Horizontal inventory coordination in supply chain based on multi-objective genetic algorithm

Abstract

In this paper, under the circumstance of uncertain customer demand, the enterprises on the same node in multiple supply chains conduct horizontal inventory coordination according to their own inventory and demand. Based on the combination of horizontal inventory replenishment and vertical normal replenishment, the related mathematical model has been established. By studying the inventory strategy in the decentralized and centralized decision-making, the dual marginalization effects are found in the network system composed of multiple supply chain. So the revenue sharing contract is introduced to solve this problem. It has been found in the study that after adopting the horizontal inventory coordination mechanism of the supply chain, the profit of the members in the supply chain system and the overall profit of the system are both higher than those which didn’t adopt the mechanism. The improved multi-objective genetic algorithm is used to calculate and verify the problem. In particular, after the revenue sharing contract is adopted, the profits are further enhanced.

Keywords

Inventory coordination economic order quantity inventory strategy revenue sharing multi-objective genetic algorithm

1 Introduction

In recent years, many scholars have made corresponding researches on the inventory coordination mechanism of supply chain from different perspectives. For example, Hao et al. put forward an optimal integer ratio cooperative inventory strategy for inventory replenishment in multi-level integrated supply chain considering the company’s supply chain management practice [1]. Lee et al. collaborated with the supply chain in inventory management, analysed the replenishment decision and system performance of integrated supply chain system under limited storage capacity [2]. Costantino et al. studied the multi-echelon supply chain with information sharing and different inventory control strategies in view of the impact of information sharing on supply chain inventory coordination, and revealed how information sharing can improve inventory changes and service levels [3]. Capar et al. set up two-tier supply chain of two to two by using (Q, R) inventory strategy as a research background and established an inventory coordination decision-making model and verified that this model can effectively reduce inventory carrying costs by numerical simulation [4].

Contract is one of the key tools for coordinating supply chain partnerships. The appropriate contract has been set to motivate supply chain partners to maximize their overall interest in making decisions. Chen, s. et al. focused on the analysis of the impact of different risk attitudes of each party in the supply chain on the investment decision under the two conditions of synergy and non-synergy [5]. Dai, H. et al. aimed at the problem of inaccurate inventory in the downstream of the secondary supply chain, and the possible impact on bullwhip effect, supply chain cost and supply chain coordination, and then analysed the different impact of sharing inventory deviation real-time information in the supply chain on the upstream and downstream [6]. Xu, G. et al. put forward an analytical framework for price decision-making in a centralized and decentralized dual-channel supply chain with risk aversion, and put forward a coordination scheme for the dual-channel supply chain. Coordination contract can make the dual-channel supply chain achieve win-win situation [7]. Aiming at the delay of the retail price, Xu et al. designed the wholesale price contract of a supply chain composed of a single manufacturer and a single retailer, established the profit function model and deduced the sufficient conditions for the optimal solution [8]. Babich et al. studied the buyback contracts between single suppliers and single retailers under the asymmetric information [9].

Yang, Y. and Sindhya, K. have proposed a variety of hybrid multi-objective algorithms that improve the traditional multi-objective evolutionary algorithm [10, 11].

2 Description of the research question

This paper studies a supply chain system composed of K pieced of single chains. Each single chain is a three-level supply chain and each level has one supplier, one manufacturer and one retailer respectively. All members of the system are risk-neutral and fully rational, and each single chain in the system operates with the same product that can be completely interchangeable. Under the normal replenishment strategy, the downstream retailers use economic order quantity (EOQ) strategy to determine the order timing and order quantity. The manufacturer will send the products to the retailer after they receive the order. However, under this ordering mechanism, some retailers may be out of stock due to too high market demand in the current period and unable to meet their coordination ordering requirements in the upstream. On the contrary, some retailers may need to bear higher inventory cost because the current market demand is too low. When each retailer is out of stock due to demand changes and the upstream links in this chain can’t meet the downstream order requirements, the retailers with less demand can coordinate a certain amount of inventory to the retailer on another single chain in the supply chain system which is out of stock due to high demand through the horizontal inventory coordination mechanism of the retail to provide them with coordination replenishment which can change the situation of too high inventory carrying costs and out-of-stock on both sides, as shown in Fig. 1.

