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EN
This paper deals with modelling and evaluating the availability and profit of a linear consecutive 2-out-of-4 system exposed to three consecutive stages of deterioration before failure. The system will pass through three consecutive stages of deterioration: slow, medium and fast before failure. The failure and repair times are assumed to be exponentially distributed. Explicit expressions for the system availability, the probability of a repairman being busy due to the failure of a unit, or due to the replacement of failed units, and the profit function have been derived using a probabilistic approach. The impacts of the failure and repair rate on system availability and profit have been investigated. The results of this paper will enhance system performance and ensure the timely execution of appropriate maintenance and improvement, and thus is a major tool for decision making, planning and optimisation.
EN
The present paper deals with an EOQ model for deteriorating items with time-dependent exponential demand rate and partial backlogging. Shortages are allowed and completely backlogged in this model. The backlogging rate of unsatisfied demand is assumed as a function of waiting time. The concept of penalty cost is introduced in the proposed model because there are many perishable products that do not deteriorate for some period of time and after that period they continuously deteriorate and lose their values. This loss can be incurred as penalty cost to the wholesalers/retailers. In any business organization, the penalty cost has an important role for special types of seasonal products and short life products. Therefore, the total cost of the product can be reduced by maximizing the demand rate and minimizing the penalty cost during a given period of time. The purpose of our study is to optimise the total variable inventory cost. A numerical example is also given to show the applicability of the developed model.
EN
This paper deals with integrated models joining maintenance and quality. We consider a manufacturing system composed of a single machine subject to an increased random failure rate and producing conforming and non-conforming items. In order to decrease the random failure rate and its impact on the quality of output products, a bloc type preventive maintenance strategy with minimal repair is considered. Our study consists in developing integrated analytical models joining maintenance and quality in order to determine the optimal preventive maintenance plan taking into account the progressive quality perturbation and the economic impact of reworking activities. Two strategies are developed. In fact, for the first strategy, we propose reworking activities for all non-conforming products in order to improve their quality condition and to sell all batches at the best price Pmax. The aim of this strategy is to find the optimal number of batches produced and reworked N* before each preventive maintenance action, maximizing the total net profit per time unit PT1. For the second strategy, the same problem is studied but for a finite horizon. Two mathematical models are developed in order to find the optimal value of the decision variable N* for both strategies. Numerical examples are presented in order to illustrate the proposed models and a sensitivity study is developed to evaluate the influence of the variation of some parameters.
EN
A supply chain system has been investigated in which a single manufacturer procures raw materials from a single supplier, processes them to produce finished products, and then delivers the products to a single retailer. The customer’s demand rate is assumed to be time-sensitive in nature (ramp type) that allows two-phase variation in the demand and production rate. Our adoption of ramp type demand reflects a real market demand for a newly launched product. Shortages are allowed with partial backlogging of demand (only for the retailer), i.e. the rest represent lost sales. The effects of inflation of the cost parameters and deterioration are also considered separately. We show that the total cost function is convex. Using this convexity, a simple algorithm is presented to determine the optimal order quantity and optimal cycle time for the total cost function. The results are discussed with numerical examples and particular cases of the model discussed briefly. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.
EN
In the business world, it is generally observed that the supplier gives a cash discount due to advance payment. The buyer may either pay off the total purchase cost or a fraction of the total purchase cost before receiving the products. If the buyer makes full payment then he receives a cash discount instantly. If the buyer pays a fraction of the total pur chase cost, then he receives the cash discount while paying the remaining amount at the time of receiving the lot. Moreover, in most of the inventory models, it is generally assumed that the delivered lot contains only perfect items. But in reality, the presence of imperfect items in the received lot cannot be overlooked as it will affect the total profit of the system. Thus, the study of inventory models considering the presence of imperfect items in the lot makes the model more realistic and it has received much attention from inventory managers. This paper develops a model that jointly considers imperfect quality items and the concept of an advance payment scheme (full and partial). The objective is to determine optimal ordering quantity to maximise the total profit of the system. The necessary theoretical results showing the existence of global maximum is derived. The model is illustrated with the help ofnumerical examples, and sensitivity analysis is carried out on some important system parameters to see the effects on the total profit of the system. The study shows that a full advance payment scheme is beneficial for the buyer.
LogForum
|
2017
|
vol. 13
|
issue 1
61-76
EN
Background: This model presents a significant model for analyzing the effect of deteriorating items and promotional effort in fuzzy optimal instantaneous replenishment model for finite planning horizon. Accounting for holding cost per unit per unit time and ordering cost per order have traditionally been the case of modeling inventory systems in fuzzy environment. These imprecise parameters defined on a bounded interval on the axis of real numbers and the physical characteristics of stocked items dictate the nature of inventory policies implemented to manage and control in the production system. Methods: This model postulates the promotional effort cost to frame total inventory cost. Thus a modified fuzzy EOQ (FEOQ) model with promotional effort factor is introduced, it assumes that a percentage of the on-hand inventory is wasted due to deterioration and considered as an enhancement to EOQ model to determine the optimal promotional effort and the replenishment quantity so that the net profit is maximized. In theoretical analysis, the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are proved and further the concavity of the fuzzy net profit function is established. Computational algorithm using the software LINGO 13.0 version is developed to find the optimal solution. Results and conclusions: The results of the numerical analysis enable decision-makers to quantify the effect of promotion policy on optimizing the net profit for the retailer and wasting the percentage of on-hand inventory due to deterioration respectively. Finally, sensitivity analyses of the optimal solution with respect the major parameters are also carried out. Furthermore fuzzy decision making is shown to be superior then crisp decision making without promotional effort in terms of profit maximization.
PL
Wstęp: Tematem pracy jest model istotności służący do analizy efektów zniszczenia towarów oraz efektu promocyjnego w modelu rozmytym ciągłego uzupełniania w określonym horyzoncie czasu. Głównym parametrem tworzenia modelu zarządzania zapasem w rozmytym środowisku jest zazwyczaj koszt jednostkowy na jednostkę zamówienia w określonej jednostce czasu. Te nieprecyzyjne parametry, oparte o oś liczb rzeczywistych, tworzą otoczenie, w którym stosuje się system zarządzania zapasem. Metody: Model określa wpływ promocyjny na całkowity koszt zapasu. W tym celu został stworzony rozmyty model ekonomicznej wielkości zakupu uwzględniający efekt promocyjny oraz procentowe zniszczenie zapasu, tak, aby osiągnąć maksymalny zysk netto. W trakcie analizy teoretycznej, niezbędne i wystarczające warunki istnienia i unikalności rozwiązań optymalizacyjnych wykazały słuszność dalszych badań nad funkcją rozmytej zyskowności netto. W celu znalezienie optymalnego rozwiązania stworzono algorytm przy użyciu oprogramowania LINGO 13.0. Wyniki i wnioski: Wyniki analizy numerycznej umożliwiają oszacowanie efektu polityki promocyjnej na optymalizację zysku netto dla detalisty jak również poziomu zniszczeń towaru. Również zostały przeprowadzone analizy wrażliwości uwzględniające najważniejsze parametry, które wykazały celowość stosowania proponowanej metody dla maksymalizacji zysku przy uwzględnieniu efektu promocyjnego.
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