scholarly journals Optimal Policies for a Finite-Horizon Production Inventory Model

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Lakdere Benkherouf ◽  
Dalal Boushehri
Keyword(s):  
Simple Procedure ◽  
Optimal Schedule ◽  
Planning Horizon ◽  
Inventory Model ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Integer Variable ◽  
Optimal Production ◽  
Production Inventory ◽  
Varying Demand

This paper is concerned with the problem of finding the optimal production schedule for an inventory model with time-varying demand and deteriorating items over a finite planning horizon. This problem is formulated as a mixed-integer nonlinear program with one integer variable. The optimal schedule is shown to exist uniquely under some technical conditions. It is also shown that the objective function of the nonlinear obtained from fixing the integrality constraint is convex as a function of the integer variable. This in turn leads to a simple procedure for finding the optimal production plan.

scholarly journals Integration of Mixed-Integer Nonlinear Program and Project Management Tool to Support Sustainable Cost-Optimal Construction Scheduling

2021 ◽  
Vol 13 (21) ◽  
pp. 12173
Author(s):  
Borna Dasović ◽  
Uroš Klanšek
Keyword(s):  
Project Management ◽  
Optimal Schedule ◽  
Indirect Costs ◽  
Management Tool ◽  
Mixed Integer ◽  
Task Completion ◽  
Nonlinear Program ◽  
Project Schedule ◽  
Construction Scheduling ◽  
Optimal Construction

This paper presents the integration of mixed-integer nonlinear program (MINLP) and project management tool (PMT) to support sustainable cost-optimal construction scheduling. An integrated structure of a high-level system for exact optimization and PMT was created. To ensure data compatibility between the optimization system and PMT and to automate the process of obtaining a cost-optimal schedule, a data transformation tool (DTT) was developed within a spreadsheet application. The suggested system can determine: (i) an optimal project schedule with associated network diagram and Gantt chart in continuous or discrete time units; (ii) optimal critical and non-critical activities, including their early start, late start, early finish, late finish along with total and free slack times; and (iii) minimum total project cost along with the allocation of direct and indirect costs. The system provides functionalities such as: (i) MINLP can be updated, and schedules can be re-optimized; (ii) the optimal schedule can be saved as a baseline to track changes; (iii) different optimization algorithms can be engaged whereby switching between them does not require model changes; (iv) PMT can be used to track task completion in the optimized schedule; (v) calendar settings can be changed; and (vi) visual reports can be generated to support efficient project management. Results of cost-optimal project scheduling are given in a conventional PMT environment, which raises the possibility that the proposed system will be more widely used in practice. Integration of MINLP and PMT allows each software to be used for what it was initially designed. Their combination leads to additional information and features of optimized construction schedules that would be significantly more difficult to achieve if used separately. Application examples are given in the paper to show the advantages of the proposed approach.

An Imperfect Production Model for Breakable Multi-Item with Dynamic Demand and Learning Effect on Rework over Random Planning Horizon

2021 ◽  
Vol 14 (12) ◽  
pp. 574
Author(s):  
Amalesh Kumar Manna ◽  
Leopoldo Eduardo Cárdenas-Barrón ◽  
Barun Das ◽  
Ali Akbar Shaikh ◽  
Armando Céspedes-Mota ◽  
...  
Keyword(s):  
Learning Effect ◽  
Planning Horizon ◽  
Inventory Model ◽  
Inventory System ◽  
Production Model ◽  
Inventory Models ◽  
Imperfect Production ◽  
Production Inventory ◽  
Random Planning Horizon ◽  
Production Inventory System

In recent times, in the literature of inventory management there exists a notorious interest in production-inventory models focused on imperfect production processes with a deterministic time horizon. Nevertheless, it is well-known that there is a high influence and impact caused by the learning effect on the production-inventory models in the random planning horizon. This research work formulates a mathematical model for a re-workable multi-item production-inventory system, in which the demand of the items depends on the accessible stock and selling revenue. The production-inventory model allows shortages and these are partial backlogged over a random planning horizon. Also, the learning effect on the rework policy, inflation, and the time value of money are considered. The main aim is to determine the optimum production rates that minimize the expected total cost of the multi-item production-inventory system. A numerical example is solved and a detailed sensitivity analysis is conducted in order to study the production-inventory model.

scholarly journals A Production-Inventory Model for a Deteriorating Item Incorporating Learning Effect Using Genetic Algorithm

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
Debasis Das ◽  
Arindam Roy ◽  
Samarjit Kar
Keyword(s):  
Genetic Algorithm ◽  
Time Horizon ◽  
Planning Horizon ◽  
Inventory Model ◽  
Sensitivity Analyses ◽  
Optimal Decision ◽  
Possibility Measure ◽  
Random Mutation ◽  
Production Inventory ◽  
Value Of Money

