A bilinear reduction based algorithm for solving capacitated multi-item dynamic pricing problems

Abstract

In a capacitated multi-item dynamic pricing problem one maximizes the profit by choosing a proper production level as well as pricing policy, where the latter depends on a satisfied demand. The objective function involves inventory, production and setup costs, and revenue functions. The products are required to satisfy joined production capacities. We consider a bilinear reduction of the linear mixed integer formulation of the problem and prove that the problem is equivalent to finding a global maximum of the bilinear problem. A heuristic algorithm is proposed, based on the reduction technique. Numerical experiments confirm the efficiency of the proposed technique.

An inventory model for imperfect production system with rework and shortages

“…Because little attention was paid to the area of imperfect quality EPQ model with backlogging, rework and machine breakdown taking place in stock piling time, Cardenas-Barron (2008) determined the optimal solution for two inventory policies that were proposed by Jamal et al (2004) in algebraic procedure which contains four simple algebraic steps and also proposed the range of real values for proportion of defectives, the closed form for the total inventory cost for both policies and the mathematical expressions to compute the cost penalty. Nahapetyan and Pardalos (2008) proposed an algorithm to solve the capacitated multi-item dynamic pricing problems. Cardenas- Barron (2009) develops an EPQ type inventory model with planned backorders for determining the EPQ for a single product, which is manufactured in a single-stage manufacturing system that generates imperfect quality products and all these defective products are reworked in the same cycle and also establish the range of real values of the proportion of defective products for which these is an optimal solution and the close form for the total cost of inventory system.…”

An inventory model for imperfect production system with rework and shortages

“…Because little attention was paid to the area of imperfect quality EPQ model with backlogging, rework and machine breakdown taking place in stock piling time, Cardenas-Barron (2008) determined the optimal solution for two inventory policies that were proposed by Jamal et al (2004) in algebraic procedure which contains four simple algebraic steps and also proposed the range of real values for proportion of defectives, the closed form for the total inventory cost for both policies and the mathematical expressions to compute the cost penalty. Nahapetyan and Pardalos (2008) proposed an algorithm to solve the capacitated multi-item dynamic pricing problems. Cardenas- Barron (2009) develops an EPQ type inventory model with planned backorders for determining the EPQ for a single product, which is manufactured in a single-stage manufacturing system that generates imperfect quality products and all these defective products are reworked in the same cycle and also establish the range of real values of the proportion of defective products for which these is an optimal solution and the close form for the total cost of inventory system.…”

Perspective envelopes for bilinear functions

“…Bilinear expressions are the most common nonconvex components in mathematical formulations modeling problems arising in chemical engineering [20,19,26,8,38,12,37,10], pooling and blending [13,5], supply chain and transportation science [16,35,34,36], and energy systems [22,15,23,11], to name NICTA is funded by the Australian Government through the Department of Communications and the Australian Research Council through the ICT Centre of Excellence Program.…”