Research note on the criteria for the optimal solution of the inventory model with a mixture of partial backordering and lost sales

Abstract

Perishable products are commonly seen in inventory management. By allowing shortages and backlogging, the impact on the cost from the decay of the products can be balanced out. In a recent paper published in Computers and Industrial Engineering [P.L. Abad, Optimal lot size for a perishable good under conditions of finite production and partial backordering and lost sale, Comput. Ind. Eng. 38 (2000) 457-465] considered a problem in such context. However, his algorithm was incomplete due to flaws in his solution procedure. The purpose of this note is to explore the same production inventory models with a mixture of partial backordering and lost sales for deteriorated items. We find the criteria for the optimal solution for different cases and derive a formulated minimum value. By theoretical analysis, we develop a few lemmas to reveal parameter effects and optimal solution procedure. The solutions are illustrated by solving the same examples from Abad's paper to illustrate the accuracy and completeness of our procedure.

Inventory Model with Fixed Shelf Life under Generalized Non-Increasing Demand

“…We list comparisons among our new model and those existing systems to illustrate our contribution to the academic society (Table 1). Aiello et al [20] Avinadav [34] Avinadav and Arponen [13] Avinadav et al [14] Avinadav et al [18] Avinadav et al [27] Bhuiya et al [40] Chernonog [35] Chernonog andAvinadav [31] Chuang and Lin [21] De Giovanni [9] Demirag [28] Ganguly et al [41] Gładysz et al [7] Hanukov et al [32] Hanukov et al [36] Herbon [19] Hota et al [42] Khan et al [43] Kim et al [44] Krommyda et al [37] Lee et al [3] Leśniewski and Bartoszewicz [15] Lin et al [11] Ma [22] Malik and Sarkar [10] Mishra et al [45] Muriana [23] Muriana [25] Muriana [29] Muriana [38] Orynycz et al [8] Sarkar et al [1] Sharma et al [30] Taleizadeh et al [46] Yang et al [12] Zimpel-Leal and Lettice [4] Sarkar [47] Sarkar [48] Sepehri et al [49] This study Abbreviations for the first row: S1: Sustainable; B: Backordering; L: Lean management; S2: Supply chain; P1: Pricing; S3: Shelf-life; W: Waste management; P2: Perishable.…”

“…Most inventory models dealing with deteriorated items have a constant decay rate. For example, Lin et al [11] developed a production inventory model with the constant deteriorated date and the production rate dependent on demand and inventory level, and Yang et al [12] studied an inventory model with a constant decay rate proportional to the inventory level. In these models, a dichotomous shelf-life effect for perishable items is assumed.…”