A Note on an Order Level Inventory Model with Varying Two-Phased Demand and Time-Proportional Deterioration

The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. The two-phased demand function states the constant function for a certain period and the quadratic function of time for the rest part of the cycle time. No shortages as well as partial backlogging are allowed to occur. The mathematical expressions are derived for determining the optimal cycle time, order quantity and total cost function. An easy-to-use working procedure is provided to calculate the above quantities. A couple of numerical examples are cited to explain the theoretical results and sensitivity analysis of some selected examples is carried out.

Analysis of Economic Order Quantity Under Fuzzy Environments

In the economic order quantity （EOQ） model, the decision maker has vague information about holding cost, ordering cost and market demand. With these uncertainties characterized as fuzzy variables, a new formula is developed by analyzing the fuzzy total cost. By comparing with other four EOQ formulas, i.e., using the crisp numbers with the highest membership values in classic EOQ formula, using the expected values of fuzzy parameters in classic EOQ formula, using the fuzzy variables in classic EOQ formula and then calculating the expected value, and calculat- ing EOQ by hybrid intelligent algorithm simulation, the effectiveness of this formula Js illustrated.

Short-Term Financing of Economic Order Quantity （EOQ） Inventory Model With Probabilistic Quality

In this paper, the classical economic order quantity （EOQ） inventory model assumption that all items of a certain product received from a supplier are of perfect quality is relaxed. Another basic assumption that the payment for the items is made at the beginning of the inventory cycle when they are received is also eased. We consider an inventory situation where items received from the supplier are of two types of quality, perfect and imperfect, and a short deferral in payment is allowed. The split between perfect and imperfect quality items is assumed to follow a known probability distribution. Both qualities of items have continuous demands, and items of imperfect quality are sold at a discount. A mathematical model is developed using the net present value of all cash flows involved in the inventory cycle. A numerical method for obtaining the optimal order quantity is presented, and the impact of the short-term financing is analyzed. An example is presented to validate the equations and illustrate the results.

Research on Optimization of Component Stock

A set of model is established to optimize BSW Company’s component stock. By analyzing the company’s current part stock condition in terms of the occupation of capitals in the precondition of continuous production, it describes how to control the purchase parameters of import parts. The model describes how to adjust slightly product output sequence and how to control the components’ purchase parameters: purchasing risk time and purchase order quantity. Then simulation is developed to illustrate the model.

Financial Derivatives Market and Storage Management

It’s known to all that under ideal condition the s to rage cost is kept in lower level when storage management be arranged by Economic Order Quantity(EOQ).Does this mean that any companies should set up their own storing system in proportion to the scale of the commodities’ producing or sell ing Furthermore, even if they manage storage in EOQ, because of different oper ation scale, geographical condition or ability borrowing money from financial ma rket, different companies pay unequal cost in storing the same commodity.In thi s paper, except for supplying commodities from our own storage system, the autho rs have analyzed other two supplying ways without whole storage system, they are forward contracts and futures contracts.The authors have discussed variable su pply cost for above different supply measures.According to the cost of each sup ply way, the managers can choose the most economical way in supplying the commod ity and predict the price of futures from storage management arranged by EOQ.Th e summary content is as follow: 1. The comparing of supply cost between forward contracts and storing system a rranged by EOQ. (1) The supply cost from forward contracts (2) The supply cost from storage system arranged by Economic Order Quantity (3) The application example for comparing cost in different supply way 2.The comparing of supply cost between futures going physical and storing syst em arranged by Economic Order Quantity. (1) The supply cost from futures going physical (2) The correlation between futures contracts and storage management arranged b y EOQ (3) The application example for comparing cost in different supply way 3.How does storing system of scale economic affect the price of forward and fu tures contracts (1) How does the price of forward and futures contracts fluctuate (2) How do we calculate the price of a commodity at future point from the cost of scale economic storing (3) How do we operate efficiently in derivatives market by using the cost of sc ale economic storing (4) The application example for analyzing the price of futures 4.The correlation among storage managementforward contracts and futures mark et.