Fig.1

Cross-chain inventory coordination model of supply chain.

The inventory coordination mechanism proposed in this paper is as follows:

The two parties for coordination should negotiate the coordination order quantity and the coordination offer amount. When the retailer of certain a single chain finds that the demand for the current period exceeds the economic order quantity, this retailer is the demander of the inventory coordination mechanism at this time. The demander will provide the coordination orders to the retailers of other supply chains in the cluster. The order quantity is the coordination order quantity; and when the current demand is too low (that is, the actual demand is lower than the economic order quantity), this retailer is a supplier of the inventory coordination mechanism. The supplier can provide part of the inventory to the demander. The amount that can be coordinated to the demander at most is the coordination offer amount. From the perspective of the demander, the inventory coordination mechanism can make the demander get additional products from the supplier thus to increase the sales volume to get a higher revenue. From the perspective of the supplier, the inventory coordination mechanism can make the supplier transfer the additional inventory to the demander, thus to reduce the inventory carrying costs and get profits by selling to the demander at a purchase price higher than that of the unit product.

However, under this inventory coordination mechanism, coordination replenishment will lead to additional costs and all members of the supply chain are completely rational. So the entire supply chain system can’t operate. This paper will study how to determine the optimal coordination order quantity and coordination offer amount in order to obtain the optimal profit and study how to use the revenue sharing contract to eliminate the double marginalization effect under the horizontal inventory coordination mechanism to realize the coordination of the entire supply chain system.

3 Construction of horizontal inventory coordination model

3.1 Symbol description and basic assumption

The main symbols and their descriptions used in this paper are as follows:

Q_e ——coordination order quantity between retailers when the inventory is coordinated.

Q_s ——coordination offer amount of supplier when the inventory is coordinated

Q^* ——optimal order quantity

ρ ——sale price for unit product, which is a market-determined exogenous variable

c_e ——the coordination purchase price of the unit product of the coordination demand retailers when coordination replenishment is done, which is a market-determined exogenous variables

c_h ——holding cost of the unit product

c_o ——it’s the purchase price of unit product when the retailer purchases from the upstream manufacturers during normal replenishment;

c_t ——transportation cost for unit coordination product that is borne by the coordination supply retailer during normal replenishment.

f (x) ——density function of the demand probability for a single replenishment cycle

F (x) ——demand distribution function for a single replenishment cycle $F (x) = \int_{0}^{x} f (t) dt$ ;

n ——the number of normal replenishment each year for retailers under the EOQ strategy,

Q^* ——optimal order quantity for retailers under EOQ strategy

φ ——revenue distribution coefficient between retailers under revenue sharing contract

$c_{e}^{*}$ ——coordination purchase price of unit product under revenue sharing contract.

For modeling needs, the basic assumptions of this paper is as follows:

Horizontal inventory coordination of the supply chain is a single product and single-phase planning model. Suppose the retailers in the supply chain order the goods from the upstream suppliers in this chain, they all adopt the EOQ strategy to decide the order timing and order quantity. Under the economy order quantity strategy, goods are ordered from the upstream every fixed time. When the market demand changes, the upstream links in this chain can’t meet the downstream emergency replenishment requirements. When the downstream retailer completes the normal replenishment under the current EOQ strategy, manufacturers in this chain can’t provide emergency replenishment if the current market demand is too high and exceeds the optimal order quantity under its EOQ strategy.

The market demand faced by all downstream retailers in the supply chain system follows the same and independent normal distribution N (μ, σ²). Because the enterprises engaged in inventory coordination are generally in a relatively close geography and face the similar needs, this paper assumes that the market demands faced by retailers in a cluster follow the same and independent probability distribution.

