Constraint-Based Job Shop Scheduling with IILOG SCHEDULER

We introduce constraint-based scheduling and discuss its main principles. An approximation algorithm based on tree search is developed for the job shop scheduling problem using ILOG SCHEDULER. A new way of calculating lower bounds on the makespan of the job shop scheduling problem is presented and we show how such results can be used within a constraint-based approach. An empirical performance analysis shows that the algorithm we developed performs well. Finally, taking the job shop scheduling problem as a start point, we discuss how constraint-based scheduling can be used to solve more general scheduling problems.     

Profit maximization in simultaneous lot-sizing and scheduling problem

This paper extends the simultaneous lot-sizing and scheduling problem, to include demand choice flexibility. The basic assumption in most research about lot-sizing and scheduling problems is that all the demands should be satisfied. However, in a business with a goal of maximizing profit, meeting all demands may not be an optimum decision. In the profit maximization simultaneous lot-sizing and scheduling problem with demand choice flexibility, the accepted demand in each period, lot-sizing and scheduling are three problems which are considered simultaneously. In other words the decisions pertaining to mid-term planning and short-term planning are considered as one problem and not hierarchically. According to this assumption, the objective function of traditional models changes from minimizing costs to maximizing profits.     

A distributed exact algorithm for the multiple resource constrained sequencing problem

Sequencing problems arise in the context of process scheduling both in isolation and as subproblems for general scenarios. Such sequencing problems can often be posed as an extension of the Traveling Salesman Problem. We present an exact parallel branch and bound algorithm for solving the Multiple Resource Constrained Traveling Salesman Problem (MRCTSP), which provides a platform for addressing a variety of process sequencing problems. The algorithm is based on a linear programming relaxation that incorporates two families of inequalities via cutting plane techniques. Computational results show that the lower bounds provided by this method are strong for the types of problem generators that we considered as well as for some industrially derived sequencing instances. The branch and bound algorithm is parallelized using the processor workshop model on a network of workstations connected via Ethernet. Results are presented for instances with up to 75 cities, 3 resource constraints, and 8 workstations.     

Solving the capacitated lot-sizing problem with backorder consideration

In this research, we formulate and solve a type of the capacitated lot-sizing problem. We present a general model for the lot-sizing problem with backorder options, that can take into consideration various types of production capacities such as regular time, overtime and subcontracting. The objective is to determine lot sizes that will minimize the sum of setup costs, holding cost, backorder cost, regular time production costs, and overtime production costs, subject to resource constraints. Most existing formulations for the problem consider the special case of the problem where a single source of production capacity is considered. However, allowing for the use of alternate capacities such as overtime is quite common in many manufacturing settings. Hence, we provide a formulation that includes consideration of multiple sources of production capacity. We develop a heuristic based on the special structure of fixed charge transportation problem. The performance of our algorithm is evaluated by comparing the heuristic solution value to lower bound value. Extensive computational results are presented.     

Lot-sizing with non-stationary cumulative capacities

We study a new class of capacitated economic lot-sizing problems. We show that the problem is NP-hard in general and derive a fully polynomial-time approximation algorithm under mild conditions on the cost functions. Furthermore, we develop a polynomial-time algorithm for the case where all cost functions are concave.     

An Ant Colony Optimization Algorithm for Shop Scheduling Problems

We deal with the application of ant colony optimization to group shop scheduling, which is a general shop scheduling problem that includes, among others, the open shop scheduling problem and the job shop scheduling problem as special cases. The contributions of this paper are twofold. First, we propose a neighborhood structure for this problem by extending the well-known neighborhood structure derived by Nowicki and Smutnicki for the job shop scheduling problem. Then, we develop an ant colony optimization approach, which uses a strong non-delay guidance for constructing solutions and which employs black-box local search procedures to improve the constructed solutions. We compare this algorithm to an adaptation of the tabu search by Nowicki and Smutnicki to group shop scheduling. Despite its general nature, our algorithm works particularly well when applied to open shop scheduling instances, where it improves the best known solutions for 15 of the 28 tested instances. Moreover, our algorithm is the first competitive ant colony optimization approach for job shop scheduling instances.     

Loss-based quality costs and inventory planning: General models and insights

In this paper, we examine a joint lot-sizing and process investment problem with random yield and backorders. We allow for inspection and develop stochastic models which provide the optimal inspection and lot-sizing policy as well as the optimal process investment for variance reduction. The process quality loss profile around the target is captured via a modification of the Reflected Normal loss function. We conduct numerical experiments assuming that the proportion of defectives follows a Uniform distribution while the process quality characteristic follows either a Normal or Uniform distribution. We also develop closed-form solutions that depend on at most the first two moments of any general probability distribution of defective units and which allow us to examine the nature of optimal policies. We demonstrate via numerical experiments the value of our integrated approach for jointly determining optimal inventory, inspection, and investment policies. Overall, our models and analyses provide some interesting insights into this reasonably complex inventory-quality problem and open up several avenues for future work in this area.     

Lower bound on size of branch-and-bound trees for solving lot-sizing problem

We show that there exists a family of instances of the lot-sizing problem, such that any branch-and-bound tree that solves them requires an exponential number of nodes, even in the case when the branchings are performed on general split disjunctions. This result is of interest since there exists dynamic programming algorithm that solves lot-sizing in polynomial-time. To the best of our knowledge, this is the first study that shows that dynamic programming can be exponentially faster than branch-and-bound.     

