A Heuristic Algorithm for the Multi-Item Lot-Sizing Problem with Capacity Constraints

Karni, Reuven; Roll, Yaakov

doi:10.1080/05695558208975237

Cited by 43 publications

(16 citation statements)

References 9 publications

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“…Similarly to the treatment of Karni and Roll (1982), shifts of production quantities from an origin period to a destination period can be divided into two classes: right shifts (R) in which the origin period chronologically precedes the destination period and left shifts (L) when the opposite is true. In the case ofleft shifts, the quantity Qmax" must be calculated, defined as the maximum quantity which can be shifted from period t to destination period r.…”

Section: The Shiftsmentioning

confidence: 99%

“…This category can also include certain inventory management models such as the OP-EOQ model and the more sophisticated Wagner and Whitin method (1958), based on dynamic programming. The classic multi-item models include that of Magee and Boodman (1967), derived from an inventory management model, the Eisenhut model (1975)and the more recent ones of Dogramaci et al (1981), Dixon and Silver (1981) and Karni and Roll (1982).…”

Section: Introductionmentioning

confidence: 99%

“…A heuristic model is faster than a mixed integer linear programming type solution, so preference was given to a heuristic solution based on the shirt concept introduced in Karni and Roll (1982) also because, as has already been said, apart from the formal completeness of the modelling, some of the critical factors for the success of a PP&C model are the dimensions of the problem and a speed of execution which permits very frequent rapid rescheduling of production plans and the utilization of the model as a decision support system, which rapidly generates 'optimized' solution as the scenario described by the input data changes.…”

Section: Introductionmentioning

confidence: 99%

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A heuristic algorithm for master production schedule generation with finite capacity and sequence dependent setups

Arosio

Sianesi

1993

International Journal of Production Research

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Correct formulation of the master production schedule is critically important for the optimization of the management ofa production planning and control system. Most of the models described in the literature solve the problem in two separate sequential stages: lot sizing and then sequencing. This often produces an MPS which is not optimized or even not feasible. On the other hand, when the problem is tackled with models based on mixed integer linear programming, then dimensional constraints have to be respected which can limit the field of applications of the model itself.A complete heuristic algorithm is presented in this paper which solves the problem oflot-sizingand sequencing in a single logic stage, together with the results of an extensive series oftests carried out to compare, in different types of production systems, the performances of the proposed heuristic and those of another algorithm taken from literature. The model concerns a single production line situation with relevant setup problems; on this production line component availability constraints are not considered (the model refers to mono-level bill of material products, but it can be applied also to the most critical level in multi-levels production systems). IntroductionMany industrial sectors attach great importance to (levels of) service, flexibility and elasticity as the company's basic competitive weapons. Phenomena which tend to create a market demand which is extremely variable in time, both in terms of quantity and type of products, are becoming increasingly frequent.Thus, there is a search for solutions in terms of production planning, programming and control models (PP&C) which are both as complete as possible in terms of ability to model the problem and, also, are capable of rapidly regenerating the production schedules which have been prepared when there are modifications or variations in the marketing input. In the case of process production, the basic problems which the PP&C system has to solve relate to the lot-sizing and sequencing stages, since the stage of requirement planning is simplified by the limited number oflevels involved in the bill of materials. Therefore, the primary objective of PP&C systems is the formulation of a master production schedule (MPS) in terms of:

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Section: The Shiftsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A heuristic algorithm for master production schedule generation with finite capacity and sequence dependent setups

Arosio

Sianesi

1993

International Journal of Production Research

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“…Previous research on the lot sizing problem has focused on single and multi-levels, as well as capacitated and uncapacitated resources. There are a number of studies in the literature (see for example, [1,[11][12][13]20,21]). Also, the cutting stock problem has been greatly studied since the seminal paper of Gilmore and Gomory [5] (see for example [3,5,6,10,14,15,22]).…”

Section: Introductionmentioning

confidence: 98%

A linear optimization approach to the combined production planning model

Gramani¹,

França

Arenales

2011

Journal of the Franklin Institute

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“…Dogramaci et al (1981) propose left-shift procedure that searches for shifts with the largest reduction in overall cost. Karni and Roll (1982) introduce 10 types of shifts with calculating cost-saving coefficient which is based on the tradeoff between setup and holding costs. Tabu search is also applied to improve CLSP solution; see examples in Hindi (1996) and Karimi et al (2006).…”

Section: Single-level Clspmentioning

confidence: 99%

The Order Selection and Lot Sizing Problem in the Make-to-Order Environment

Zhai¹

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Professor Chin-Sheng Chen, Major ProfessorThis research is motivated by the need for considering lot sizing while accepting customer orders in a make-to-order (MTO) environment, in which each customer order must be delivered by its due date. Job shop is the typical operation model used in an MTO operation, where the production planner must make three concurrent decisions; they are order selection, lot size, and job schedule. These decisions are usually treated separately in the literature and are mostly led to heuristic solutions.The first phase of the study is focused on a formal definition of the problem.Mathematical programming techniques are applied to modeling this problem in terms of its objective, decision variables, and constraints. A commercial solver, CPLEX is applied to solve the resulting mixed-integer linear programming model with small instances to validate the mathematical formulation. The computational result shows it is not practical for solving problems of industrial size, using a commercial solver.The second phase of this study is focused on development of an effective solution approach to this problem of large scale. The proposed solution approach is an iterative process involving three sequential decision steps of order selection, lot sizing, and lot v scheduling. A range of simple sequencing rules are identified for each of the three subproblems. Using computer simulation as the tool, an experiment is designed to evaluate their performance against a set of system parameters.For order selection, the proposed weighted most profit rule performs the best. The shifting bottleneck and the earliest operation finish time both are the best scheduling rules. For lot sizing, the proposed minimum cost increase heuristic, based on the DixonSilver method performs the best, when the demand-to-capacity ratio at the bottleneck machine is high. The proposed minimum cost heuristic, based on the Wagner-Whitin algorithm is the best lot-sizing heuristic for shops of a low demand-to-capacity ratio. The proposed heuristic is applied to an industrial case to further evaluate its performance. The result shows it can improve an average of total profit by 16.62%. This research contributes to the production planning research community with a complete mathematical definition of the problem and an effective solution approach to solving the problem of industry scale.

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A Heuristic Algorithm for the Multi-Item Lot-Sizing Problem with Capacity Constraints

Cited by 43 publications

References 9 publications

A heuristic algorithm for master production schedule generation with finite capacity and sequence dependent setups

A heuristic algorithm for master production schedule generation with finite capacity and sequence dependent setups

A linear optimization approach to the combined production planning model

The Order Selection and Lot Sizing Problem in the Make-to-Order Environment

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