Under the horizontal inventory coordination mechanism, the transportation cost of the coordination ordering is borne by the coordination supply retailers and the coordination replenishment is delivered in the current period

When the coordination replenishment is done, one coordinating order of the demander can only be satisfied by one supplier and the inventory cannot be provided by many suppliers. That is to say, one coordinating order cannot be split into multiple sub orders and the coordination is provided by multiple coordination supplier.

3.2 System profit model under the inventory coordination mechanism

When the current demand of the retailer in a single chain is larger than the economic order quantity Q^*, this retailer will become the demander of the inventory coordination mechanism. Denote current demand X, the probability of this retailer to be the demander of this current inventory coordination mechanism is $a = P (X ⩾ Q^{*}) = \int_{Q^{*}}^{\infty} f (x) dx$ (1)

At this time, the demander will submit the inventory coordination order to the retailers of other chains in the cluster to order Q_dpcs of products. Certain retailer of other supplier chains in the cluster is willing to provide the inventory to demander only when the current demand quantity is less than or equal to (Q^* - Q_d). So the failure probability of the single coordination replenishment is $θ = P (X ⩾ Q^{*} - Q_{d}) = \int_{Q^{*}}^{\infty} f (x) dx$ (2)

There are K pieces of supply chains in the cluster, so the demander can seek for the inventory coordination from other (K - 1) pcs of supply chains at most. Since the failure probability of the single coordination replenishment of the inventory coordination is θ, for the demander, the probability for at least one to provide the coordination is (1 - θ^K-1).

The annual expected coordination profit for the demander is that the coordination revenue minuses the inventory cost and coordination order cost generated by coordination. So the annual expected coordination revenue of the demander is $\begin{matrix} E (π_{d}) & = & np (\int_{Q^{*}}^{Q^{*} + Q_{d}} (x - Q^{*}) f (x) dx \\ + Q_{d} \int_{Q^{*} + Q_{d}}^{\infty} f (x) dx) (1 - θ^{K - 1}) \\ - {nc}_{e} α Q_{d} (1 - θ^{K - 1}) - \frac{c_{h}}{2} n (1 - θ^{K - 1}) (α Q_{d} \\ + \int_{Q^{*}}^{Q^{*} + Q_{d}} (Q^{*} + Q_{d} - x) f (x) dx) \end{matrix}$ (3)

For the suppliers under the inventory coordination mechanism, if the extra inventory coordination can be given to the demander, it will bring additional benefits to the suppliers and can reduce inventory costs.

The first revenue of the supplier under the inventory coordination mechanism comes from the revenue of the coordination difference in price. Since when the demander orders products from the supplier, the supplier of the horizontal coordination will generally asks for the price higher than that of the product the upstream manufacturer purchases, which lives up to the fact. The horizontal inventory coordination will lead to the urgent order due to the uncertainty of the market demand. When the demander orders Q_dpcs of products from the supplier through a coordination order, the supplier will receive the coordination revenue of c_eQ_d. Another revenue for suppliers under the inventory coordination mechanism comes from the reduced inventory costs.

The annual expected coordination revenue of the supplier is that the coordination revenue plus the reduced inventory cost and then minus the purchase cost and transportation cost of the coordination offer amount. Therefore, the annual expected coordination revenue of the supplier is $\begin{matrix} E (π_{s}) = {nQ}_{d} c_{e} α (1 - θ^{K - 1}) \\ + \frac{Q_{d}}{2} α c_{h} n (1 - θ^{k - 1}) - {nQ}_{d} α (c_{o} + c_{t}) \\ (1 - θ^{K - 1}) \end{matrix}$ (4)

The annual expected coordination revenue for the whole system is $E (π_{sys}) = E (π_{d}) + E (π_{s})$ (5)

