scholarly journals Application of the surrogate gradient method for a multi-item single-machine dynamic lot size scheduling problem

2021 ◽  
Vol 3 (7) ◽  
Author(s):  
Minoru Kobayashi
Keyword(s):  
Single Machine ◽  
Gradient Method ◽  
Optimal Solution ◽  
Constraint Equation ◽  
Circuit Board ◽  
Simultaneous Optimization ◽  
Scheduling Problem ◽  
Lot Size ◽  
Setup Cost ◽  
Dynamic Lot Size

AbstractThis study treats a multi-item single-machine dynamic lot size scheduling problem with sequence-independent setup cost and setup time. This problem has various heterogeneous decision features, such as lot sizing and lot sequencing. Traditionally, the problem has been treated by putting artificial constraints on the other feature in order to determine one of them. The proposed model is a Lagrange decomposition and coordination method that aims at simultaneous optimization of these decision features; however, smooth convergence to a feasible near-optimal solution has been a problem. So, in this paper, we propose a model that improves the constraint equation of the existing model and showed that it satisfies the Karush–Kuhn–Tucker (KKT) condition when we obtained a feasible solution. In addition, by applying the surrogate gradient method, which has never been applied to this problem before, it was shown that smoother convergence than before can be achieved through actual example of printed circuit board.

scholarly journals Inventory Model with Demand Dependent on Unit Price under Fuzzy Parameters and Decision Variables

2019 ◽  
Vol 8 (3) ◽  
pp. 784-788
Keyword(s):  
Numerical Solutions ◽  
Unit Cost ◽  
Optimal Solution ◽  
Unit Price ◽  
Lot Size ◽  
Setup Cost ◽  
Eoq Model ◽  
Decision Variables ◽  
Holding Cost ◽  
Cost Parameters

An EOQ model with demand dependent on unit price is considered and a new approach of finding optimal demand value is done from the optimal unit cost price after defuzzification. Here the cost parameters like setup cost, holding cost and shortage cost and also the decision variables like unit price, lot size and the maximum inventory are taken under fuzzy environment. Triangular fuzzy numbers are used to fuzzify these input parameters and unknown variables. For the proposed model an optimal solution has been determined using Karush Kuhn-Tucker conditions method. Graded Mean Integration (GMI) method is used for defuzzification. Numerical solutions are obtained and sensitivity analysis is done for the chosen model

Supply Chain Scheduling with Transportation Cost on a Single Machine

2011 ◽  
Vol 382 ◽  
pp. 106-109
Author(s):  
Jing Fan
Keyword(s):  
Supply Chain ◽  
Single Machine ◽  
System Integration ◽  
Production Cost ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Transportation Cost ◽  
Programming Algorithm ◽  
Scheduling Problem ◽  
Supply Chain Scheduling

Supply chain scheduling problem is raised from modern manufacturing system integration, in which manufacturers not only process orders but also transport products to customer’s location. Therefore, the system ought to consider how to appropriately send finished jobs in batches to reduce transportation costs while considering the processing sequence of jobs to reduce production cost. This paper studies such a supply chain scheduling problem that one manufacturer produces with a single machine and deliveries jobs within limited transportation times to one customer. The objective function is to minimize the total sum of production cost and transportation cost. The NP hard property of the problem is proved in the simpler way, and the pseudo-dynamic programming algorithm in the literature is modified as the MDP algorithm to get the optimal solution which is associated with the total processing times of jobs.

A Pareto-Optimal Solution for a Multi-Objective Scheduling Problem with Periodic Maintenance Requirement

2012 ◽  
Vol 3 (2) ◽  
pp. 24-45 ◽  
Author(s):  
Deniz Mungan ◽  
Junfang Yu ◽  
Bhaba R. Sarker ◽  
Mohammad Anwar Rahman
Keyword(s):  
Objective Function ◽  
Single Machine ◽  
Pareto Optimality ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Neighborhood Search ◽  
Pareto Optimal ◽  
Scheduling Problem ◽  
Objective Functions ◽  
Periodic Maintenance

A Pareto-optimal solution is developed in this paper for a scheduling problem on a single machine with periodic maintenance and non-preemptive jobs. Most of the scheduling problems address only one objective function, while in the real world, such problems are always associated with more than one objective. In this paper, both multi-objective functions and multi-maintenance periods are considered for a machine scheduling problem. To avoid complexities, multiple objective functions are consolidated and transformed into a single objective function after they are weighted and assigned proper weighting factors. In addition, periodic maintenance schedules are also considered in the model. The objective of the model addressed is to minimize the weighted function of the total job flow time, the maximum tardiness, and the machine idle time in a single machine problem with periodic maintenance and non-preemptive jobs. An algorithm is developed to solve this multiple criterion problem and to construct the Pareto-set. The parametric analysis of the trade-offs of all solutions with all possible weighted combination of the criteria is performed. A neighborhood search heuristic is also developed. Results are provided to explore the best schedule among all the Pareto-optimality sets and to compare the result of the modified Pareto-optimality algorithm with the result of the neighborhood search heuristic.

scholarly journals Hybridization Simulated Annealing Algorithm in a Single Machine Scheduling Problem

2021 ◽  
Vol 20 ◽  
pp. 597-605
Author(s):  
Hafed M. Motair
Keyword(s):  
Simulated Annealing ◽  
Single Machine ◽  
Simulated Annealing Algorithm ◽  
Optimal Solution ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Metaheuristic Algorithm ◽  
Annealing Algorithm ◽  
Completion Times

In this paper, we investigate a single machine scheduling problem (SMSP). We try to reach the optimal or near optimal solution which minimize the sum of three objective functions: total completion times, total tardiness and total earliness. Firstly, we solve this problem by Branch and bound algorithm (BAB alg) to find optimal solutions, dominance rules (DR)s are used to improve the performance of BAB alg, the resulting is BABDR, secondly, we solve this problem by simulated annealing algorithm (SA alg) as metaheuristic algorithm (MET alg). It is known that combining MET alg with other algorithms can improve the resulting solutions. In this paper we developed the concept of insertion preselected jobs one by one through all positions of remaining jobs of considered sequence, the proposed MET alg called Insertion Metaheuristic Algorithm (IMA). This procedure improves the performance of SA alg in two directions: in the first one, we use the IMA to generate initial solution for SA alg, in the second one, we use the IMA to improve the solution obtained through the iterations of SA alg. The experiments showed that IMA can improve the performance of SA alg in these two directions.

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