Joint Pricing and Inventory Model for Deteriorating Items with Maximum Lifetime and Controllable Carbon Emissions under Permissible Delay in Payments

Abstract

Reducing carbon emissions plays a significant role in developing sustainable inventory systems. In a seller-buyer relationship, an allowable delay in payment is considered for the buyer to manage the stock and simulate the demand. Deteriorating items that usually have specific maximum lifetimes have become a challenge for most firms. Contrary to the importance of these issues, very little research has studied the impact of carbon emissions on deteriorating inventory systems. This paper provides a price-dependent demand for perishable items when carbon cap-and-trade regulation fills the mentioned gap. This model provides a carbon reduction investment scheme and illustrates this investment’s effect on the inventory system. This paper determines the optimal replenishment cycle and selling price, in which: (a) perishable items have specific maximum lifetimes, (b) a specific period of delay in payment is allowed for the buyer to accumulate revenue, (c) carbon is emitted due to ordering and storage operations and carbon cap and trade is regulated along with allowable carbon reduction investment. After developing the model, optimal values are obtained from necessary and sufficient conditions of optimality. Numerical experiments are proposed to validate the model. By developing an algorithm, the optimal values of replenishment cycle, selling price, and carbon reduction technology investment are obtained, and the impact of carbon emissions and efforts to control emissions are outlined. Finally, some managerial applications are mentioned, and future research directions are exposed.

Controlling defective items in a complex multi-phase manufacturing system

“…They proved that the circular economy concept could be formed by lowering total cost minimization waste. Sepheri et al [11] reduced waste from the deteriorated products under an inventory system through the idea of preservation policy. They proved that waste and the total cost could be minimized through an effective preservation strategy.…”

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.…”

“…There are three papers: Sarkar [47], Sarkar [48], and Sepehri et al [49] that are worth mentioning for the direction of future research. Sarkar [47] developed a maximized profit model for deteriorated items where the deterioration rate is a reciprocal of a linear function and the demand is a quadratic polynomial function of time.…”

“…Based on Sarkar [48], we may try to generalize our inventory model with deterioration cost, transportation cost, and handling cost. Sepehri et al [49] considered deteriorating inventory models with shelf life, delay in payment, and carbon emissions. They tried to find the optimal replenishment cycle, selling price, and carbon reduction investment.…”

“…They tried to find the optimal replenishment cycle, selling price, and carbon reduction investment. Based on Sepehri et al [49], in the future, we may try to extend our inventory model with deteriorated items, payment delays, and carbon emissions.…”