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Elemental images of rice leaves with lesion parts were taken with an in-air submilli-PIXE camera at Tohoku University. The rice leaves were analyzed in vivo and it resulted that the elements of Ca and Mn are accumulated in the lesion parts. It was confirmed by checking the intactness of cells that the living leaves were not seriously damaged. The surface of japan bowls (the Edo period), Japanese vessels (Shigaraki wares, the Edo period) and wooden tablets (the Meiji period) were directly surveyed by submilli-beams (3 MeV protons). Japanese vessels and wooden tablets were not discolored by the beam irradiation. Shigaraki vessels were discolored first, but their color disappeared after 10 days from the irradiation. It is concluded that such samples are not seriously deteriorated in in-air PIXE analysis.

The paper studies the joint inventory model between supplier and retailer relying on mutual cooperation. Unlike other studies, the deteriorated rate and partial back-ordering are consistent with assumptions for dealing with more general cases. Since it is difficult to solve this problem directly, we derived the sufficient and necessary conditions in the planning horizon, and proposed a procedure to find the optimal solution. Numerical examples and sensitivity analyses are also provided to illustrate the solution procedure. The results reveal that the extensions of the model provide a wider and reasonable situation in practice, and that they also reduce the total cost.

An order level inventory model is developed for deteriorating items with a constant rate of deterioration and vendor offering delay in payments. The model is developed under probabilistic demand. It is shown that the model derived can be related to the existing model for non-deteriorating items and when delay in payments is not permissible. The model is supported by a probability distribution function.

In this paper, we discuss why it is appropriate maximize the profits, instead of minimizing the costs, in an inventory system with an inventory-level-dependent demand rate. In addition, we restate Urban's viewpoint that the restriction of zero ending-inventory is not necessary in an inventory-level-dependent demand model. Consequently, we amend Giri and Chaudhuri's inventory model for deteriorating items by changing the objective to maximize the profits and relaxing the restriction of zero ending-inventory. Finally, we provide a couple of examples to show that both the order quantity and the profit obtained from our proposed model are significantly larger than those in Giri and Chaudhuri's model, in which the objective is to minimize the costs.

An inventory model is discussed with generalized ramp-type demand where the time to deterioration follows Weibull distribution. Shortages of inventories are allowed and completely backlogged. Total cost is derived by trading off setup cost, holding cost, deterioration cost, and shortage cost. The optimal replenishment policy for a single period is derived by minimizing the total cost per unit time over infinite time horizon. A numerical example is presented and sensitivity analysis is also carried out. The rationale for generalized ramp-type demand is discussed.

In this paper, an inventory model for deteriorating items with ramp-type time and price dependent consumption rate over a finite planning horizon is considered. In contrast to the traditional deterministic inventory model with static price over the entire planning horizon or fixed number of price changes over the finite time horizon, an alternative model is derived in which prices and the number of price change are to be decision variables. We show that the total profit function is concave. With the concavity, a solution procedure is presented to determine optimal prices, optimal number of pricing cycles and optimal lot size and optimal profit. We illustrate the model with numerical examples. Sensitivity analysis of the model is also carried out.

This study develops a mathematical inventory model for deteriorating item taking into account a vertical integration of a three-echelon supply chain (one supplier, one distributor, and one retailer) through strategic alliances. The objective is to minimize the joint total relevant cost for the integrated inventory model. A simple but efficient heuristic technique is used to derive the optimal solution. A numerical example and sensitivity analysis on the optimal results are presented to validate the results of the proposed integrated model. The proposed mathematical model has demonstrated how an integrated approach to decision making can achieve a global optimum and outperform three typically individual models (i.e., independent model, dominant supplier's model and dominant retailer's model).

In this article, we generalize Lev and Weiss's (1990) finite horizon economic order quantity (EOQ) model with cost change to the inventory system with deterioration. Supplier announces some or all of cost parameters may change after a decided time. Depending on whether the inventory is depleted at the time of the last opportunity to purchase before some or all of the cost parameters may change, there are two types of inventory models to be discussed. The main objective of this paper is to identify the optimal ordering policy of the inventory system by comparing the minimum cost of the two types of models. We suggest a finite horizon EOQ model to combine the above two types and propose a theorem that can quickly identify the optimal policy of the suggested model. In considering temporary price discount problem and discrete-time EOQ problem, in general, there are integer operators in mathematical models, but our approach offers a closed-form solution to these kinds of problems. Numerical examples are presented to demonstrate the results of the proposed properties and theorem.

In this paper, we consider parallel-machine scheduling with past-sequence-dependent (p-s-d) delivery times and deteriorating maintenance. The delivery time of a job is proportional to its waiting time in the system. Each machine has a deteriorating maintenance activity, i.e., delaying the maintenance increases the time required to perform it. We consider three versions of the problem to minimize the total absolute deviation of job completion times, the total load on all the machines, and the total completion time. We develop polynomial-time algorithms to solve them.

In this paper, we consider a coordinated scheduling problem on a single batching machine with transportation and deterioration. The jobs are transported by a vehicle to the single batching machine for further processing. The processing time of a job is a step increasing function of its exposure time which is equivalent to the time interval from the beginning of the transportation to the starting of the job on the machine. The objective is to find Pareto-optimal schedules with two performance criteria (total completion time and the number of batches) to balance the inventory level and the production costs. We prove that the general problem is strongly NP-hard. We further develop polynomial-time algorithms for two special cases with a fixed job sequence and without exposure time limit, respectively. For the general problem, we develop a heuristic algorithm and a branch and bound algorithm. Computational experiments show that the heuristic algorithms perform well on randomly generated problem instances, and the branch and bound algorithm can obtain Pareto-optimal solutions for the small-scaled instances.