4 Inventory coordination model underrevenue sharing contract mechanism

Without adopting revenue sharing contract mechanism, the whole system is regarded as being in an absolutely coordination state. The annual expected coordination revenue for the whole system is $\begin{matrix} E (π_{sys}^{c}) & = & np [\int_{Q^{*}}^{Q^{*} + Q_{d}} (x - Q^{*}) f (x) dx \\ + Q_{d} \int_{Q^{*} + Q_{d}}^{\infty} f (x) dx] (1 - θ^{K - 1}) \\ - n α Q_{d} (c_{o} + c_{t}) (1 - θ^{K - 1}) - \frac{c_{n} h (1 - θ^{K - 1})}{2} \\ \int_{Q^{*}}^{Q^{*} + Q_{d}} (Q^{*} + Q_{d} - x) f (x) dx \end{matrix}$ (6)

Coordination demand retailers and coordination supply retailers are as a whole, with the goal of maximizing the overall profit of the supply chain system, and they jointly determine the optimal coordination order quantity $Q_{d}^{c}$ under the horizontal inventory coordination mechanism. Therefore, for formula (6), we get the first-order optimality condition for Q_d. According to the function’s property, the optimal coordination order quantity $Q_{d}^{c}$ of the coordination demand retailers satisfies: $\begin{matrix} n (p - \frac{c_{h}}{2}) [(θ^{K - 1} - 1) F (Q^{*} + Q_{d}^{c}) - \\ (1 - K) θ^{K - 2} f (Q^{*} - Q_{d}^{c}) \int_{Q^{*}}^{Q^{*} + Q_{d}^{c}} F (x) dx] + \\ [1 - θ^{K - 1} + Q_{d}^{c} θ^{K - 2} (1 - K) f (Q^{*} - Q_{d}^{c})] \times \\ n [\frac{c_{h}}{2} F (Q^{*}) + p + α (c_{e} + C_{t})] = 0 \end{matrix}$ (7)

Under the revenue sharing contract mechanism of the supply chain, the coordination demand retailers distributes their 1 - φ proportion of revenue to the coordination supply retailers, thus to get the coordination replenishment from the coordination supply retailer with a lower coordination purchase price of $c_{e}^{*} of$ the unit product to stimulate the coordination demand retailers to choose the optimal coordination order quantity in the system to carry out the coordination replenishment to achieve the overall coordination of the entire supply chain system.

Under the revenue sharing contract mechanism, the annual expected coordination profit $E (π_{d}^{*})$ of the demander under the inventory coordination mechanism, the annual expected coordination revenue $E (π_{s}^{*})$ of the supplier retailer and the annual expected coordination profit $E (π_{sys}^{*})$ of the whole system are respectively: $\begin{matrix} E (π_{d}^{*}) & = & np φ (\int_{Q^{*}}^{Q^{*} + Q_{d}} (x - Q^{*}) f (x) dx \\ + Q_{d} \int_{Q^{*} + Q_{d}}^{\infty} f (x) dx) (1 - θ^{K - 1}) \\ - {nc}_{e} α Q_{d} (1 - θ^{K - 1}) - \frac{c_{h}}{2} n (1 - θ^{K - 1}) \\ [α Q_{d} + \int_{Q^{*}}^{Q^{*} + Qd} (Q^{*} + Q_{d} - x) f (x) dx] \end{matrix}$ (8) $\begin{matrix} E (π_{s}^{*}) & = & {nQ}_{d} c_{e} α (1 - θ^{K - 1}) + \frac{Q_{d}}{2} α c_{h} n (1 - θ^{K - 1}) \\ - {nQ}_{d} α (c_{o} + c_{t}) (1 - θ^{K - 1}) + np (1 - φ) \\ [\int_{Q^{*}}^{Q^{*} + Q_{d}} (x - Q^{*}) f (x) dx + Q_{d} \int_{Q^{*} + Q_{d}}^{\infty} \\ f (x) dx] (1 - θ^{K - 1}) . \end{matrix}$ (9)

