A novel class of scheduling policies for the stochastic resource-constrained project scheduling problem.

We study the resource-constrained project scheduling problem with stochastic activity durations. We introduce a new class of scheduling policies for this problem, which make a number of a-priori sequencing decisions in a pre-processing phase, while the remaining decisions are made dynamically during project execution. The pre-processing decisions entail the addition of precedence constraints to the scheduling instance, hereby resolving some potential resource conflicts. We compare the performance of this new class with existing scheduling policies for the stochastic resource-constrained project scheduling problem, and we observe that the new class is significantly better when the variability in the activity durations is medium to high.Project scheduling; Uncertainty; Stochastic activity durations; Scheduling policies;

A new approach for cell formation and scheduling with assembly operations and product structure

In this paper, a new formulation model for cellular manufacturing system (CMS) design problem is proposed. The proposed model of this paper considers assembly operations and product structure so that it includes the scheduling problem with the formation of manufacturing cells, simultaneously. Since the proposed model is nonlinear, a linearization method is applied to gain optimal solution when the model is solved using direct implementation of mixed integer programming. A new genetic algorithm (GA) is also proposed to solve the resulted model for large-scale problems. We examine the performance of the proposed method using the direct implementation and the proposed GA method. The results indicate that the proposed GA approach could provide efficient assembly and product structure for real-world size problems

A simple approach to the two-dimensional guillotine cutting stock problem

Cutting stock problems are within knapsack optimization problems and are considered as a non-deterministic polynomial-time (NP)-hard problem. In this paper, two-dimensional cutting stock problems were presented in which items and stocks were rectangular and cuttings were guillotine. First, a new, practical, rapid, and heuristic method was proposed for such problems. Then, the software implementation and architecture specifications were explained in order to solve guillotine cutting stock problems. This software was implemented by C++ language in a way that, while running the program, the operation report of all the functions was recorded and, at the end, the user had access to all the information related to cutting which included order, dimension and number of cutting pieces, dimension and number of waste pieces, and waste percentage. Finally, the proposed method was evaluated using examples and methods available in the literature. The results showed that the calculation speed of the proposed method was better than that of the other methods and, in some cases, it was much faster. Moreover, it was observed that increasing the size of problems did not cause a considerable increase in calculation time. In another section of the paper, the matter of selecting the appropriate size of sheets was investigated; this subject has been less considered by far. In the solved example, it was observed that incorrect selection from among the available options increased the amount of waste by more than four times. Therefore, it can be concluded that correct selection of stocks for a set of received orders plays a significant role in reducing waste

A novel class of scheduling policies for the stochastic resource-constrained project scheduling problem

We study the resource-constrained project scheduling problem with stochastic activity durations. We introduce a new class of scheduling policies for this problem, which make a number of a-priori sequencing decisions in a pre-processing phase, while the remaining decisions are made dynamically during project execution. The pre-processing decisions entail the addition of precedence constraints to the scheduling instance, hereby resolving some potential resource conflicts. We compare the performance of this new class with existing scheduling policies for the stochastic resource-constrained project scheduling problem, and we observe that the new class is significantly better when the variability in the activity durations is medium to high.status: publishe

A joint pricing and lot sizing models with discount: A geometric programming approach

We propose a novel joint pricing and lot sizing model to enable manufacturers plan production and pricing. These types of models have proven to be very popular and are collectively known as the Joint Pricing and Lot sizing Models. We include a discount factor in our model to increase profit for the manufacturer. Our proposed model relies on the fact that demand influences production cost indirectly, while it is dependent on price and the discount offered. By considering the form of demand and production cost, it is apparent that the presented model is a Signomial Geometric Programming problem. We obtain optimal solutions for price, lot size and discount factor by applying the modified transformation method of geometric programming. Numerical examples, which include sensitivity analysis of the objective function and parameters, illustrate our model. References C. J. Corbett and X. de Groote. A supplier's optimal quantity discount policy under asymmetric information. Management Science, 46(3):444--450, 2000. R. J Duffin, E. L Peterson, and C. Zener. Geometric programming, Theory and Application. John Wiely and Sons, 1967. J. R. Freeland. Coordination strategies for production and marketing in a functionally decentralized firm. AIIE Transactions, 12:126--132, 1982. Woon J.Lee, Daesoo Kim, and A. Cabot. Optimal demand rate, lot sizing, and process reliability improvement decisions. IIE Transactions, 28:941--952, 1996. http://cat.inist.fr/?aModele=afficheN&cpsidt=2490704. Daesoo Kim and Woon J. Lee. Optimal joint pricing and lot sizing with fixed and variable capacity. European Journal of Operational Research, 109(1):212--227, 1998. http://www.sciencedirect.com/science/article/B6VCT-3TMR6M6-H/2/2d166a9b5fc0a9a27e923c495f256663. Woon J. Lee. Determining order quantity and selling price by geometric programming. Decision Sciences, 24:76--87, 1993. doi:10.1111/j.1540-5915.1993.tb00463.x. Woon J. Lee and Daesoo Kim. Optimal and heuristic decision strategies for integrated product and marketing planning. Decision Sciences, 24(6):1203--1213, 1993, doi:10.1111/j.1540-5915.1993.tb00511.x. Seyed J. Sajadi, Maryam Orouge, and M. B. Aryanezhad. Optimal production and marketing planning. Computational Optimization and Applications, 30(2):195--203, 2005. http://portal.acm.org/citation.cfm?id=1062644.1062668. Richard J. Tersine. Principles of Inventory And Materials Management. PTR Prentice Hall, Englewood Cliffs, New Jersey 07632, 1994. S. Viswanathan and Q.Wang. Discount pricing decisions in distribution channels with price sensitive demand. European Journal of Operational Research, 149(3):571--587, 2003. http://ideas.repec.org/a/eee/ejores/v149y2003i3p571-587.html. Prakash L. Abad. Determining optimal selling price and the lot size when the supplier offers all-unit quantity discounts. Decision Sciences, 3(19):622--634, 1988. Z. Kevin Weng. Channel coordination and quantity discounts. Management Sciences, 41(9):1509--1522, 1995. http://www.jstor.org/view/00251909/di012962/01p03025/0. Prakash L. Abad. Supplier pricing and lot sizing when demand is price sensitive. European Journal of Operational Research, (78):334--354, 1994. http://cat.inist.fr/?aModele=afficheN&cpsidt=3309143. Charles S. Beightler. Applied Geometric Programming. John Wiely and Sons, 1976. C. W. Chiang, J. Fitzsimmons, Z. Huang, and S. Li. A game theoretic approach to quantity discount problem. Decision Sciences, 25(1):153--168, 1994. doi:10.1111/j.1540-5915.1994.tb00521.x

A game theory approach in seller-buyer supply chain

In this paper, several seller-buyer supply chain models are proposed which incorporate both cost factors as well as elements of competition and cooperation between seller and buyer. We assume that unit marketing expenditure and unit price charged by the buyer influence the demand of the product being sold. The relationships between seller and buyer will be modeled by non-cooperative and cooperative games, respectively. The non-cooperative game is based on the Stackelberg strategy solution concept, where we consider separately the case when the seller is the leader (Seller-Stackelberg) and also when the buyer is the leader (Buyer-Stackelberg). Pareto efficient solutions will be provided for the cooperative game model. Numerical examples presented in this paper, including sensitivity analysis of some key parameters, will compare the results between different models considered.Cooperative and non-cooperative game theory Marketing Pricing Seller-buyer supply chain