We consider the time-dependent scheduling with proportional and delivery times on a single machine. Three models of the processing times are addressed here, they are proportional deterioration, proportional-linear shortening and proportional-linear increasing. The objective is to minimize the time by which all jobs are delivered. For the first model, we prove that the problem is polynomial solvable when jobs have identical release dates. When jobs arrive dynamically, we first give the proof of the NP-hardness and present a two-approximation algorithm. Then we propose a fully polynomial time approximation scheme for the case where the number of distinct release dates is a constant by applying the “rounding-the-input-data” technique. For the second and third models, when jobs have identical release dates, we prove that they are polynomial solvable, when jobs have different release dates, we present two-approximation algorithms for each of them.

The proposed EOQ model is a genuine attempt to manage retailer’s inventory when retailer’s stock is comprised of defective as well as constantly deteriorating items. Defective items in inventory are managed by selling them at discounted rate after a quality check process. Deterioration of items is controlled by investing suitable amount in preservation technology. The study assumes price sensitive quadratic demand incorporating the effect of inflation leading to a realistic situation. The objective of this paper is to maximize the retailer’s total profit with respect to cycle time, selling price, and preservation technology investment. Numerical examples are given to validate the model, and sensitivity analysis of inventory parameters is done to understand their effect. The outcome of this paper is applicable to goods like utility vehicles, stationary items, Fashion accessories, Cloths, Footwears, etc.

In a declining market for goods, we optimize the net profit in business when inventory management allows change in the selling prices n times over time horizon. We are computing optimal number of changes in prices, respective optimal prices, and optimal profit in each of the cycle for a deteriorating product. This paper theoretically proves that for any business setup there exists an optimal number of price settings for obtaining maximum profit. Theoretical results are supported by numerical examples for different setups (data set) and it is found that for every setup the dynamic pricing policy outperforms the static pricing policy. In our model, the deterioration factor has been taken into consideration. The deteriorated units are determined by the recurrence method. Also we studied the effect of different parameters on optimal policy with simulation. For managerial purposes, we have provided some "suggested intervals" for choosing parameters depending upon initial demand, which help to predict the best prices and arrival of customers (demand).

In a wholesale shop, the retailer is required to keep an inventory of various ranges of a product due to uncertainty in consumer preferences and behavior. Different Economic Order Quantity (EOQ) models for each variety of a product are needed for optimum level of inventory. EOQ model decides how much stock a shopkeeper has to store, according to demand and deterioration of different items to optimize the inventory policy of multiple products. Items like fashion, food, vegetables, pharmaceuticals, etc., deteriorate in the retailer’s warehouse during storage. An investment is required in preservation technology to significantly reduce the deterioration rate, reduce economic losses, and increase business competitiveness. Here, a multi-item deteriorating EOQ model with a fixed cycle duration has been developed incorporating the preservation technology. The demands for the items are a quadratic function of the selling price, and shortages are allowed. The main objective is to determine the optimal selling price, investment under preservation, the time length up to zero inventory, order quantity of the proposed inventory model such that the overall profit will be maximized. First, we prove that the optimal selling price and investment in preservation exist and are unique. Next, the total profit per unit time is a concave function of selling price and preservation technology investment. An algorithm is designed to obtain the optimum joint policy. A numerical example has been given to illustrate the model, and sensitivity analysis is conducted, which gives some managerial insights.

In today’s advanced society, customers are influenced by products full of choices. For more sales, the retailer should maintain an inventory of each variety of items. These varieties have been seen in most food shops, fruit shops, fashion shops, electronic shops, etc., where the products deteriorate with time elapse. Depending on the customer’s demand, the stock out time of different deteriorating items is different. Assimilating all these varieties, in this paper, we have developed a multi-item inventory model for deteriorating items where demands depend on the sales price of the product. Shortages are allowed and partially backlogged with a time-dependent backlogging rate. The multi-item mechanism’s prime objective is to find the optimal sales price, order quantity, time length up to zero inventory, and cycle length to maximize the retailer’s overall profit. Finally, numerical examples are provided to illustrate the model with some managerial insights.

Integrated microscopic investigations of bipolar junction damages in silicon detectors following neutron irradiation and studies of the degradation of the performance of bipolar transistors, due to generation of defects in silicon irradiated with neutron and ion carbons, were performed. The integrated microscopic investigations were studied by means of an advanced contact potential difference (CPD) method in atomic force microscopy (AFM). It was shown that gain degradation appears and that the density of generated defects is the same for neutron and carbon irradiation, but the density of created Frenkel pairs (interstitial-vacancy) is smaller for neutrons than for carbon ions. The value of Δ(1/β) of the transistor was evaluated from the density of Frenkel pairs (CF), for given value of Φ. The dependence of Δ(1/β) on concentration of CF for lateral and vertical pnp juntions at I_c=1μm, was shown. Fron the data of density of Frenkel pairs as a function of ratio Φ (R), was obtained, R=CF/Φ. Ratio R was independent on Φ, for a given type of irradiation (neutrons or carbon ions). For carbon ions, R depends on the value of the energy of incident particles (medium energy 11.1 MeV/a and high energy 95.0 MeV/a of the carbon ions.