.
Asia-Pacific Journal of Operational Research, Oct 1, 2009
In this paper, we consider a seller–buyer channel in which marketing expenditure is an endogenous... more In this paper, we consider a seller–buyer channel in which marketing expenditure is an endogenous decision for the buyer. We assume that both the unit marketing expenditure and the unit price charged by the buyer influence the end demand for the product. We model the seller–buyer relationship as a non-cooperative as well as a cooperative game. We investigate the non-cooperative game from two perspectives: the Seller–Stackelberg model and the Buyer–Stackelberg model. In the cooperative game, we provide a procedure for outlining Pareto efficient solutions. For each model, we present a numerical example as well as sensitivity analysis with respect to the two key parameters in the model.
European Journal of Operational Research, Oct 1, 1987
An optimal control model of a joint finance-marketing-production system is formulated. The market... more An optimal control model of a joint finance-marketing-production system is formulated. The marketing subsystem in the model is represented by the Nerlove-Arrow model of advertising and the production subsystem is represented by the HMMS model of production planning. Using the model as a reference point, a decentralized procedure for coordinating finance, marketing and production decisions is designed. The procedure appears to have the following two characteristics: (1) a discontinuous discount interest rate and (2) a time-varying transfer price between marketing and production functions. An example is presented to illustrate the procedure. The case of sequential planning of marketing-production and finance decisions is considered and the resultant marketing-production subsystem model is described. A solution procedure is outlined for the subsystem model.
Decision Sciences, Nov 12, 1991
ABSTRACTA new LP‐based algorithm is developed to determine the optimal solution to the two‐group ... more ABSTRACTA new LP‐based algorithm is developed to determine the optimal solution to the two‐group classification problem. The procedure is efficient when compared to current research in a simulation study.
Computers & Operations Research, 2003
Manufacturers and other suppliers offer temporary reduction in the price charged to resellers for... more Manufacturers and other suppliers offer temporary reduction in the price charged to resellers for a variety of reasons. Typically the trade promotion lasts for some finite time-span. In addition, in reselling situations, the end demand tends to be sensitive to selling price. Thus, when the trade promotion takes place, there is possibility that not all the quantity purchased by the
Decision Sciences, Sep 1, 1988
... count EOQ model. In the retailer problem, however. there are two decision variables:price and... more ... count EOQ model. In the retailer problem, however. there are two decision variables:price and lot size. The retailer has to determine the lot size for purchasing the prod-uct and the price for selling the product. The two decisions ...
Computers & Operations Research, Feb 1, 1994
... 492506. Full Text via CrossRef. 9. E. Kalai and D. Smordinsky, Other solutions to Nash'... more ... 492506. Full Text via CrossRef. 9. E. Kalai and D. Smordinsky, Other solutions to Nash's bargaining problem. ... Prakash L. Abad is Associate Professor of Management Science at the Michael G. DeGroote School of Business, McMaster University, Hamilton, Canada. ...
International Journal of Production Economics, Mar 1, 2008
Omega, 1982
An interdependent marketing-production planning model is developed based on control theory. T he ... more An interdependent marketing-production planning model is developed based on control theory. T he overall model is a composition of the Vidale-Wolfe model relating advertising rates to sales rates, and the HMMS production/ inventory plann ing model. Using the overall model as a reference point, it is shown that in certain circllll lS tances a de�entralized (separate) marketing production planning process can yield near optimal results. A transfer pricing mechanism provides the best results and several examples are presented to illustrate the cases in which decentralized planning does and does not work well.
Decision Sciences, Jul 1, 1997
A common practice in product distribution is the case in which the supplier offers a temporary re... more A common practice in product distribution is the case in which the supplier offers a temporary reduction in price. It is suggested in the literature that in such situations, the reseller may engage in forward buying (i.e., purchasing additional stock at the reduced price offered by the supplier for later sale at the regular selling price). In this paper, a model is formulated of the reseller's response when the supplier offers a temporary reduction in price. It is assumed that the market demand for the product is elastic with respect to the selling price the reseller sets. A procedure for determining the optimal response of the reseller is developed. The model presented in this paper can easily be adapted to the case in which the reseller faces a permanent increase in the price charged by the supplier.
