This paper proposes two relax and fix heuristics for the simultaneous lot sizing and sequencing problem in permutation flow shops involving sequence-dependent setups and capacity constraints. To evaluate the effectiveness of mentioned heuristics, two lower bounds are developed and compared against the optimal solution. The results of heuristics are compared with the selected lower bound .

An important special case of the economic lot-sizing problem is the one in which there are no speculative motives to hold inventory, i. e., the marginal cost of ]n'oducing one unit m some period plus the cost of holding it until some future period is at least the marginal production cost in the latter period. It is already known that this special case can be solved in linear time. In this paper...

NP{hard cases of the single{item capacitated lot{sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known which produces solutions with a relative deviati...

Loss of customer goodwill in uncapacitated single level lot-sizing is studied with a mixed integer programming model extending the well-known Wagner-Whitin (WW) model. The objective is to maximize profit from production and sales of a single good over a finite planning horizon. Demand, costs, and prices vary with time. Unsatisfied demand cannot be backordered. It leads to the immediate loss of ...

In this paper we extend the generalized surrogate optimization approaches and the stochastic comparison so as to tackle the lot-sizing problem in manufacturing system. In practice, with the surrogate methodology, the lot sizes are continuously adjusted on-line by the gradient-based approaches. The lot sizing determines the number of parts batched together for production. We utilize the queueing...

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 ...

Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by many researchers. Considering the quantity discount in purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In this paper, stochastic dynamic...

In this paper we consider a multi-item, multi-machine discrete lot sizing and scheduling problems (DLSP) which consists of finding a minimal cost production schedule over a finite discrete horizon, where in each period a machine may be either producing one item at full capacity or is idle. The demand for each item in each period is known, and can be satisfied either by production in the period,...

Non-stationary stochastic lot sizing problem appears in many industrial environments where demand is nonstationary and stochastic, and replenishments require fixed freight fees. This paper presents the cost performance assessment of three inventory control strategies proposed for the stochastic lot sizing problem, namely Hua et al. (2008)’s strategy (HYHX), Tarim and Kingsman (2006)’s model (TK...

We give multi-stage stochastic programming formulations for lot-sizing problems where costs, demands and order lead times follow a general discrete-time stochastic process with finite support. We characterize the properties of an optimal solution and give a dynamic programming algorithm, polynomial in input size, when orders do not cross in time.