Incorporating machine reliability issue and backlogging into the EMQ model - Part I: Random breakdown occurring in backorder filling time

This study is concerned with determination of the optimal replenishment policy for economic manufacturing quantity (EMQ) model with backlogging and machine reliability issue. Classic EMQ model does not consider nonconforming items generated during a production cycle, nor does it deal with the machine breakdown situation. It is noted that in manufacturing system when back-ordering is permitted, a random machine failure can take place in either backorder filling time or in on-hand inventory piling period. The first phase of this study examines the aforementioned practical issues by incorporating rework process of defective items, scrap and random machine failure taking place specifically in backorder satisfying time into the EMQ model. The objective is to determine the optimal replenishment lot-size that minimizes the overall production-inventory costs. Mathematical modelling and analysis is used and the renewal reward theorem is employed to cope with the variable cycle length. Theorem on conditional convexity of total cost function is proposed and proved. The optimal lot size for such a real-life imperfect manufacturing system is derived. A numerical example is given to demonstrate its practical usage

Incorporating machine reliability issue and backlogging into the EMQ model - Part II: Random breakdown occurring in inventory piling time

This paper presents the second part of a research which is concerned with incorporating machine reliability issues and backlogging into the economic manufacturing quantity (EMQ) model. It may be noted that in a production system when back-ordering is permitted, a random machine failure can take place in either backorder filling stage or in on-hand inventory piling time. The first part of the research investigates the effect of a machine failure occurring in backorder filling stage on the optimal lot-size; while this paper (the second part of the research) studies the effect of random breakdown happening in inventory piling time on the optimal batch size for such an imperfect EMQ model. The objective is to determine the optimal replenishment lot-size that minimizes the overall productioninventory costs. Mathematical modelling is used and the renewal reward theorem is employed to cope with the variable cycle length. Hessian matrix equations are utilized to prove convexity of the cost function. Then, the optimal lot size for such a real-life imperfect manufacturing system is derived. Practitioners and managers in the field can adopt these replenishment policies to establish their own robust production plan accordingly

Finite production rate model with backlogging, service level constraint, rework, and random breakdown

In most real-life production systems, both random machine breakdown and the production of nonconforming items are inevitable, and adopting a backlogging policy with a predetermined minimum acceptable service level can sometimes be an effective strategy to help the management reduce operating cost or smoothen the production schedule. With the aim of addressing the aforementioned practical situations in production, this study explores the optimal production runtime for the finite production rate (FPR) model with allowable backlogging and service level constraint, rework of defective products, and random machine breakdown. Mathematical modelling is employed along with optimization techniques to derive the optimal production runtime that minimizes the long-run average system costs for the proposed FPR model. The joint effects of the allowable backlogging with a planned service level, rework, and random machine breakdown on optimal runtime decision have been carefully investigated through a numerical example and sensitivity analysis. As a result, important insights regarding various system parameters are revealed in order to enable the management to better understand, plan, and control such a practical production system

Volume flexible multi items inventory system with imprecise environment

This paper addresses a multi items volume flexible system for time dependent decaying items with the concept of machine breakdown and imprecise environment. In this study, partially backlogged shortages have been discussed. All the costs are fuzzified with signed distance method. Numerical examples are given to illustrate the theoretical results and sensitivity analysis is given to validate the results for various parameters

Replenishment Decision Making with Permissible Shortage, Repairable Nonconforming Products and Random Equipment Failure

Abstract: This study is concerned with replenishment decision making with repairable nonconforming products, backordering and random equipment failure during production uptime. In real world manufacturing systems, due to different factors generation of nonconforming items and unexpected machine breakdown are inevitable. Also, in certain business environments various situations between vendor and buyer, the backordering of shortage stocks sometimes is permissible with extra cost involved. This study incorporates backlogging, random breakdown and rework into a production system, with the objective of determination of the optimal replenishment lot size and optimal level of backordering that minimizes the long-run average system costs. Mathematical modeling along with the renewal reward theorem is employed for deriving system cost function. Hessian matrix equations are used to prove its convexity. Research result can be directly adopted by practitioners in the production planning and control field to assist them in making their own robust production replenishment decision

Finite production rate model with backlogging, service level constraint, rework, and random breakdown

In most real-life production systems, both random machine breakdown and the production of nonconforming items are inevitable, and adopting a backlogging policy with a predetermined minimum acceptable service level can sometimes be an effective strategy to help the management reduce operating cost or smoothen the production schedule. With the aim of addressing the aforementioned practical situations in production, this study explores the optimal production runtime for the finite production rate (FPR) model with allowable backlogging and service level constraint, rework of defective products, and random machine breakdown. Mathematical modelling is employed along with optimization techniques to derive the optimal production runtime that minimizes the long-run average system costs for the proposed FPR model. The joint effects of the allowable backlogging with a planned service level, rework, and random machine breakdown on optimal runtime decision have been carefully investigated through a numerical example and sensitivity analysis. As a result, important insights regarding various system parameters are revealed in order to enable the management to better understand, plan, and control such a practical production system

Operations research models and methods for safety stock determination: A review

In supply chain inventory management it is generally accepted that safety stocks are a suitable strategy to deal with demand and supply uncertainty aiming to prevent inventory stock-outs. Safety stocks have been the subject of intensive research, typically covering the problems of dimensioning, positioning, managing and placement. Here, we narrow the scope of the discussion to the safety stock dimensioning problem, consisting in determining the proper safety stock level for each product. This paper reports the results of a recent in-depth systematic literature review (SLR) of operations research (OR) models and methods for dimensioning safety stocks. To the best of our knowledge, this is the first systematic review of the application of OR-based approaches to investigate this problem. A set of 95 papers published from 1977 to 2019 has been reviewed to identify the type of model being employed, as well as the modeling techniques and main performance criteria used. At the end, we highlight current literature gaps and discuss potential research directions and trends that may help to guide researchers and practitioners interested in the development of new OR-based approaches for safety stock determination.This work has been supported by FCT – Fundação para a Ciência e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020, and by the European Structural and Investment Funds in the FEDER component, through the Operational Competitiveness and Internationalization Program (COMPETE 2020) [Project no. 39479, Funding reference: POCI-01-0247-FEDER-39479]

Optimal Cyclic Control of a Buffer Between Two Consecutive Non-Synchronized Manufacturing Processes

This thesis presents methods for efficiently controlling a buffer that is located between two non-synchronized manufacturing processes. Several machines with different cycle times and/or batch sizes perform each manufacturing process. The overall operation cycles every T time units. The first objective of the problem is to minimize the average buffer inventory level during one cycle. The second objective is to minimize the maximum inventory level observed at any point during the cycle. This new optimization problem has not been previously considered in the literature. An integer program is developed to model this problem. In addition, two heuristic methods—a simulated annealing algorithm and random algorithm—are devised for addressing this problem. Extensive experiments are conducted to compare the performance of four methods for attacking this problem: pure integer programming using the solver CPLEX; integer programming where CPLEX is initialized with a feasible solution; simulated annealing; and a random algorithm. The advantages and disadvantages of each method are discussed