This note tries to provide a patch work for the paper of Chang Dye and Chuang. Their paper contains an important finding of smoothly connected property that can very dramatically simplify the solution procedure of many inventory models with ramp type demand and trapezoidal type demand. Our improvement will arouse attention of the researchers and help them apply their important findings in the pending research projects. | Yugoslav Journal of Operations Research 24 (2014) Number 1, 111-118 DOI: NOTE ON INVENTORY MODELS WITH A PERMISSIBLE DELAY IN PAYMENTS Cheng-Tan TUNG Department of Information Management, Central Police University, Taiwan tung@ Peter Shaohua DENG Department of Information Management, Central Police University, Taiwan pdeng@ Jones P. C. CHUANG Department of Traffic Science, Central Police University, Taiwan una050@ Received: June 2012 / Accepted: April 2013 Abstract: This note tries to provide a patch work for the paper of Chang Dye and Chuang (published in Yugoslav Journal of Operational Research 2002, number 1, 73-84). Their paper contains an important finding of smoothly connected property that can very dramatically simplify the solution procedure of many inventory models with ramp type demand and trapezoidal type demand. Our improvement will arouse attention of the researchers and help them apply their important findings in the pending research projects. Keywords: Fuzzy sets, convex combination. MSC: 90B05. 1. INTRODUCTION Hill [1] was the original researcher to develop an inventory model with ramp type demands, thereafter many papers were done on this topic. For examples, Mandal and Pal [2] considered inventory system with deterioration items. Wu et al. [3] constructed an inventory model in which the backlogging rate is relative to the waiting time. Wu and Ouyang [4] studied inventory systems with two different strategies, starting with stock or , , / Note on Inventory Models 112 shortage. Wu [5] and Giri et al. [6] developed inventory models with the Weibull distributed deterioration. Deng [7] revised Wu et al. [3] to provide a complete solution structure. Manna and Chaudhuri [8] extended inventory models with variable deteriorating rate. Deng et al. [9] modified Mandal, and Pal [2] and Wu and Ouyang [4] to find the optimal solution. Skouri et al. [10] .
