scholarly journals The Uncapacitatied Dynamic Single-Level Lot-Sizing Problem under a Time-Varying Environment and an Exact Solution Approach

2018 ◽  
Vol 10 (11) ◽  
pp. 3867
Author(s):  
Yiyong Xiao ◽  
Meng You ◽  
Xiaorong Zuo ◽  
Shenghan Zhou ◽  
Xing Pan
Keyword(s):  
Lot Sizing ◽  
Time Varying ◽  
Setup Cost ◽  
Single Level ◽  
Lot Sizing Problem ◽  
Dynamic Lot Sizing ◽  
Manufacturing Resources ◽  
Time Varying Environment ◽  
Forward Dynamic Programming ◽  
Varying Environment

The dynamic lot-sizing problem under a time-varying environment considers new features of the production system where factors such as production setup cost, unit inventory-holding cost, and unit price of manufacturing resources may vary in different periods over the whole planning horizon. Traditional lot-sizing theorems and algorithms are no longer fit for these situations as they had assumed constant environments. In our study, we investigated the dynamic lot-sizing problem with deteriorating production setup cost, a typical time-varying environment where the production setup is assumed to consume more preparing time and manufacturing resources as the production interval lasts longer. We proposed new lot-sizing models based on the traditional lot-sizing model considering the changing setup cost as a new constraint, called uncapacitatied dynamic single-level lot-sizing under a time-varying environment (UDSLLS-TVE for short). The UDSLLS-TVE problem has a more realistic significance and higher research value as it is closer to reality and has higher computational complexity as well. We proposed two mathematical programming models to describe UDSLLS_TVE with or without nonlinear components, respectively. Properties of the UDSLLS-TVE models were extensively analyzed and an exact algorithm based on forward dynamic programming (FDP) was proposed to solve this problem with a complexity of O (n2). Comparative experiments with the commercial MIP solver CPLEX on synthesized problem instances showed that the FDP algorithm is a global optimization algorithm and has a high computational efficiency.

scholarly journals Modeling the Capacitated Multi-Level Lot-Sizing Problem under Time-Varying Environments and a Fix-and-Optimize Solution Approach

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 377 ◽  
Author(s):  
Meng You ◽  
Yiyong Xiao ◽  
Siyue Zhang ◽  
Shenghan Zhou ◽  
Pei Yang ◽  
...  
Keyword(s):  
Lot Sizing ◽  
Time Varying ◽  
Production Environment ◽  
Setup Costs ◽  
Lot Sizing Problem ◽  
Multi Level ◽  
Varying Environments ◽  
Time Varying Environment ◽  
Production Capacities ◽  
Varying Environment

In this study, we investigated the time-varying capacitated lot-sizing problem under a fast-changing production environment, where production factors such as the setup costs, inventory-holding costs, production capacities, or even material prices may be subject to continuous changes during the entire planning horizon. Traditional lot-sizing theorems and algorithms, which often assume a constant production environment, are no longer fit for this situation. We analyzed the time-varying environment of today’s agile enterprises and modeled the time-varying setup costs and the time-varying production capacities. Based on these, we presented two mixed-integer linear programming models for the time-varying capacitated single-level lot-sizing problem and the time-varying capacitated multi-level lot-sizing problem, respectively, with considerations on the impact of time-varying environments and dynamic capacity constraints. New properties of these models were analyzed on the solution’s feasibility and optimality. The solution quality was evaluated in terms of the entropy which indicated that the optimized production system had a lower value than that of the unoptimized one. A number of computational experiments were conducted on well-known benchmark problem instances using the AMPL/CPLEX to verify the proposed models and to test the computational effectiveness and efficiency, which showed that the new models are applicable to the time-varying environment. Two of the benchmark problems were updated with new best-known solutions in the experiments.

scholarly journals Firefly Algorithm: Minimizing Cost on Single-Level Lot-Sizing Problem

2018 ◽  
Vol 3 (1) ◽  
pp. 55-63
Author(s):  
Siti Hafawati Jamaluddin ◽  
Nurul Azleeka Zulkipli ◽  
Norwaziah Mahmud ◽  
Nur Syuhada Muhamat Pazil
Keyword(s):  
Production Planning ◽  
Production Cost ◽  
Firefly Algorithm ◽  
Lot Sizing ◽  
Planning Horizon ◽  
Production Plan ◽  
Setup Cost ◽  
Single Level ◽  
Lot Sizing Problem ◽  
Industrial Company

