The Optimal Lot Sizing for Unreliable Economic Manufacturing Model

1997 ◽  
Vol 04 (04) ◽  
pp. 413-426 ◽  
Author(s):  
Tadashi Dohi ◽  
Yasunori Yamada ◽  
Naoto Kaio ◽  
Shunji Osaki
Keyword(s):  
Cost Function ◽  
Production Process ◽  
Optimal Policy ◽  
Lot Sizing ◽  
Lot Size ◽  
Expected Cost ◽  
Numerical Examples ◽  
Machine Breakdown ◽  
Special Cases ◽  
Age Replacement

This paper considers the optimal policy for an economic manufacturing model with stochastic machine breakdown and repair. The expected cost function is formulated and the optimal age replacement-like policy which minimizes it is derived analytically. The detailed properties on the resulting optimal lot size are examined for some special cases. Finally, numerical examples are devoted to show that the effect of corrective maintenance operation in the production process is remarkable.

Scheduling jobs on non-identical IFR processors to minimize general cost functions

1991 ◽  
Vol 23 (04) ◽  
pp. 909-924 ◽  
Author(s):  
Rhonda Righter ◽  
Susan H. Xu
Keyword(s):  
Cost Function ◽  
Optimal Policy ◽  
Expected Number ◽  
Expected Cost ◽  
Processing Times ◽  
Special Cases ◽  
The Cost ◽  
General Cost Functions ◽  
Tardy Jobs ◽  
Completion Times

We consider the problem of scheduling n jobs non-preemptively on m parallel, non-identical processors to minimize a weighted expected cost function of job completion times, where the weights are associated with the jobs. The cost function is assumed to be increasing and concave but otherwise arbitrary. Processing times are IFR with different distributions for different processors. Jobs may be processed on any processor and there are no precedences. We show that the optimal policy orders the jobs in decreasing order of their weights and then uses the individually optimal policy for each job. In other words, processors are offered to jobs in order, and each job considers its own expected cost function for its completion time to decide whether to accept or reject a processor. Therefore, the optimal policy does not depend on the weights of the jobs except through their order. Special cases of our objective function are weighted expected flowtime, weighted discounted expected flowtime, and weighted expected number of tardy jobs.

Scheduling jobs on non-identical IFR processors to minimize general cost functions

1991 ◽  
Vol 23 (4) ◽  
pp. 909-924 ◽  
Author(s):  
Rhonda Righter ◽  
Susan H. Xu
Keyword(s):  
Cost Function ◽  
Optimal Policy ◽  
Expected Number ◽  
Expected Cost ◽  
Processing Times ◽  
Special Cases ◽  
The Cost ◽  
General Cost Functions ◽  
Tardy Jobs ◽  
Completion Times

We consider the problem of scheduling n jobs non-preemptively on m parallel, non-identical processors to minimize a weighted expected cost function of job completion times, where the weights are associated with the jobs. The cost function is assumed to be increasing and concave but otherwise arbitrary. Processing times are IFR with different distributions for different processors. Jobs may be processed on any processor and there are no precedences. We show that the optimal policy orders the jobs in decreasing order of their weights and then uses the individually optimal policy for each job. In other words, processors are offered to jobs in order, and each job considers its own expected cost function for its completion time to decide whether to accept or reject a processor. Therefore, the optimal policy does not depend on the weights of the jobs except through their order. Special cases of our objective function are weighted expected flowtime, weighted discounted expected flowtime, and weighted expected number of tardy jobs.

