Flow shop scheduling with earliness, tardiness and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding) and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two di erent, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two di erent lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with di erent types of strongly NP-hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs

The economic lot and delivery scheduling problem: The single item case

We have studied the problem of determining the frequency of production of a single component and the frequency of delivery of that component to a customer which uses this component at a constant rate. The objective is to minimize the average cost per unit time of production setup costs, inventory holding costs at both the supplier and the customer, and transportation costs. The model allows positive production setup times. We prove that the ratio between the production interval and delivery interval must be an integer in an optimal solution. This provides the basis for a very simple, optimal solution procedure. We use these results to characterize situations in which it is optimal to have synchronized production and delivery, and discuss the ramifications of these conditions on strategies for setup cost and setup time reductions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29749/1/0000087.pd

Cyclic scheduling to minimize inventory in a batch flow line

This paper addresses the problem of determining a cyclic schedule for batch production on a flow line. We assume a constant supply of raw materials and a constant demand for all finished goods. Material that has completed processing at one stage is transferred to the next stage in small transfer batches. Inventory may be held before the line, at the end of the line, or between any pair of adjacent stations. The objective is to find a sequence of production and a cycle length that minimize the average cost per unit time of holding inventory. A linear programming formulation is given that determines the optimal cycle length and finishing times for a given set of sequences, one for each machine. Two heuristics are presented for finding near-optimal sequences: one is applicable to the special case of a two-machine flow line; the others are applicable to an m-machine line and focus on different aspects of the problem (e.g., cycle stock or work-in-process inventory). From a computational study, we have observed that: 1) permutation schedules, i.e., schedules with the same sequence on all machines, are nearly always optimal, 2) the heuristics produce near optimal solutions, 3) the batching decision, i.e., the choice of cycle length, is substantially more significant than the sequencing decision for minimizing inventory costs.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31508/1/0000430.pd

Algorithms for a class of single-machine weighted tardiness and earliness problems

We address the problem of determining schedules for static, single-machine scheduling problems where the objective is to minimize the sum of weighted tardiness and weighted earliness. We develop optimal and heuristic procedures for the special case of weights that are proportional to the processing times of the respective jobs. The optimal procedure uses dominance properties to reduce the number of sequences that must be considered, and some of the heuristic use these properties as a basis for constructing good initial sequences. A pairwise interchange procedure is used to improve the heuristic solutions. An experimental study shows that the heuristic procedures perform very well.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29324/1/0000389.pd

Characteristics of optimal workload allocation for closed queueing networks

We consider the problem of allocating a given workload among the stations in a multi-server product-form closed queueing network to maximize the throughput. We first investigate properties of the throughput function and prove that it is pseudoconcave for some special cases. Some other characteristics of the optimal workload and its physical interpretation are also provided. We then develop two computational procedures to find the optimum workload allocation under the assumption that the throughput function is pseudoconcave in general. The primary advantage of assuming pseudoconcavity is that, under this assumption, satisfaction of first order necessary conditions is sufficient for optimality. Computational experience with these algorithms provides additional support for the validity of this assumption. Finally, we generalize the solution procedure to accommodate bounds on the workloads at each station.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29251/1/0000308.pd

The optimal configuration and workload allocation problem in flexible manufacturing systems

In this article we consider the problem of determining the minimum cost configuration (number of machines and pallets) for a flexible manufacturing system with the constraint of meeting a prespecified throughput, while simultaneously allocating the total workload among the machines (or groups of machines). Our procedure allows consideration of upper and lower bounds on the workload at each machine group. These bounds arise as a consequence of precedence constraints among the various operations and/or limitations on the number or combinations of operations that can be assigned to a machine because of constraints on tool slots or the space required to store assembly components. Earlier work on problems of this nature assumes that the workload allocation is given. For the single-machine-type problem we develop an efficient implicit enumeration procedure that uses fathoming rules to eliminate dominated configurations, and we present computational results. We discuss how this procedure can be used as a building block in solving the problem with multiple machine types.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45516/1/10696_2004_Article_BF00170207.pd

Stochastic leadtimes in two-level distribution type networks

http://deepblue.lib.umich.edu/bitstream/2027.42/8403/5/bam4526.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/8403/4/bam4526.0001.001.tx

Optimal finite and infinite horizon policies for single-stage production systems with random yields

http://deepblue.lib.umich.edu/bitstream/2027.42/8393/5/ban0128.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/8393/4/ban0128.0001.001.tx

A fast, optimal procedure for the work station assignment problem

http://deepblue.lib.umich.edu/bitstream/2027.42/8382/5/bam4527.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/8382/4/bam4527.0001.001.tx