Optimal Replenishment for Perishable Products with Inventory-Dependent Demand and Backlogging under Continuous and Discrete Progressive Payments

Longfei He,Han Gao,Xiao Zhang,Qinpeng Wang,Chenglin Hu

doi:10.3390/su10103723

Abstract

Managing material and cash flows attracts concerns of physical and financial departments in most companies. We, therefore, focus on optimizing the replenishment policy for a channel with stock-dependent demand considering item deterioration and order backlogging under two financial schemes of progressive trade credit periods. We take both the continuous payment regime (CPR) and discrete payment regime (DPR) into account in the progressive trading process, which generates ten distinct scenarios. We show that the profit functions may not necessarily be concave and accordingly give a corresponding computing algorithm, which relaxes the convexity assumptions of objective functions in the existing literature and consequently enrich the research. We address the formulation characterization and the logic of pursuing global optimization from models arising in all settings. Computational studies and simulations are conducted to illustrate the effect of various parameters on the optimal replenishing policy and profit. Numerical experiments show that the CPR scheme is dominantly prior to DPR for long replenishment time intervals, whereas it is exactly the opposite for short time intervals. We also examine the impact of the shortage cost and deteriorating rate on optimum ordering policy and channel performance. Finally, future research directions are addressed in the end.

Highlights

Managing material and cash flows is the common concern for both physical and financial departments both in most of business organizations [1]
We investigated the optimizing ordering policy for a perishable product supply chain with stock-dependent demand facing items deterioration and order backlogging under progressive payment schemes
We considered the continuous payment regime (CPR) and discrete payment regime (DPR) both in the progressive trading process to generate piecewise nonlinear optimization problem of ten distinct scenarios

Summary

Introduction

Managing material and cash flows is the common concern for both physical and financial departments both in most of business organizations [1]. We investigate the optimal reordering problem of deteriorating items with inventory-dependent demand in the scenario with a plausible delay payment scheme newly proposed. For this purpose, we clearly define two different delay payment regimes, Continuous Payment Regime (hereinafter referred as CPR) and Discrete Payment Regime (hereinafter referred as DPR) as follows: (1) Continuous Payment Regime: over some specific period, the buyer pays the supplier the money owed using the instantaneous revenue continuously until all purchasing cost has been paid back completely; (2) Discrete Payment Regime: the buyer accumulates revenue by depositing it in bank and pay money at some discrete specific time instants until all purchasing cost are cleared off.

Literature Review

Preliminaries and Notations

Subcase 2-2 The Revenue Is Insufficient to Repay the Wholesale Cost at Time M

Subcase 3-2 The Revenue Is Insufficient to Repay the Wholesale Cost at Time M

Findings

Concluding Remarks