CORE

Abstract This article is a polyhedral study of a generalization of the mixing set where two different, divisible coefficients are allowed for the integral variables. Our results generalize earlier work on mixed integer rounding, mixing, and extensions. They also directly apply to applications such as production planning problems involving lower bounds or start-ups on production, when these are modeled as mixed-integer linear programs.

Abstract The main result of this paper is an O (n 3) algorithm for the single-item lot-sizing problem with constant batch size and backlogging. We consider a general number of installable batches, ie, in each time period t we may produce up to mt batches, where the mt are given and time-dependent. This generalizes earlier results as we consider backlogging and a general number of maximum batches. We also give faster algorithms for three special cases of this general problem.

Abstract In the fixed-charge transportation problem, the goal is to optimally transport goods from depots to clients when there is a fixed cost associated to transportation or, equivalently, to opening an arc in the underlying bipartite graph. We further motivate its study by showing that it is both a special case and a strong relaxation of the big-bucket multi-item lot-sizing problem, and a generalization of a simple variant of the single-node flow set.

Abstract In this paper, we present a mathematical model which integrates tactical-operational production and distribution decisions in a shared resources environment. More precisely, we integrate lot sizing production and distribution decisions with vehicle routing decisions. We obtain a global multi-period multi-item multi-vehicle model where a capacity constraint models the link between production and distribution decisions. Three heuristics are presented in order to solve this global model.

Mixed integer programming (MIP) formulations are typically tightened through the use of a separation algorithm and the addition of violated cuts. Using extended formulations involving new variables is a possible alternative, but this often results in prohibitively large MIPs where even the linear programming relaxations are hard or impossible to solve. In this paper, we demonstrate how, in certain cases, it is possible and interesting to define``approximate''extended formulations.

Abstract Strict Linear Pricing in non-convex markets is a mathematical impossibility. In the context of electricity markets, two different classes of solutions have been proposed to this conundrum on both sides of the Atlantic. We formally describe these two approaches in a common framework, review and analyze their main properties, and discuss their shortcomings.

Abstract We consider several variants of the two-level lot-sizing problem with one item at the upper level facing dependent demand, and multiple items or clients at the lower level, facing independent demands. We first show that under a natural cost assumption, it is sufficient to optimize over a stock-dominant relaxation. We further study the polyhedral structure of a strong relaxation of this problem involving only initial inventory variables and setup variables.

Abstract The main result of this paper is to provide an O (n3) algorithm for the single item constant capacity lotsizing problem with backlogging and a general number of installable batches, ie in each time period t we may install up to mt multiples of the batch capacity, where the mt are given and are time-dependent. This generalizes earlier results [12, 16] as we consider backlogging and a general number of installable batches. We also give faster algorithms for three special cases of this general problem.

Abstract. The fixed-charge transportation problem is a basic problem in supply chain management. It is also both a special case and a strong relaxation of the big-bucket multi-item lot-sizing problem and a special case of the more general fixed charge network flow problem.

In the current competitive world, technological advancement does not guarantee that the machineries do not break down during their life. A machine's condition can turn into an out-of-control condition gradually or at once. This implies that the products would not have their potential perfect quality. Besides, such situation questions the validity of the utilized lot sizing model, in that the portion of defective products in each lot increases.