International Journal of Systems Science, Nov 1, 1989
A multi-product multi-market segment optimal control model for coordinating marketing and product... more A multi-product multi-market segment optimal control model for coordinating marketing and production decisions in a firm is presented. On the marketing side, the model considers pricing and the rate of advertising expenditure for each product for each market segment as decision (i.e. control) variables. On the production side, the production rate for an individual product is considered as a decision variable. The model assumes that demand for a product in each market segment is subject to seasonal and other exogenous effects. The model includes the following two special cases: (a) single-product multiple-market segments, (b) multiple products having purely exogenous, time-varying demand. The production planning subproblem in the model represents a class of partially singular optimal control problems. A solution procedure using Pontryagin's maximum principle is designed to solve the partially singular control problem. A hierarchical approach is then used in designing the solution procedure for the overall ...
Optimal Control Applications & Methods, Jul 1, 1993
Consider a production process whose performance deteriorates over time. It is assumed that the pr... more Consider a production process whose performance deteriorates over time. It is assumed that the process performance can be measured in terms of the proportion of 'good' (non-defective) units of end items produced. Preventive maintenance may be applied to the process to slow down the rate of decline of (or improve) the process performance. This paper incorporates a dynamic maintenance problem into a production control model and proposes a simultaneous determination of optimal production and maintenance policies. It focuses on the study of possible trade-offs between the cost (level) of preventive maintenance applied to the process and the output of the production process. KEY WORDS Production-maintenance models Optimal production policies Optimal maintenance policies Singular arc optimal control Decomposition of serial systems q (t) =a (t) + h (m)k (u) q (t)
European Journal of Operational Research, May 1, 1993
Three heuristic procedures for the two group discriminant problem are developed that minimize the... more Three heuristic procedures for the two group discriminant problem are developed that minimize the total expected cost of miselassification in the training sample. The approach is shown through a systematic experiment to generate near optimal solutions and to be efficient in terms of computational effort when compared to existing research.
Management Science, Aug 1, 1996
We formulate a generalized model of dynamic pricing and lot-sizing by a reseller who sells a peri... more We formulate a generalized model of dynamic pricing and lot-sizing by a reseller who sells a perishable good. We assume that when it is economic to backlog demand, the reseller can plan for periods of shortage during which demand can be partially backordered. When the good is highly perishable, the reseller may need to backlog demand in order to market the good at a reasonable price. We present a simple solution procedure for solving the optimization problem. The procedure entails solving first a single nonlinear equation and then, if required, two nonlinear equations.
An optimal control model of a marketing-production system is formulated. The Marketing subsystem ... more An optimal control model of a marketing-production system is formulated. The Marketing subsystem in the model is represented by the Nerlove-Arrow model of advertising and the production subsystem by the HMM S model of production planning. Using the proposed model as a reference point, a decentralized procedure is designed for coordinating pricing, advertising, production and workforce level related decisions in a firm. Attention is especially devoted to the case when the demand for the product is highly seasonal. An example is presented to illustrate the procedure.
International Journal of Systems Science, May 1, 1985
A two-level algorithm is presented for decentralized control of a serially connected dynamic syst... more A two-level algorithm is presented for decentralized control of a serially connected dynamic system. The algorithm exploits the special structure of serially connected systems. Convergence of the algorithm is proved for linear-quadratic systems.
European Journal of Operational Research, 1994
... pp. 422 (this issue). Eisenbeis and Avery, 1972R.A. Eisenbeis and RB Avery, Discriminant Ana... more ... pp. 422 (this issue). Eisenbeis and Avery, 1972R.A. Eisenbeis and RB Avery, Discriminant Analysis and Classification Procedures, Lexington Books, Lexington, MA (1972). Erenguc ... pp. 179188. Freed and Glover, 1981N. Freed ...
Iie Transactions, Nov 1, 1998
In this paper, we consider the inventory control problem in a periodic review returnable system. ... more In this paper, we consider the inventory control problem in a periodic review returnable system. In a returnable system, containers are returned by consumers to the manufacturer for reuse. We view the returns in a given period to be a stochastic function of the number of containers out in the field. Using dynamic programming, we derive the optimal inventory control policy for the system.