$\begin{matrix} E (π_{sys}^{*}) & = & np [\int_{Q^{*}}^{Q^{*} + Qd} (x - Q^{*}) f (x) dx \\ + Q_{d} \int_{Q^{*} + Q_{d}}^{\infty} f (x) dx] (1 - θ^{k - 1}) \\ - n α Q_{d} (c_{o} + c_{t}) (1 - θ^{k - 1}) - \frac{{nc}_{h (1 - θ^{K - 1})}}{2} \\ \int_{Q^{*}}^{Q^{*} + Q_{d}} - (Q^{*} + Q_{d} - x) f (x) dx \end{matrix}$ (10)

Under the mechanism of the revenue sharing contract, the demander retailer of the inventory coordination mechanism aims at maximizing its own interests. Therefore, the first-order optimality condition for Q_d is obtained from formula (8). According to the properties of the function, the optimal coordination order quantity $Q_{d}^{*}$ of the coordination demand retailer under the revenue sharing contract mechanism satisfies: $\begin{matrix} n (φ p - \frac{c_{h}}{2}) [(θ^{K - 1} - 1) F (Q^{*} + Q_{d}^{*}) - \\ (1 - K) (θ^{K - 2} f (Q^{*} - Q_{d}^{*}) \int_{Q^{*}}^{Q^{*} + Q_{d}^{*}} F (x) dx] + \\ [1 - θ^{K - 1} + Q_{d}^{*} θ^{K - 2} (1 - K) f (Q^{*} - Q_{d}^{*})] \times \\ n [\frac{c_{h}}{2} F (Q^{*}) + φ p + α c_{e} - \frac{c_{h}}{2} α] = 0 \end{matrix}$ (11)

Under the revenue sharing contract mechanism, in order to make the whole supply chain system achieve the operation effect under the centralized decision and achieve the overall coordination of the system, the reasonable contract parameters should be designed to encourage the coordination demand retailers to choose the optimal coordination order quantity under the inventory coordination mechanism for coordination replenishment, that is, make $Q_{d}^{*} = Q_{d}^{c}$ , formula (7) and formula (11) are simultaneous, then get $C_{e}^{*} = \frac{φ p (2 c_{o} + 2 c_{t} + c_{h}) + c_{h} (2 c_{o} + c_{t} + p)}{c_{h} + 2 p} - \frac{c_{h}}{2}$ (12)

Since under the mechanism of revenue sharing contract, it is necessary to ensure that the coordination purchase price of the unit product is $c_{e}^{*} > 0$ . It can be obtained from (12) that $\frac{c_{h} (c_{h} - 2 c_{o} - 2 c_{t} + 4 p)}{2 p (c_{h} + 2 c_{o} + 2 c_{t})} < φ < 1$ (13)

Because all the members in the supply chain system are completely rational and maximizing their own interests are their primary goals, the realization of pareto improvement of the annual expected coordination revenue of all members under the revenue sharing contract mechanism is the necessary precondition for the revenue sharing contract to be accepted by each member of the system. That is to say, after the revenue sharing contract is introduced, the profit of each member is greater than the profit when it is not introduced into the revenue sharing contract under the decentralized decision-making. Therefore, it can be seen that it must meet the following requirement: ${\begin{matrix} E (π_{d}^{*}) > E (π_{d}^{d}) \\ E (π_{s}^{*}) > E (π_{s}^{d}) \end{matrix}$ (14)

Formulas (13) and (14) are simultaneous finally, and the revenue distribution coefficient φ obtained satisfies: ${\begin{matrix} \frac{c_{h} (c_{h} - 2 c_{o} - 2 c_{t} + 4 p)}{2 p (c_{h} - 2 c_{o} - 2 c_{t})} < φ < 1 \\ E (π_{d}^{*}) > E (π_{d}^{d}) \\ E (π_{s}^{*}) > E (π_{s}^{d}) \end{matrix}$ (15)

At this time, ${c_{e}^{*}, Q_{d}^{*}} =$ ${\frac{(2 φ p + c_{h}) (c_{o} + c_{t}) - c_{h} p (1 - φ)}{c_{h} + 2 p} - \frac{c_{h}}{2}, Q_{d}^{c}}$ is the optimal joint strategy for the inventory coordination mechanism. Under this strategy, the overall profit of the system reaches maximum to achieve the overall coordination.