Optimal production lot sizing for an imperfect manufacturing system with machine breakdown and emergency maintenance policy

Kybernetes ◽  
2019 ◽  
Vol 49 (5) ◽  
pp. 1533-1560
Author(s):  
Xinfeng Lai ◽  
Zhixiang Chen ◽  
Bhaba R. Sarker
Keyword(s):  
Manufacturing System ◽  
Lot Sizing ◽  
Lot Size ◽  
Maintenance Policy ◽  
Managerial Implication ◽  
Optimal Production ◽  
Expected Cost ◽  
Content Type ◽  
Machine Breakdown ◽  
Production Lot Size

Purpose The purpose of this paper is to study a production lot sizing problem with consideration of imperfect manufacturing and emergency maintenance policy, providing managerial implication for practitioners. Design/methodology/approach In this study, the authors introduce two models, where in Model I, shortages are not allowed and repair times are negligible. In Model II, shortages are allowed and are partially backlogged, and repair times are assumed to be exponentially distributed, algorithm is developed to solve the models, numerical examples were demonstrated the applications. Findings Results show that in the Model I, demand rate is the most significant parameter affecting the average expected cost, whereas the time needed to breakdown after machine shift is the most significant factor affecting the production lot size. Therefore, reduction in the time needed to breakdown after machine shift would be helpful for determining an appropriate production lot size in Model I. In Model II, repair time parameter is the most significant factor affecting the average expected cost. Reducing the value of machine shift parameter would be helpful for determining an adequate production lot size and reducing decision risk. Practical implications This paper can provide important reference value for practitioners with managerial implication of how to effectively maintain equipment, i.e. how to make product lot size considering the influence of the maintenance policy. Originality/value From the aspect of academia, this paper provides a solution to the optimal production lot sizing decision for an imperfect manufacturing system with consideration of machine breakdown and emergency maintenance, which is a supplement to imperfect EMQ model.

Optimum replacement policies with delay

1974 ◽  
Vol 11 (01) ◽  
pp. 102-110 ◽  
Author(s):  
Toshio Nakagawa ◽  
Shunji Osaki
Keyword(s):  
Delay Time ◽  
Expected Cost ◽  
Numerical Examples ◽  
Special Cases ◽  
Replacement Theory

Replacement theory for equipment has been investigated by several authors. This paper introduces the ‘delay’ time preparing for replacement, derives the expected cost per unit time, and discusses the optimum replacement policies under several conditions. Three special cases are discussed and numerical examples are presented.

Random Age Replacement Policies with Periodic Planning Times

2019 ◽  
Vol 26 (05) ◽  
pp. 1950023 ◽  
Author(s):  
Satoshi Mizutani ◽  
Xufeng Zhao ◽  
Toshio Nakagawa
Keyword(s):  
Weibull Distribution ◽  
Failure Time ◽  
Optimal Solutions ◽  
Expected Cost ◽  
Numerical Examples ◽  
Cost Rate ◽  
Modeling Approaches ◽  
Maintenance Policies ◽  
Age Replacement

The random age replacement policies discussed in literatures are helpful to complete the nonstopping works with random working cycles, however, maintenance policies are more easily performed at periodic times in real applications. For such a viewpoint, this paper proposes that age replacement policies are planned at periodic times while considering the random working cycles. Using the modeling approaches of replacement first and last policies, we discuss two models such that the unit is replaced at periodic times [Formula: see text] and working cycles [Formula: see text], whichever occurs first and whichever occurs last. The expected cost rate models are obtained and their optimal solutions for [Formula: see text] and [Formula: see text] are discussed. The comparisons between the policies of [Formula: see text] and [Formula: see text], and replacement first and last are made from the point of cost. Numerical examples are illustrated when the failure time has a Weibull distribution.

Optimum replacement policies with delay

1974 ◽  
Vol 11 (1) ◽  
pp. 102-110 ◽  
Author(s):  
Toshio Nakagawa ◽  
Shunji Osaki
Keyword(s):  
Delay Time ◽  
Expected Cost ◽  
Numerical Examples ◽  
Special Cases ◽  
Replacement Theory

Replacement theory for equipment has been investigated by several authors. This paper introduces the ‘delay’ time preparing for replacement, derives the expected cost per unit time, and discusses the optimum replacement policies under several conditions. Three special cases are discussed and numerical examples are presented.

