A Linear Programming Approach to Production and Employment Scheduling

Hanssmann, Fred; Hess, Sidney W.

doi:10.1287/mantech.1.1.46

Cited by 128 publications

(43 citation statements)

References 2 publications

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“…Research on scheduling problems started as early as in 1960 by Hanssman and Hess [5] when they implemented linear programming approach to production planning and employment scheduling. To date, the research in machine scheduling has grown into various machine environments, objectives, and methodologies.…”

Section: Chapter 2 Literature Reviewmentioning

confidence: 99%

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

Suhaimi

Nguyen

Damodaran

2016

Computers & Industrial Engineering

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Batch Processing Machines (BPMs) are commonly used in electronics manufacturing, semi-conductor manufacturing, and metal-working -to name a few. Scheduling these machines are not an easy task; practical considerations and the exponential number of decision variables involved impede schedulers (or decision makers) from making good decisions. This research focuses on minimizing the makespan of a set of non-identical parallel batch processing machines. In order to schedule jobs on these machines, two decisions are to be made. The first decision is to group jobs to form batches such that the machine capacity is not exceeded. The second decision is to sequence the batches formed on the machines such that the makespan is minimized. Both the decisions are intertwined as the processing time of the batch is determined by the composition of the jobs in the batch. The problem under study is shown to be NP-hard. A mathematical model from the literature is adopted to develop a solution approach which would help the decision maker to make meaningful decisions.Lagrangian Relaxation approach has been shown to be very effective in solving scheduling problems. Using this decomposition approach, the mathematical model is decomposed and a sub-gradient approach was used to update the multipliers. Two sets of constraints were relaxed to consider two Lagrangian Relaxation models. Experiments were conducted with data sets from the literature. The solution quality of the proposed approach was compared with meta-heuristic (i.e. Particle Swarm Optimization (PSO) and Random Key Genetic Algorithm (RKGA)) published in the literature and a commercial solver (i.e. IBM ILOG CPLEX). On smaller instances (i.e. 10 and 20 jobs), the proposed approach outperformed PSO and RKGA. However, the proposed approach and CPLEX report the same results. On larger instances (i.e. 50, 100 and 200 job instances) with two and four-machines, the proposed approach was better than PSO whenever the variability in the processing times were smaller. The proposed approach generally outperformed RKGA and CPLEX on larger problem instances. Out of 200 experiments conducted, the proposed approach helped to find new improved solution on 34 instances and comparable on 105 instances when compared to PSO. The PSO approach was much faster than all other approaches on larger problem instances. The experimental study clearly identifies the problem instances on which the proposed approach can find a better solution. The proposed Lagrangian Relaxation solution approach helps the schedulers to make more informed decisions. Minor modifications can be made to use the proposed solution approach for other practical considerations (e.g. job ready times, tardiness objective, etc.) The main contribution of this research is the proposed solution approach which is effective in solving a class of non-identical batch processing machine problems with better solution quality when compared to existing meta-heuristic. NORTHERN

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Section: Chapter 2 Literature Reviewmentioning

confidence: 99%

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

Suhaimi

Nguyen

Damodaran

2016

Computers & Industrial Engineering

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“…Holt develops a quadratic cost model that includes both the costs of maintaining a workforce and the cost of changing the workforce. Holt's quadratic cost model is converted to a linear cost model in (Hanssmann and Hess 1960) and solved via linear programming. The Holt model is also extended in (Ebert 1976) with the inclusion of time varying productivity.…”

Section: Literaturementioning

confidence: 99%

New Project Staffing for Outsourced Call Centers with Global Service Level Agreements

Robbins

Harrison

2011

Service Science

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e consider the issue of new project staffing in an outsourced call center required to meet a monthly Service Level Agreement (SLA). We present empirical analysis generated during a field study with a provider of outsourced call center services to illustrate the unique issues related to staffing a new project. Our work shows that during the start-up phase of a project agents experience significant improvements in productivity that reduce the staffing requirements over time. We also find that turnover, which is typically high in a call center environment, may be even higher for a project launch dominated by newly hired agents. These factors interact with the uncertainty of call volumes and talk time to create a difficult hiring challenge. We develop a model that finds the level of hiring with the lowest total expected cost of operation while meeting service level commitments.

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“…The pioneering Linear Decision Rule (LDR) was developed by Holt, Modigliani, Muth and Simon (HMMS) in the mid 1950s (Holt et al, 1955(Holt et al, , 1956. Extensions and refinements to this rule have been proposed (Hanssmann and Hess, 1960;Bergstrom and Smith, 1970;Goodman, 1974;Deckro and Hebert, 1984;Parlar, 1985). While the HMMS model and its variations incorporate demand uncertainty, these models treat capacity, specifically workforce levels, as a decision variable that can be varied continuously, which avoids the problem of lead times encountered under fixed capacity limits.…”

Section: Approaches With Stochastic Demandmentioning

confidence: 99%

Production planning with load-dependent lead times and safety stocks for a single product

Ravindran

Kempf

Uzsoy

2011

IJPS

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Queuing models have demonstrated the nonlinear relationship between resource utilisation, which is determined by production planning decisions, and lead times. Both production planning decisions and safety stock levels are driven by lead times, and are thus tightly interrelated. However, production planning and safety stock calculations have generally been carried out separately. We propose a production planning model for a single-stage single-product system that integrates release planning and safety stock considerations. Concave clearing functions are used to capture the nonlinear relationship between resource utilisation and lead times, while chance constraints represent the need to plan inventories to achieve desired service levels. Extensive computational experiments indicate that the proposed model provides an excellent tradeoff between customer service and inventory costs.

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A Linear Programming Approach to Production and Employment Scheduling

Cited by 128 publications

References 2 publications

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

New Project Staffing for Outsourced Call Centers with Global Service Level Agreements

Production planning with load-dependent lead times and safety stocks for a single product

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