It can be seen from formula (12) that $c_{e}^{*}$ and φ has the linear relation under the revenue sharing contract. As φ increases, the linear of $c_{e}^{*}$ increases, indicating that the coordination demand retailer will provide higher coordination purchase price of the unit product to the coordination supply retailer in order to keep more revenue. Otherwise, with the decreasing of $φ, the linear of c_{e}^{*} drcreases$ indicating that the coordination demand retailer will make up the decrease of its retained revenue by decreasing the coordination purchase price of the unit product. In addition, it can be seen that: $c_{e}^{*} - (c_{o} + c_{t}) = \frac{p (c_{h} + 2 c_{o} + 2 c_{t})}{c_{h} + 2 p} (φ - 1) - \frac{c_{h}}{2} < 0$ (16)

That is to say, $c_{e}^{*} < c_{o} + c_{t}$ , ie, under the revenue sharing contract mechanism, the coordination purchase price of the unit product provided by the coordination supply retailer is smaller than its cost. In return, it gets 1-φ proportion of the revenue of the coordination demand retailer. In addition, the specific value of φ needs to be negotiated between the two coordination parties, and it generally depends on the current situation differences the two coordination parties face and the mutual negotiating ability when signing the contract.

5 Numerical simulation and analysis

Assuming that the market demand faced by each downstream retailer should satisfy normal distribution N (70,400), the number of downstream retailers in the supply chain system is K = 10, and the number of the normal replenishment that the retailers should do to the upstream manufacturers every year under the EOQ strategy is n = 6. The rest of the parameters are set as shown in Table 1. These parameters have the characteristics of high sale price of unit product, high purchase price and high inventory carrying cost, which is suitable to adopt retailer horizontal inventory coordination mechanism to carry out coordination replenishment to increase the revenue of the two coordination parties and reduce the overall inventory carrying level. Based on the above parameters setting, MATLAB software is used for simulation experiments and analysis.

Table 1
Setting for simulation parameters

Parameter Setting value (Yuan)

p 12000

$C_{e}^{}$ 6000

Q ^ 80

c _h 2000

c _t 3800

c _o 200

Parameter	Setting value (Yuan)
p	12000
$C_{e}^{*}$	6000
Q ^*	80
c _h	2000
c _t	3800
c _o	200

The range of revenue distribution coefficient φ obtained from the above parameter setting is 0.3500 < φ < 0.5003, , but the specific value needs to be negotiated with both parties to confirm. In order to facilitate the discussion, several simulations analysis of φ = {0.40, 0.43, 0.46, 0.49} are carried out in this paper. Based on the above conclusions and assumptions, the equilibrium values of all parameters under the horizontal inventory coordination mechanism of retailers can be obtained as shown in Table 2.

Table 2

The equilibrium value of each parameter under retailer cross-chain coordination replenishment mechanism

	φ	$c_{e} / c_{e}^{*}$	$Q_{d}^{c} / Q_{d}^{*}$	$E (π_{d}^{*})$	$E (π_{s}^{*})$	$E (π_{sys}^{*})$
Centralized decision-making		6000	13.14	16925.04	74003.99	90929.03
Revenue sharing contract mechanism	0.40	230.93	13.14	40564.32	503614.71	90929.03
	0.43	369.40	13.14	43082.10	47846.92	90929.03
	0.46	507.88	13.14	45599.89	45329.14	90929.03
	0.49	646.35	13.14	48117.67	42811.35	90929.03

As can be seen from Table 2 that under the horizontal inventory coordination mechanism of the retailer, the expected revenue of the whole system in the centralized decision-making status is significantly higher than that of the decentralized decision-making status, and the supply chain system does not achieve overall coordination. In addition, under the centralized decision-making status, although the whole system can reach the coordination status, the expected revenue of the coordination demand retailer is far lower than that under the decentralized decision-making status. Therefore, there is no incentive to choose the optimal coordination order quantity in the system to carry out the coordination replenishment. However, through the introduction of a reasonable revenue sharing contract, the coordination demand retailers can be effectively motivated to increase the coordination order quantity to reach the level of centralized decision, so that the whole system can reach the best of the whole interest. Meanwhile, compared with the level when it is not introducing the revenue sharing contact under the decentralized decision, the annual expected revenue of the coordination demand retailer and coordination supply retailer can realize Pareto improvement respectively.

