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The retailer’s optimal policies are developed when the product has fixed lifetime and also the units in inventory are subject to deterioration at a constant rate. This study will be mainly applicable to pharmaceuticals, drugs, beverages, and dairy products, and so forth. To boost the demand, offering a credit period is considered as the promotional tool. The retailer passes credit period to the buyers which is received from the supplier. The objective is to maximize the total profit per unit time of the retailer with respect to optimal retail price of an item and purchase quantity during the optimal cycle time. The concavity of the total profit per unit time is exhibited using inventory parametric values. The sensitivity analysis is carried out to advise the decision maker to keep an eye on critical inventory parameters.

In business transactions, the offer of settling dues against the purchases without any interest charges from the supplier is attractive for the retailer. During this permissible delay period, the retailer can sell the item and generate the revenue and incur interest on it by depositing in the bank or financial firms. Goyal [

Huang [

Another important parameter for inventory modeling is deterioration of items, namely, volatile and radioactive chemicals, medicines and drugs, fruits and vegetables, electronic gadgets, and so forth. Ghare and Schrader [

Actually, every product (including human being) has its maximum lifetime [

In this paper, we analyze an EOQ model for the retailer under the following assumptions: (1) items in inventory are deteriorating continuously and have maximum lifetime and (2) the retailer follows two-level trade credit financing. The goal is to maximize total profit per unit time for retailer with respect to cycle time. Finally, we carry out sensitivity analysis to study the effects of an inventory parameter at a time on optimal solution. Based on it managerial insights are discussed for the retailer. The paper is organized as follows. The introduction is given in Section

We will use following notations and assumptions to develop the mathematical model of the problem under consideration.

constant demand rate,

ordering cost per order,

purchase cost per unit,

unit sale price, where

inventory holding cost (excluding interest charges) per unit per unit time,

interest earned per $ per year,

interest charged per $ for unsold stock per annum by the supplier,

credit period offered by the supplier to the retailer,

credit period offered by the retailer to the customer,

time varying deterioration rate at time

maximum lifetime (in years) of the deteriorating item,

inventory level at any instant of time

cycle time (a decision variable),

procurement quantity per cycle (a decision variable),

retailer’s total profit per unit time.

The inventory system under study deals with deteriorating items having expiry rate. The deterioration rate tends to 1 when time tends to maximum lifetime

The planning horizon is infinite.

Shortages are not allowed. Lead time is zero or negligible.

The credit period

When

The retailer generates revenue by selling items and earns interest during

The retailer’s initial inventory of

The purchase cost of

The holding cost is

Here, the retailer has sold all the items before the permissible time

Here, the retailer lacks the fund to settle the account at

The necessary condition to optimize profit function is to set

Assign values to all inventory parameters.

For

If

For

We consider the following examples to validate the mathematical formulation.

Consider

Concavity of total profit with respect to cycle time

Take

Concavity of total profit with respect to cycle time

To demonstrate the scenario

Concavity of total profit with respect to cycle time

Next, we study the variations in cycle time (Figure

Sensitivity analysis for cycle time (

Sensitivity analysis for total profit.

(1) (Figure

(2) (Figure

The retailer must maintain the balance between the credit periods

Figure

Procurement quantity versus delay period.

In this paper, ordering strategy is studied for the retailer when the product has fixed lifetime and is deteriorating in nature. It is established that the retailer should intelligently decide the payment time for the settlement of the accounts to the supplier and from the customer. This will reduce the risk of default from customers. The future study for stochastic demand or fuzzy demand will be more practical. Further research can be on the analysis of risk reduction using reliability theory.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to thank all the reviewers for their constructive suggestions.