Peterson Julian

We developed a maximum profit inventory model with a generalized deterioration rate where the selling rate is dependent on the inventory level that is an extension of two published papers. A complete solution structure is provided to decide the optimal solution with reasonable conditions supported by numerical examples, and then we prove that the optimal solution is independent of the demand pattern. Numerical examples are provided to illustrate our findings. In a previously published paper, three examples had symmetric conditions to decide the local maximum solution. Our approach provides a reasonable explanation for this symmetric phenomenon. Our findings will help researchers develop new inventory models in the future.

In 2004, Macharis et al. proposed a consistent comparison matrix. In this study, we provide a patch work for discussing the construction and restrictions of their consistent comparison matrix. Their study is important in academia and has been cited by over 200 papers. However, in the article, the authors neither provide a detailed explanation on how to construct the proposed revised consistent comparison matrix nor mention any restriction when constructing it. In this study, we not only propose an algorithm to construct the consistent matrix, but also prove that two restrictions exist when developing a sequence of their consistent comparison matrices, which are: (a) the changing of entries should follow a decreasing order with respect to the row index and (b) there is at most one entry in each row that can be revised by experts. The results of this study will help researchers properly apply the consistent matrices proposed by Macharis et al. (2004) in the future.

We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower‐side attainment index motivated our work. In this paper, we worked on a revision for both‐side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both‐side attainment index, but also provide a theoretical extension from lower‐side attainment index to the both‐side attainment index.

Most inventory models dealt with deteriorated items. On the contrary, just a few papers considered inventory systems under amelioration environment. We study an amelioration inventory model with Weibull distribution. However, there are some questionable results in the amelioration paper. We will first point out those questionable results in the previous paper that did not derive the optimal solution and then provide some improvements. We will provide a rigorous analytical work for different cases dependent on the size of the shape parameter. We present a detailed numerical example for different ranges of the sharp parameter to illustrate that our solution method attains the optimal solution. We developed a new amelioration model and then provided a detailed analyzed procedure to find the optimal solution. Our findings will help researchers develop their new inventory models.

In this paper, we derive two new iterative algorithms to simplify the complicated alternative sequence approach of Yang et al. (2013). The purpose of this paper is threefold. First, we prove our approach generates monotonic and convergent sequences. Second, based on the same numerical example, we demonstrate that our monotonic sequence will converge faster than that of Yang et al. (2013). Third, we provide a reasonable explanation to the inconsistent results derived by our increasing sequence and decreasing sequence, with different starting point. Our findings will help researcher in the future construct faster iterative method to locate the optimal solution for traffic model.

Similarity measures are power tool to deal pattern recognition problems. Zhang and Fu (2006) constructed an extended similarity measure. Yusoff et al. (2011) further generalized to contain the hesitancy in their new similarity. Chao (2014) pointed out two questionable results of Yusoff et al. (2011) and then provided his revision. The purpose of this paper is twofold. First, we show that the analytical approach of Chao (2014) can not finish the proof. Second, the counter example of Chao (2014) for the extended hesitancy can be simplified.

This paper discusses why the selection of a finite planning horizon is preferable to an infinite one for a replenishment policy of production inventory models. In a production inventory model, the production rate is dependent on both the demand rate and the inventory level. When there is an exponentially decreasing demand, the application of an infinite planning horizon model is not suitable. The emphasis of this paper is threefold. First, while pointing out questionable results from a previous study, we propose a corrected infinite planning horizon inventory model for the first replenishment cycle. Second, while investigating the optimal solution for the minimization problem, we found that the infinite planning horizon should not be applied when dealing with an exponentially decreasing demand. Third, we developed a new production inventory model under a finite planning horizon for practitioners. Numerical examples are provided to support our findings.

We use the smoothly connected property to simplify the solution process for inventory model with ramp-type demand under stock-dependent consumption rate. This article is a response to a complicated solution process of Wu et al. [“Retailer's optimal ordering policy for deteriorating items with ramp-type demand under stock-dependent consumption rate,” International Journal of Information and Management Sciences, 19, 245–262 (2008)]. They extended a minimum cost inventory model to a maximized profit problem and presented a detailed analysis for the solution procedure. However, their solution process may be too lengthy to involve many right but unnecessary results. In this article, we use the smooth connected property to dramatically simplify their solution structure. Our approach is also applied to minimum cost inventory models that were demonstrated by simplifying the paper of Deng et al. [“A note on the inventory models for deteriorating items with ramp type demand rate,” European Journal of Operational Research, 178, 112–120 (2007)]. Our findings will help ordinary readers to understand their important inventory models.