A collaborative strategy for deteriorating inventory system with imperfect items and supplier credits

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Abstract

In this study, we develop a deteriorating inventory system consisting of one supplier and one buyer. The system considers supplier–buyer collaboration and trade credit. The objective is to maximize the total profit of the whole system when shortage is completely backordered. In order to entice buyer and compensate his shortage loss, the supplier allows the buyer's permissible delay in payment. Four proposed mathematical scenarios demonstrate how a collaborative approach to decision making can achieve a global optimality. A negotiation mechanism is incorporated to share fairly the profit between the players. The sensitivity analysis of the demand rate, replenishment rate, deterioration factor and other related parameters show that the collaboration strategy and the deterioration factor have significantly affected the total profit.

Introduction

Recently, due to rising costs, globalization, decreasing resources, shortening product life cycles and quicker response time, increasing attention has been placed on supply chain collaboration. Supply chain collaboration is when members in a supply chain have a common objective to construct a collaborative network and share information, such as sales and stock levels. Through collaboration, different facilities develop their partnership to achieve long-term benefits and global optimality of the system (Chikán, 2007).

This study discusses a high-priced item for a monopolistic market channel. Imperfect items are produced due to faulty production process, damaged items and breakages during handling or transport; therefore the lot sizes produced/received may contain certain percentage of defective items. The imperfect items may cause shortages and lead to massive losses for the buyer. Due to our monopolistic market assumption, there is only one supply source. Therefore, the supplier has a close vender–buyer relationship with the buyer. Thus, complete backorder for the defective items and trade credit financing as compensation are assumed to maintain the win–win relationship. In order to compare the effects regarding collaboration and compensation, we classify the decision-making policies into four types according to the relationship of the supplier and the retailer (buyer). The scenario matrix is shown in Fig. 1. Scenario 1 is an individual model and the decisions of the supplier and retailer are independently made. Scenario 2 is also an individual model except the retailer is more dominant than the supplier, supplier offers a permissible delay in payment as compensation and entice buyer to buy more. Scenario 3 is a collaborative model without permissible delay in payment because the supplier is more dominant than the retailer. Scenario 4 considers both compensation and collaboration.

Scenario 1 and Scenario 4 often are used in a two leader supply chain (SC) where both supplier and retailer are dominant. The choice of policy is dependent on their cooperative relationship. In Scenario 4, supplier and buyer have a close relationship, and form a strategic alliance. The decision in Scenario 2 is from the retailer's perspectives. The retailer is a leader in the SC. WAL-MART is a typical example for this scenario. Scenario 3 is from the supplier's perspectives. The supplier is a leader in the SC. INTEL is a typical example for this scenario. Comparing the effects of the four scenarios, this study develops a win–win collaborative strategy model for deteriorating items with permissible delay in payment, finite replenishment rate and price sensitive demand. To ensure mutually beneficial strategy, a negotiation factor is incorporated to enable profit sharing between both players.

Section snippets

Literature review

An effective supply chain network requires a cooperative relationship between the supplier and the buyer. Based on mutual trust, cooperation includes the sharing of information, resources and profit. The result of close cooperation is a mutually beneficial environment, which increases the joint profit as well as enables quicker response to customer demand. One of the most common strategies of a collaborative system is to develop an optimal replenishment and mutually beneficial policy acceptable

Mathematical modeling and analysis

The mathematical models in this paper are developed on the basis of the following assumptions:

  • (a)

    Single item with a constant rate of deterioration is considered.

  • (b)

    Single supplier and single buyer are considered.

  • (c)

    The annual demand rate is a linearly increasing function of retail price.

  • (d)

    Supplier allows the buyer's permissible delay in payment to entice the buyer and compensate his shortage loss.

  • (e)

    The defective items are instantaneously detected at the beginning of the buyer's replenishing cycle.

  • (f)

    The

Numerical example

The preceding theory can be illustrated using the numerical example adopted from Yu (2010) where the parameters are given as follows:

  • Price-sensitive demand rate, di=(ab) ρr units per year.

  • Scale parameter, a=3000; price sensitive parameter, b=35.

  • Buyer's purchasing cost, ρb=$35.

  • Buyer's backordering cost per unit, Cb=$20.

  • Buyer's percentage holding cost per year per dollar, ν=0.2.

  • Buyer's ordering cost per order, Co=$100.

  • The defective percentage,δ=0.05.

  • Supplier's setup cost, Cs=$6000.

  • Supplier's

Sensitivity analysis

With scenario 4, the optimal values of ρr, di, ni, qbi, S, ωi, ηi, Tbi1, Tbi2, TPbi, TPsi, TPi, and for a fixed set of parameters Φ={a, b, Cs, Co, Cb, ν, μ, δ, θ, ζ, P}are denoted byρr, di, ni , qbi, S,ωi,ηi, Tbi1, Tbi2, TPbi, TPsi and TPi, respectively. The changes inρr, di, ni , qbi, S, ωi, ηi, Tbi1, Tbi2, TPbi, TPsi and TPi are then considered when the parameters in the set Φ vary. Sensitivity analysis where the parameters in the set Φ changes by {−20%, −10%, +10%,

Conclusions

In this study, four scenarios are developed to optimize the finite replenishment rate policy for a deteriorating inventory system with imperfect items, price-sensitive demand and supplier credits. The numerical example demonstrates that the supplier-buyer collaboration results in an extra profit gain of approximately 6.16%. The win-win collaboration strategy with the compensation and the profit-sharing policies is the most beneficial for both players. The compensation policy is used when the

Acknowledgments

The author would like to thank the Editor, the anonymous referees, Dr. Huei-Ming Wee and Dr. Po-Chung Yang for their helpful suggestions, and the National Science Research Council of Taiwan for financing this research project NSC 99-2410-H-147-012.

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