Journal of the Operational Research Society, Jun 1, 1988
This paper considers the joint pricing and the lot-size determination problem faced by a retailer... more This paper considers the joint pricing and the lot-size determination problem faced by a retailer when he purchases a product for which the supplier offers incremental quantity discounts. Two common demand functions are considered:(1) the constant price-elasticity ...
Asia-Pacific Journal of Operational Research, Mar 1, 2006
Manufacturers and suppliers offer temporary reductions (or permanent increases) in the price char... more Manufacturers and suppliers offer temporary reductions (or permanent increases) in the price charged to the resellers for a variety of reasons. The trade promotion may be offered to the reseller at a single point in time or over a finite time-span. In addition, in reselling situations, the end demand tends to be sensitive to selling price. It is commonly found that under such trade promotion (or in stockpiling to an announced price increase), not all the quantity purchased by the reseller at discount may be passed on to the final consumer at a reduced selling price. In fact, previous studies have shown that it is optimal for the reseller to carry forward some of the quantity purchased at discount and sell it later at the regular price. It has been suggested in the literature that by placing a restriction on the reseller's purchase quantity, the supplier can restrict the reseller's forward buy quantity. In this paper, we evaluate this approach. In the rest of the paper, we present alternate schemes which are easy to administer and which insure that the supplier avoids the spike in demand that occurs in the unconstrained problem.
International Journal of Systems Science, Oct 1, 1974
In this paper a solution is presented to an important marketing problem : the timing of advertisi... more In this paper a solution is presented to an important marketing problem : the timing of advertising expenditure. Using a differential equation to model the relationship between the sales and advertising rates and using profit as a criterion, a synthesis of the optimal dynamic advertising policy as a function of the current sales level and length of the campaign is derived. In addition, using profit as a criterion, the profitability under an optimal dynamic advertising policy is compared with the profits obtained using an optimal static policy. It is shown that a significant increase in profits can result from employing the optimal dynamic policy.
Asia-Pacific Journal of Operational Research, Oct 1, 2009
In this paper, we consider a seller–buyer channel in which marketing expenditure is an endogenous... more In this paper, we consider a seller–buyer channel in which marketing expenditure is an endogenous decision for the buyer. We assume that both the unit marketing expenditure and the unit price charged by the buyer influence the end demand for the product. We model the seller–buyer relationship as a non-cooperative as well as a cooperative game. We investigate the non-cooperative game from two perspectives: the Seller–Stackelberg model and the Buyer–Stackelberg model. In the cooperative game, we provide a procedure for outlining Pareto efficient solutions. For each model, we present a numerical example as well as sensitivity analysis with respect to the two key parameters in the model.
European Journal of Operational Research, Oct 1, 1987
An optimal control model of a joint finance-marketing-production system is formulated. The market... more An optimal control model of a joint finance-marketing-production system is formulated. The marketing subsystem in the model is represented by the Nerlove-Arrow model of advertising and the production subsystem is represented by the HMMS model of production planning. Using the model as a reference point, a decentralized procedure for coordinating finance, marketing and production decisions is designed. The procedure appears to have the following two characteristics: (1) a discontinuous discount interest rate and (2) a time-varying transfer price between marketing and production functions. An example is presented to illustrate the procedure. The case of sequential planning of marketing-production and finance decisions is considered and the resultant marketing-production subsystem model is described. A solution procedure is outlined for the subsystem model.
Decision Sciences, Nov 12, 1991
ABSTRACTA new LP‐based algorithm is developed to determine the optimal solution to the two‐group ... more ABSTRACTA new LP‐based algorithm is developed to determine the optimal solution to the two‐group classification problem. The procedure is efficient when compared to current research in a simulation study.
Computers & Operations Research, 2003
Manufacturers and other suppliers offer temporary reduction in the price charged to resellers for... more Manufacturers and other suppliers offer temporary reduction in the price charged to resellers for a variety of reasons. Typically the trade promotion lasts for some finite time-span. In addition, in reselling situations, the end demand tends to be sensitive to selling price. Thus, when the trade promotion takes place, there is possibility that not all the quantity purchased by the
Decision Sciences, Sep 1, 1988
... count EOQ model. In the retailer problem, however. there are two decision variables:price and... more ... count EOQ model. In the retailer problem, however. there are two decision variables:price and lot size. The retailer has to determine the lot size for purchasing the prod-uct and the price for selling the product. The two decisions ...