Material Flow Optimization for Make-to-Stock Production System

Under the condition of the market competition becom in g more and more drastic, the demands of market take on some new features such as individuation, diversification, small batch, unstableness and quick delivery et c. The Make-to-Stock mode is usually adopted by many enterprises to improve th e balance and stableness of production process. In such enterprises, order batch , production batch and sales batch are the important factors, which affect the s atisfaction of clients, efficiency and benefit of the enterprise. It takes purch ase, production and sales into account respectively when optimizing product batc h in traditional way. However, it ignored the influences of relations between ea ch links of whole system. It is assumed that the consumption and market demand a re continuous process whereas the factual demands are batched when economic batc h is determined. So there exist some deviations between the economic batch deter mined by traditional way and that by integral optimization. Through the integral analysis of Logistics in the production system, we know that from materials are purchased, then manufactured, finally sold, the material changed in appearance and value, it still exist in different links of production system. The amount of materials occupied varies just in different status, from stock status to produc tion status, then to waiting-be-sold status, there is not any substantial chan ge in quantity until they are sold. So we must comprehensively analyze the relat ions among each link based on integral production system, to optimize the materi al batch and cut short production cycle in order to optimize the whole system. In this paper, the production system is taken as a global entity, and in which m aterials variation law and their relations of each link are analyzed; To optimiz e the whole materials flow, a new model of multi-product systems’ economic orde r batch, economic production batch and optimal sale lot multi-product syste ms’ is developed which based on the limit of capitals and stock area.

Optimal production lot size with process deterioration under an extended inspection policy

A mathematical model to determine the optimal production lot size for a deteriorating production system under an extended product inspection policy is developed. The last-K product inspection policy is considered so that the nonconforming items can be reduced, under which the last K products in a production lot are inspected and the nonconforming items from those inspected are reworked. Consider that the products produced towards the end of a production lot are more likely to be nonconforming, is proposed an extended product inspection policy for a deteriorating production system. That is, in a production lot, product inspections are performed among the middle K1 items and after inspections, all of the last K2 products are directly reworked without inspections. Our objective here is the joint optimization of the production lot size and the corresponding extended inspection policy such that the expected total cost per unit time is minimized. Since there is no closed form expression for our optimal policy, the existence for the optimal production inspection policy and an upper bound for the optimal lot size are obtained. Furthermore, an efficient solution procedure is provided to search for the optimal policy. Finally, numerical examples are given to illustrate the proposed model and indicate that the expected total cost per unit time of our product inspection model is less than that of the last-K inspection policy.

The revision of classical stock model

On the basis of the analysis of classical stock model, according to the limitation of the model, the article puts forward the revision of classical model and enforces the applicability of the stock model.

Simultaneous determination of manufacturer’s process mean and production run length,and retailer’s order quantity

In Chen and Liu’s optimum profit model with a traditional production system,they did not consider the effect of product quality on the customer’s demand order quantity,and also ignored the used cost of customers for product.In fact,the customer’s demand quantity is always seriously related to product quality.Hence,in the present paper,we modify Chen and Liu’s model to address the determination of the optimal process parameters by employing the idea of quality loss and single sampling rectifying inspection plan.Assuming that the quality characteristic of the product is normally distributed,Taguchi’s symmetric quadratic quality loss function is applied in evaluating the product quality.Three decision variables,i.e.,the mean of the process characteristic,the production run length of the product and the retailer’s order quantity,are jointly determined in our modified model to maximize the expected total profit of society,which includes both the manufacturer and the retailer.A heuristic solution procedure is developed for this optimization problem,and a numerical example is provided for illustration.From the numerical results,it can be seen that both the sale price per unit and the intercept of the mean demand of the customer are two major(or significant)parameters in the model and should be more accurately estimated in practice.Finally,the quality investment policy is provided to compare its effect on the optimum profit model with quality improvement.