Demand for a seasonal product persists for a fixed period of time. Normally the “finite time horizon inventory control problems” are formulated for this type of demands. In reality, it is difficult to predict the end of a season precisely. It is thus represented as an uncertain variable and known as random planning horizon. In this paper, we present a production-inventory model for deteriorating items in an imprecise environment characterised by inflation and timed value of money and considering a constant demand. It is assumed that the time horizon of the business period is random in nature and follows exponential distribution with a known mean. Here, we considered the resultant effect of inflation and time value of money as both crisp and fuzzy. For crisp inflation effect, the total expected profit from the planning horizon is maximized using genetic algorithm (GA) to derive optimal decisions. This GA is developed using Roulette wheel selection, arithmetic crossover, and random mutation. On the other hand when the inflation effect is fuzzy, we can expect the profit to be fuzzy, too! As for the fuzzy objective, the optimistic or pessimistic return of the expected total profit is obtained using, respectively, a necessity or possibility measure of the fuzzy event. The GA we have developed uses fuzzy simulation to maximize the optimistic/pessimistic return in getting an optimal decision. We have provided some numerical examples and some sensitivity analyses to illustrate the model.

scholarly journals Solution procedures for block selection and sequencing in flat-bedded potash underground mines

OR Spectrum ◽  
2021 ◽  
Author(s):  
Cinna Seifi ◽  
Marco Schulze ◽  
Jürgen Zimmermann
Keyword(s):  
Crop Yields ◽  
Decisive Role ◽  
Planning Horizon ◽  
Underground Mines ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Constructive Heuristic ◽  
Processing Plants ◽  
Problem Instances ◽  
Feasible Solutions

AbstractPhosphates, and especially potash, play an essential role in the increase in crop yields. Potash is mined in Germany in underground mines using a conventional drill-and-blast technique. The most commercially valuable mineral contained in potash is the potassium chloride that is separated from the potash in aboveground processing plants. The processing plants perform economically best if the amount of potassium contained in the output is equal to a specific value, the so-called optimal operating point. Therefore, quality-oriented extraction plays a decisive role in reducing processing costs. In this paper, we mathematically formulate a block selection and sequencing problem with a quality-oriented objective function that aims at an even extraction of potash regarding the potassium content. We, thereby, have to observe some precedence relations, maximum and minimum limits of the output, and a quality tolerance range within a given planning horizon. We model the problem as a mixed-integer nonlinear program which is then linearized. We show that our problem is $${\mathcal {NP}}$$ NP -hard in the strong sense with the result that a MILP-solver cannot find feasible solutions for the most challenging problem instances at hand. Accordingly, we develop a problem-specific constructive heuristic that finds feasible solutions for each of our test instances. A comprehensive experimental performance analysis shows that a sophisticated combination of the proposed heuristic with the mathematical program improves the feasible solutions achieved by the heuristic, on average, by $$92.5\%$$ 92.5 % .

scholarly journals A Production Model for Deteriorating Inventory Items with Production Disruptions

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Yong He ◽  
Ju He
Keyword(s):  
Inventory Model ◽  
Deteriorating Items ◽  
Production Model ◽  
Active Area ◽  
Disruption Management ◽  
Optimal Production ◽  
Numerical Example ◽  
Production Inventory

Disruption management has recently become an active area of research. In this study, an extension is made to consider the fact that some products may deteriorate during storage. A production-inventory model for deteriorating items with production disruptions is developed. Then the optimal production and inventory plans are provided, so that the manufacturer can reduce the loss caused by disruptions. Finally, a numerical example is used to illustrate the model.

scholarly journals Planning Horizon for Production Inventory Models with Production Rate Dependent on Demand and Inventory Level

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jennifer Lin ◽  
Henry C. J. Chao ◽  
Peterson Julian
Keyword(s):  
Production Rate ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Inventory Model ◽  
Inventory Level ◽  
Inventory Models ◽  
New Production ◽  
Production Inventory ◽  
Infinite Planning Horizon ◽  
Finite Planning Horizon

This paper discusses why the selection of a finite planning horizon is preferable to an infinite one for a replenishment policy of production inventory models. In a production inventory model, the production rate is dependent on both the demand rate and the inventory level. When there is an exponentially decreasing demand, the application of an infinite planning horizon model is not suitable. The emphasis of this paper is threefold. First, while pointing out questionable results from a previous study, we propose a corrected infinite planning horizon inventory model for the first replenishment cycle. Second, while investigating the optimal solution for the minimization problem, we found that the infinite planning horizon should not be applied when dealing with an exponentially decreasing demand. Third, we developed a new production inventory model under a finite planning horizon for practitioners. Numerical examples are provided to support our findings.

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