Nowadays, the industrial company plays a very important role to our country. However, the manufacturer industry has big issues in the production planning which called planning horizon where, the lot-sizing problem is one of the most important issues in the production planning area. In lot-sizing problem, the manufacturers are facing the problems in determining the setup cost when there is no consistency and efficiency in organizing the production plan. From the problem emerge, the minimum of production cost is determined by using firefly algorithm. From the minimum production cost obtained, the optimal setup cost on single-level lot-sizing problem is defined. In this study, the result is obtained by using MATLAB R2017a software to minimize the production cost on single-level lot-sizing problem where the minimum production cost is are for one month is $154 while, the minimum production cost for 12 months is $1760.89. From those minimum total cost obtained by using firefly algorithm, the optimal setup cost for one month is $86.83 while optimal setup cost for 12 months are $86.51, $86.81, $88.30, $95.39, $112.01, $102.92, $93.30, $85.90, $106.50, $85.77, $99.46 and $115.30 respectively. As a conclusion, firefly algorithm is applicable to use in minimizing production cost on single-level lot-sizing problem since the result obtained gives the better solution compared to the exact solution

scholarly journals A Heuristic Solution of Multi-Item Single Level Capacitated Dynamic Lot-Sizing Problem with Setup Time

2011 ◽  
Vol 264-265 ◽  
pp. 1794-1801
Author(s):  
Sultana Parveen ◽  
Md. Ahsan Akthar Hasin
Keyword(s):  
Lot Sizing ◽  
Research Work ◽  
Real Life ◽  
Optimal Solution ◽  
Setup Time ◽  
Heuristic Solution ◽  
Single Level ◽  
Solution Algorithms ◽  
Lot Sizing Problem ◽  
Dynamic Lot Sizing

The multi-item single level capacitated dynamic lot-sizing problem consists of scheduling N items over a horizon of T periods. The objective is to minimize the sum of setup and inventory holding costs over the horizon subject to a constraint on total capacity in each period. No backlogging is allowed. Only one machine is available with a fixed capacity in each period. In case of a single item production, an optimal solution algorithm exists. But for multi-item problems, optimal solution algorithms are not available. It has been proved that even the two-item problem with constant capacity is NP-hard, that is, it is in a class of problems that are extremely difficult to solve in a reasonable amount of time. This has called for searching good heuristic solutions. For a multi-item problem, it would be more realistic to consider the setup time, since switching the machine from one item to another would require a setup time. This setup time would be independent of item sequences and this could be a very important parameter from practical point of view. The current research work has been directed toward the development of a model for multiitem problem considering this parameter. Based on the model a program has been executed and feasible solutions with some real life data have been obtained.

Modeling and solving the constrained multi-items lot-sizing problem with time-varying setup cost

2018 ◽  
Vol 116 ◽  
pp. 202-207 ◽  
Author(s):  
Shenghan Zhou ◽  
Yuliang Zhou ◽  
Xiaorong Zuo ◽  
Yiyong Xiao ◽  
Yang Cheng
Keyword(s):  
Lot Sizing ◽  
Time Varying ◽  
Setup Cost ◽  
Lot Sizing Problem

scholarly journals A heuristic solution of multi-item single level capacitated dynamic lot-sizing problem

1970 ◽  
Vol 38 ◽  
pp. 1-7 ◽  
Author(s):  
Sultana Parveen ◽  
AFM Anwarul Haque
Keyword(s):  
Lot Sizing ◽  
Research Work ◽  
Optimal Solution ◽  
Point Of View ◽  
Lot Size ◽  
Heuristic Solution ◽  
Single Level ◽  
Solution Algorithms ◽  
Lot Sizing Problem ◽  
Dynamic Lot Sizing

The multi-item single level capacitated dynamic lot-sizing problem consists of scheduling N items over a horizon of T periods. The objective is to minimize the sum of setup and inventory holding costs over the horizon subject to a constraint on total capacity in each period. No backlogging is allowed. Only one machine is available with a fixed capacity in each period. In case of a single item production, an optimal solution algorithm exists. But for multi-item problems, optimal solution algorithms are not available. It has been proved that even the two-item problem with constant capacity is NP (nondeterministic polynomial)-hard. That is, it is in a class of problems that are extremely difficult to solve in a reasonable amount of time. This has called for searching good heuristic solutions. For a multi-item problem, it would be more realistic to consider an upper limit on the lot-size per setup for each item and this could be a very important parameter from practical point of view. The current research work has been directed toward the development of a model for multi-item problem considering this parameter. Based on the model a program has been executed and feasible solutions have been obtained. Keywords: Heuristics, inventory, lot-sizing, multi-item, scheduling.DOI: 10.3329/jme.v38i0.893 Journal of Mechanical Engineering Vol.38 Dec. 2007 pp.1-7

scholarly journals Dynamic lot sizing problem for a warm/cold process

2006 ◽  
Vol 38 (11) ◽  
pp. 1027-1044 ◽  
Author(s):  
Ayhan Özgür Toy ◽  
Emre Berk
Keyword(s):  
Lot Sizing ◽  
Lot Sizing Problem ◽  
Dynamic Lot Sizing
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