Simultaneous settings of order quantity,wholesale price,production run length,process mean,and warranty period

In this article,the authors propose a modified version of S.L.Chen and Liu’s model with a two-stage production system.Assume that the retailer’s order quantity is concerned with the manufacturer’s selling price and the warranty period of product.The used cost of the customer is measured under the Taguchi’s quadratic quality loss function and concluded in the retailer’s profit function.The quality of the lot for the manufacturer is determined by adopting a two-stage single sampling rectifying inspection plan.The modified economic manufacturing quantity(EMQ)model is addressed in formulating the manufacturer’s expected profit.The retailer’s order quantity,manufacturer’s wholesale price,production run length,process mean,and warranty period of product will be jointly determined by maximizing the total expected profit of the supply chain system including the manufacturer and the retailer.Finally,the quality investment policy is introduced to illustrate the profit improvement for the supply chain system.

FUZZY EPQ INVENTORY MODELS WITH BACKORDER

This paper considers the economic production quantity （EPQ） problem with backorder in which the setup cost, the holding cost and the backorder cost are characterized as fuzzy variables, respectively. Following expected value criterion and chance constrained criterion, a fuzzy expected value model （EVM） and a chance constrained programming （CCP） model are constructed. Then fuzzy simulations are employed to estimate the expected value of fuzzy variable and c^-level minimal average cost. In order to solve the CCP model, a particle swarm optimization （PSO） algorithm based on the fuzzy simulation is designed. Finally, the effectiveness of PSO algorithm based on the fuzzy simulation is illustrated by a numerical example.

Modelling Economic Order Quantities,Considering Buy and Repair Options for Defective Items,and Allowing for Shortages and Inspection Errors

Nowadays,it is common for suppliers to be separated from their buyers by great distances.This means that,if some items in the lot turn out to be defective,the distance makes it uneconomical to order replacements from the original supplier.Moreover,both Type I and Type II errors may occur in the screening process for eliminating defective items and the combination of defective items and inspection errors may lead to shortages.Working with these assumptions,this paper develops two distinct models.Under the first model,defective items are repaired by a local repair shop subject to a repair charge and a mark-up margin.Under the second model,a local supplier replaces the defective with good ones,but at a higher cost.The expected total profit per cycle is developed,together with the expected cycle time,and,employing the renewal reward theorem,the objective function is derived,from which the optimum values are obtained for the order and shortage quantities.The paper presents numerical results and a discussion for both models.The study finds that repairing defective items generally leads to greater total profit than purchasing local replacements.

EMISSION ABATEMENT FOR PRODUCTION SYSTEM ACROSS LOCATIONS WITH HETEROGENEOUS EMISSION PROFLES

This paper investigates a production system in which the desired system state is a reduction of emissions and the controlling action plan is altering carbon price. From the operations perspective, we develop a model to study how increasing carbon emission costs may affect the joint production and location decisions for a manufacturer across different locations. Specifically, our model incorporates economies of scale and explicitly links product demand, production costs and carbon emission levels to location decisions. The firm＇s decisions in production batch size and locations are then optimised. The system state of emission are analysed under different carbon prices. Finally we check the alignment of objectives in costs and emissions for the system. The results show that for a production system with economies of scale, the production allocation is transformed to a location choice problem after optimising the costs. Raising the carbon price reduces the carbon emissions but may not be able to induce the production to be placed in an emission efficient place. We propose a hybrid policy combining carbon price and free emission allowance to fully align the cost efficiency and emission efficiency and characterise the link between the emission target and the carbon price.

Optimal inventory policies for short life cycle successive generations’ technology products

In this paper,a new Economic Order Quantity(EOQ)model for a successive generation of technology products has been discussed.The classical EOQ model is based on the assumption that the demand rate is constant.Hence it cannot be used for technology products where competition-substitution among products is a usual phenomenon.To address this problem,the EOQ model proposed in this article is considered a demand model for a technology product that follows the innovation-diffusion process.A numerical example has been illustrated and a comprehensive sensitivity analysis is conducted to understand the path of the optimal planning horizon and optimal costs under varied innovation and imitation effect.The sensitivity analysis of the introduction timing of the second generation has been performed to know the applicability of the model in actual circumstances.The behavior of the model has been discussed in detail in the numerical illustration section.