MINIMALISASI BIAYA SIMPAN DAN BIAYA SETUP PADA MULTIPLE PRODUK: SIMULASI DENGAN CAPACITATED LOT SIZING PROBLEM

2019 ◽  
Vol 4 (2) ◽  
pp. 205-214
Author(s):  
Erika Fatma
Keyword(s):  
Production Cost ◽  
Lot Sizing ◽  
Setup Time ◽  
Production Costs ◽  
Total Production ◽  
Product Cycle ◽  
Lot Size ◽  
Setup Costs ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing

Lot sizing problem in production planning aims to optimize production costs (processing, setup and holding cost) by fulfilling demand and resources capacity costraint. The Capacitated Lot sizing Problem (CLSP) model aims to balance the setup costs and inventory costs to obtain optimal total costs. The object of this study was a plastic component manufacturing company. This study use CLSP model, considering process costs, holding costs and setup costs, by calculating product cycle and setup time. The constraint of this model is the production time capacity and the storage capacity of the finished product. CLSP can reduce the total production cost by 4.05% and can reduce setup time by 46.75%.  Keyword: Lot size, CLSP, Total production cost.

Exergy-Based Ecological Optimization of an Irreversible Quantum Carnot Heat Pump with Spin-1/2 Systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiaowei Liu ◽  
Lingen Chen ◽  
Yanlin Ge ◽  
Huijun Feng ◽  
Feng Wu ◽  
...  
Keyword(s):  
Heat Pump ◽  
Performance Comparison ◽  
Ecological Function ◽  
Performance Characteristics ◽  
Numerical Examples ◽  
Ecological Performance ◽  
Special Cases ◽  
Heating Load ◽  
Ecological Optimization

AbstractBased on an irreversible quantum Carnot heat pump model in which spin-1/2 systems are used as working substance, an exergy-based ecological function and some other important parameters of the model heat pump are derived. Numerical examples are provided to investigate its ecological performance characteristics. The influences of various irreversibility factors on the ecological performance are discussed. Performance comparison and discussion among maximum points of ecological function, heating load, and so on, are conducted. At last, three special cases are discussed.

Smoothing Short Duration Capacity Problems in Enterprise Resource Planning (ERP) Systems: An Algorithmic Approach

2014 ◽  
Vol 933 ◽  
pp. 860-868
Author(s):  
Muneam Zamzeer Al-Magsoosi
Keyword(s):  
Short Duration ◽  
Enterprise Resource Planning ◽  
Lot Sizing ◽  
Environmental Parameters ◽  
Resource Planning ◽  
Successful Implementation ◽  
Erp Systems ◽  
Lot Size ◽  
Erp System ◽  
Order Release

Successful implementation of ERP systems should take full advantage of the access to information, but not be constrained by many of the deficiencies associated with infinite capacity scheduling methodologies. In this paper an algorithm is developed which improves the performance of the ERP system. Lot sizing decisions based on capacity availability are used as an instrument to integrate more effectively capacity requirements planning (CRP) and Material Requirements Planning (MRP). MRP is a planning tool for a sub-set of manufacturing system specially in hierarchal multi-product, multi-period and multi-stage production planning and inventory control system. The Vehicle used for this integration is planned order release (POR) quantity. The algorithm requires minimal deviation from the MRP logic. In this sequential process MRP first issues the action notices and then the algorithm analyses the capacity situation in the work centers. The algorithm scans all planned order release quantities of lower level items in the action bucket before orders are released to the shop. For each item a delta value is computed identifying the degree orders are contributing to capacity problems. This delta is specific to each POR. The POR causing the highest overload and the one passing through the lowest utilized work centers are selected for a lot size decrease, respectively, an increase. After identifying the candidates, a series of checks analyses the suitability of the candidates for that change. The planned order release quantities of more items can be performed. Projected capacity profile after iteration will be updated and capacity requirements over a short duration are smoothed. The experiments are performed with MAP/3000 as a simulation model for this study. The developed algorithm is added to MAP/3000 as additional subroutines. The design of the experiments consists of a base test identifying the significance of different environmental parameters of MRP systems and a main test which performs a detailed evaluation. The results are evaluated using analysis of variance techniques. Most ERP systems built on the historical development of MRP and CRP systems, and the assumption of infinite capacity is affecting the performance of those systems badly. This paper is presenting an algorithm to smooth capacity problems by using the existed capacity.

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

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