A single-item economic lot-sizing problem with a non-uniform resource: Approximation

We study a generalization of the classical single-item capacitated economic lot-sizing problem to the case of a non-uniform resource usage for production. The general problem and several special cases are shown to be non-approximable with any polynomially computable relative error in polynomial time. An optimal dynamic programming algorithm and its approximate modification are presented for the general problem. Fully polynomial time approximation schemes are developed for two NP-hard special cases: (1) cost functions of total production are separable and holding and backlogging cost functions are linear with polynomially related slopes, and (2) all holding costs are equal to zero.     

On discrete lot-sizing and scheduling on identical parallel machines

We consider the multi-item discrete lot-sizing and scheduling problem on identical parallel machines. Based on the fact that the machines are identical, we introduce aggregate integer variables instead of individual variables for each machine. For the problem with start-up costs, we show that the inequalities based on a unit flow formulation for each machine can be replaced by a single integer flow formulation without any change in the resulting LP bound. For the resulting integer lot-sizing with start-ups subproblem, we show how inequalities for the unit demand case can be generalized and how an approximate version of the extended formulation of Eppen and Martin can be constructed. The results of some computational experiments carried out to compare the effectiveness of the various mixed-integer programming formulations are presented.     

Multi-period lot-sizing with supplier selection: Structural results,complexity and algorithms

We consider a multi-period lot-sizing problem with multiple products and multiple suppliers. Demand is deterministic and time-varying. The objective is to determine order quantities to minimize the total cost over a finite planning horizon. This problem is strongly NP-hard. For a special case, we extend the classical zero-inventory-ordering principle and solve it by dynamic programming. Based on this new extension, we also develop a heuristic algorithm for the general problem and computationally show that it works well.     

HOPS – Hamming-Oriented Partition Search for production planning in the spinning industry

In this paper, we investigate a two-stage lot-sizing and scheduling problem in a spinning industry. A new hybrid method called HOPS (Hamming-Oriented Partition Search), which is a branch-and-bound based procedure that incorporates a fix-and-optimize improvement method is proposed to solve the problem. An innovative partition choice for the fix-and-optimize is developed. The computational tests with generated instances based on real data show that HOPS is a good alternative for solving mixed integer problems with recognized partitions such as the lot-sizing and scheduling problem.     

Efficient Solution of the Single-item,Capacitated Lot-sizing Problem with Start-up and Reservation Costs

A capacitated dynamic lot-sizing model, where the costs incurred are a start-up cost for switching the production facility on and another reservation cost for keeping the facility on, whether or not it is producing, is considered. The resulting scheduling problem is NP-hard. An efficient shortest path model of the uncapacitated version of the problem is developed. This model is then included, via a redefinition of variables, into a tight capacitated model; tight in the sense that sharp lower bounds can be produced from it. The lower bound problems are solved efficiently by recovering the shortest path structure through column generation, and effective upper bounds are generated by solving a small capacitated trans-shipment problem. The results of computational tests to verify the computational efficiency of the resulting solution scheme are presented.     

Application of an optimization problem in Max-Plus algebra to scheduling problems

The problem tackled in this paper deals with products of a finite number of triangular matrices in Max-Plus algebra, and more precisely with an optimization problem related to the product order. We propose a polynomial time optimization algorithm for 2×2 matrices products. We show that the problem under consideration generalizes numerous scheduling problems, like single machine problems or two-machine flow shop problems. Then, we show that for 3×3 matrices, the problem is NP-hard and we propose a branch-and-bound algorithm, lower bounds and upper bounds to solve it. We show that an important number of results in the literature can be obtained by solving the presented problem, which is a generalization of single machine problems, two- and three-machine flow shop scheduling problems. The branch-and-bound algorithm is tested in the general case and for a particular case and some computational experiments are presented and discussed.     

A computational study of constraint satisfaction for multiple capacitated job shop scheduling

We introduce the multiple capacitated job shop scheduling problem as a generalization of the job shop scheduling problem. In this problem machines may process several operations simultaneously. We present an algorithm based on constraint satisfaction techniques to handle the problem effectively. The most important novel feature of our algorithm is the consistency checking. An empirical performance analysis is performed using a well-known set of instances of the job shop scheduling problem and a newly constructed set of instances of the multiple capacitated job shop scheduling problem. We show that our algorithm performs well for both sets of instances.     

两种运输方式下的船只优化排序模型及算法

本文讨论的是在两种不同容量的船只和两条不同运输路线的情况下的库存与运输联合优化排序问题.传统的经济批量订货问题里每次定购成本固定不变,而我们的问题里面定购成本是阶跃式的,与使用的船数相关.以往运输网络优化的论文都只考虑一种容量的运输工具,没有考虑不同容量的运输工具.本文结合这两方面做了进一步的研究,并根据实际应用背景建立了数学模型,讨论最优解的性质,由最优解性质给出了复杂度为O(N4) 的多项式算法.     

Fix and Relax Heuristic for a Stochastic Lot-Sizing Problem

This paper addresses a particular stochastic lot-sizing and scheduling problem. The evolution of the uncertain parameters is modelled by means of a scenario tree and the resulting model is a multistage stochastic mixed-integer program. We develop a heuristic approach that exploits the specific structure of the problem. The computational experiments carried out on a large set of instances have shown that the approach provides good quality solutions in a reasonable amount of time.     

Approximation algorithms for single machine scheduling with one unavailability period

In this paper, we investigate the single machine scheduling problem with release dates and tails and a planned unavailability time period. We show that the problem admits a fully polynomial-time approximation scheme when the tails are equal. We derive an approximation algorithm for the general case and we show that the worst-case bound of the sequence yielded by Schrage’s algorithm is equal to 2 and that this bound is tight. Some consequences of this result are also presented.