Assuming that market demand follows normal distribution, the probability distribution of demand is shown in Table 3. K is set at 5 and 15.

Table 3

Market demand probability distribution

Demand	Demand probability distribution
D1	N (70, 250)
D2	N (70, 300)
D3	N (70, 350)
D4	N (70, 400)
D5	N (70, 450)
D6	N (70, 500)
D7	N (70, 550)

The results of Table 3 are shown in Figs. 2 and 3.

Fig.2

The influence of uncertainty of demand on the optimal collaborative ordering quantity difference in decentralized centralized decision making.

Fig.3

The influence of uncertainty of demand on the expected annual profit margin of collaborative system in decentralized centralized decision making.

As can be seen from Fig. 2, the difference of optimal cooperative order quantity under decentralized and centralized decision-making increases with the increase of demand uncertainty. This shows that under the inter-chain inventory coordination mechanism, the demand uncertainty increases, and the introduction of revenue-sharing contract increases the cooperative ordering volume more significantly, and the activity of the inter-chain trading market in the system is enhanced more significantly.

As can be seen from Fig. 3, the annual expected profit margin under decentralized and centralized decision-making also increases with the increase of demand uncertainty. This shows that under the inter-chain inventory coordination mechanism, with the increase of demand uncertainty, the double marginalization effect of the supply chain system is more obvious, so the introduction of revenue sharing contract can make the overall benefits of the system to be greatly improved, and the necessity of its introduction is also greater.

6 Conclusion

Under the premise that the normal replenishment models of the downstream retailers are to order from the upstream manufacturer according to EOQ strategy, this paper has studied the coordination issues in the multi-chain supply chain system where several retailers are included and they can carry out horizontal inventory coordination between themselves in the supply chain system. The inventory decision model under the inventory coordination mechanism of retailers is set up and the optimal strategy of each model is given. It is pointed out that under the horizontal inventory coordination mechanism; the double marginalization effect still exists in the supply chain system. However, the introduction of the revenue sharing contract can effectively increase the profit of each member in the system and achieve the overall coordination of the supply chain system. Through the numerical simulation, the optimal coordination order quantity of each model under the horizontal inventory coordination mechanism, the coordination purchase price of the unit product and the annual expected coordination profit of the supply chain system and each member in the system are calculated. The results show that there is a positive relationship between the demand uncertainty and the optimal cooperative ordering margin and the annual expected cooperative profit margin under decentralized and centralized decision-making under the horizontal inventory coordination mechanism of retailers. The above research results provide some basis and enlightenment for the decision-makers in the supply chain system to conduct scientific decision-making under the horizontal inventory coordination mechanism, and also enrich the coordination management theory of the supply chain, which is of great significance to study the coordination of the supply chain under the horizontal inventory coordination mechanism.

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Horizontal inventory coordination in supply chain based on multi-objective genetic algorithm

Abstract

Keywords

1 Introduction

2 Description of the research question

3.1 Symbol description and basic assumption

3.2 System profit model under the inventory coordination mechanism

Table 1 Setting for simulation parameters Parameter Setting value (Yuan) p 12000 C e * 6000 Q * 80 c h 2000 c t 3800 c o 200

References

Table 1
Setting for simulation parameters

Parameter Setting value (Yuan)

p 12000

$C_{e}^{}$ 6000

Q ^ 80

c _h 2000

c _t 3800

c _o 200