This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (`, S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the (`, S) inequalities to a general class of valid inequalities, called the (Q, SQ) inequalities, an...

This paper is concerned with joint determination of the optimal lot size and optimal number of shipments for an economic production quantity (EPQ) model with the reworking of random defective items produced. The classic EPQ model assumes a continuous issuing policy for satisfying product demand and perfect quality production for all items produced. However, in a real life vendor-buyer integrate...

L.A. Wolsey * A class of strong valid inequalities is described for the single-item uncapacitated economic lot-sizing problem with start-up costs. It is shown that these inequalities yield a complete polyhedral characterization of the problem. The corresponding separation problem is formulated as a shortest path problem. Finally, a reformulation as a plant location problem is shown to imply the...

We consider the single item capacitated lot–sizing problem, a well-known production planning model that often arises in practical applications, and derive new classes of valid inequalities for it. We first derive new, easily computable valid inequalities for the continuous 0–1 knapsack problem, which has been introduced recently and has been shown to provide a useful relaxation of mixed 0-1 int...

this paper deals with the single machine multi-product lot scheduling problem in which defective items are produced in any production run of each product. we have adopted the common cycle scheduling policy and assumed that the setup times for production of each product can be non-zero. further, we have assumed that defective items will be reworked and the inspection costs during the normal prod...

We consider the single item capacitated lot sizing problem a well known produc tion planning model that often arises in practical applications and derive new classes of valid inequalities for it We also derive new easily computable valid inequalities for the continuous knapsack problem The continuous knapsack problem has been introduced recently and has been shown to provide a useful relaxation...

this paper proposes a new mixed integer programming model for multi-item capacitated lot-sizing problem with setup times, safety stock and demand shortages in closed-loop supply chains. the returned products from customers can either be disposed or be remanufactured to be sold as new ones again. due to the complexity of problem, three meta-heuristics algorithms named simulated annealing (sa) al...