اثر سرمایه گذاری فن آوری حفاظت بر روی مدل موجودی وخامت غیرآنی

Considering an inventory system with a non-instantaneous deteriorating item, our objective is to study the effect of preservation technology investment on inventory decisions. The generalized productivity of invested capital, deterioration and time-depend partial backlogging rates are used to model the inventory system. The basic results of fractional programming are employed to prove the uniqueness of the global maximum for each case. We also establish several structural properties on finding the optimal replenishment and preservation technology strategies. Further, we use a couple of numerical examples to illustrate the results and conclude the paper with suggestions for possible future researches.

In the last two decades, the models for inventory replenishment policies involving deteriorating items have received the attention of several researchers. In real life, the deterioration phenomenon is observed on inventory items such as fruits, vegetables, pharmaceuticals, volatile liquids and others. The fundamental result in the development of economic order quantity model with deterioration is that of Ghare and Schrader [1] who established an exponentially decaying inventory for a constant demand. However, as evident by chemical and basic sciences, the rate of deterioration especially with regard to perishable food items is seldom constant. Consequently, Covert and Philip [2], Philip [3] and Tadikamalla [4] extended the model of Ghare and Schrader [1] for a variable rate of deterioration by assuming Weibull distribution and Gamma deterioration rates, respectively. Researchers including Datta and Pal [5], Abad [6] and [7], Wee [8], Benkherouf and Balkhi [9], Chakrabarty et al. [10], Papachristos and Skouri [11], Dye [12], Tsao and Sheen [13], Sarkar [14], Wang and Li [15] and Cai et al. [16] developed economic order quantity models that focused on time varying deterioration rate. For a detailed survey on the literature of deteriorating inventory model over the last two decades, we refer the readers to the review articles by Goyal and Giri [17] and Bakker et al. [18] and the references therein for more details on the subject. However, the existing researches often assumed that the deterioration occurs as soon as the commodities arrive in inventory. In practice, most goods would have a span of maintaining quality or original condition, i.e. no deterioration occurs during that period. It is commonly observed that food stuffs, firsthand vegetables and fruits have a short span of maintaining fresh quality, in which there is almost no spoilage. Wu et al. [19] and Ouyang et al. [20] first incorporated the phenomenon into the inventory model and termed it as “non-instantaneous deterioration”. They also found that if the retailer can effectively reduce the deteriorating rate of item by improving the storage facility, the total annual relevant inventory cost will be lowered. Chang et al. [21] then complemented the model of Wu et al. [19] for the situation that building up inventory is profitable. Meanwhile, Geetha and Uthayakumar [22] presented an extended model of Wu et al. [19] by considering reciprocal time-dependent partial backlogging rate. Maihami and Kamalabadi [23] and Maihami and Abadi [24] further extended the model of Ouyang et al. [20] by considering a price and time dependent demand. Recently, to characterize the more practical situation, Shah et al. [25] integrated time varying deterioration and holding cost rates in the inventory model where shortages were not prohibited. The main objective in their model is to find the retailer's replenishment, selling price and advertisement strategies which maximize the retailer's unit time profit. In purchasing and material management, the deterioration of items is an important consideration in settling a replenishment schedule. The goal of inventory management is to improve return on investment by reducing non-essential inventory waste. However, the deterioration rate of goods in the above-mentioned papers is viewed as an exogenous variable, which is not subject to control. In the real market, the retailer can reduce the rate of deterioration of products by means of effective capital investment in warehouse equipments. For agreement with the practical inventory situation, Hsu et al. [26] proposed a deteriorating inventory model with constant demand rate and exponential decay which the retailer is allowed to invest the preservation technology to reduce the deterioration rate. However, the preservation technology cost is assumed to be a fixed cost per inventory cycle and this seems to be unrealistic. If new equipments, such as refrigeration units, are acquired, capital costs will occur. The cost of capital is often incorporated into models using an equivalent cost per period, or a leasing fee, which would probably be a cost per period, instead of a cost that is independent of the period length. Hence, a more realistic representation of is that it should be a cost per period, not a fixed cost per inventory cycle. Dye and Hsieh [27] then presented an extended model of Hsu et al. [26] by assuming the preservation technology cost is a function of the length of replenishment cycle. They further extended the model of Hsu et al. [26] by incorporating time-varying deterioration and reciprocal time-dependent partial backlogging rates. In this paper, we study the preservation technology investment and inventory decisions for a retailer's non-instantaneous deteriorating items, and perform a sensitivity analysis to understand how they depend on cost parameters. In particular, the generalized productivity of invested capital, deterioration and time-depend partial backlogging rates are used to obtain robust and general results on inventory management. The basic concepts and results of fractional programming are used to prove the uniqueness of the global maximum for each case. At the end, a couple of numerical examples are used to illustrate the proposed model, and concluding remarks are provided.

In this paper we study a generalized non-instantaneous deteriorating inventory system with productivity of invested capital, deterioration and time-depend partial backlogging rates. The analytical formulations of the problem on the general framework described as above have been given. We discuss the joint problem where the replenishment policy and preservation technology cost are decision variables. We also provide some useful results on finding the optimal replenishment and preservation technology strategies. In addition, we analyze the effect of preservation technology investment on inventory strategy. If preservation technology investment is profitable, we show in rigorous way that a higher preservation technology investment leads to a higher optimal service rate. Several extensions to our models deserve further analysis. A potential extension is to consider the finite capacity of shelf space. Also, we could extend the model with finite replenishment rate. And further, delays in product availability are common in real-world scenario, hence the stockout compensation policy may be incorporated into the presented model to improve market efficiency and increase the retailers sales and profit.