An integrated approach for logistic and vendor managed inventory in supply chain

Abstract

In this paper, a quaternary policy system towards integrated logistics and inventory aspect of the supply chain has been proposed. A system of multi retailers and distributors, with each distributor following a unique policy, will be analysed. The first policy is continuous time replenishment policy where the retailers’ inventory is replenished in every time interval. In the next three policies, inventory of the retailers will be replenished by some definite policy factors. The vendor managed inventory (VMI) system is used for updating the inventory of the retailers. An order-up-to policy (q, Q) is used for updating the inventory of distributors. Total erstwhile demands to the retailer will be used to determine the amount of inventory acclivity. Furthermore, the distributors will be sending the delivery vehicles to few fellow retailers who are shortlisted according to the policy, followed by the retailers and associated distributors. On the basis of random demand that the retailers are facing from end customers and the total demand that has incurred in the supply chain, products are unloaded to the selected retailers from the delivery vehicle. The path of the delivery vehicle is retrieved by dynamic ant colony optimization. In addition, a framework has been developed to measure the end-customer satisfaction level and total supply chain cost incorporating the inventory holding cost, ordering cost and the transportation cost. The framework has been numerically moulded with different settings to compare the performance of the quadruplet policies.

Introduction

In the present day competitive world, businesses that achieve success works in tandem with customers and suppliers. It has become even more critical with the advancement in information technology; a supply chain has progressed lots of steps ahead through information sharing. While manufacturing of product deals only with the manufacturer, the logistics and inventory control are the current issues of concern for everyone in the supply chain. In this paper emphasis is given on the latter two aspects of the supply chain. Many researchers have shown that lowering the influence of lower echelons in supply chain, the retailers can improve the dynamic performance of the supply chain (Wikner, Naim, & Towill, 1992). Vendor managed inventory is an evident example of the same. Use of vendor managed inventory (VMI) has grown over the time in industries. Evidences have shown that it can improve the supply chain performance by decreasing the inventory levels (Emigh, 1999). Researchers over the past have shown that VMI performs better as compared to traditional supply chain and Just In Time response (Disney and Towill, 2003, Kaipia et al., 2002, Yao et al., 2007).

In VMI, the decision of timing of resupply and quantity to be supplied is completely under the supervision of the vendor. Therefore vendor should consider the best possible scheme to fulfil the random demands that are occurring at the retailers keeping the overall cost of the supply chain abated. Over the time, researchers have proposed few models concerning these factors in mind (Cetinkaya and Lee, 2000, Zhang et al., 2006). Trappey, Trappey, Lin, Liu, and Lee (2007) presents an integrated business and logistics hub (IBLH) model, which integrates information flows (via the business hub) and material flows (via the logistics hub). Choy, Lee, and Lo (2002) presents an intelligent supplier management tool (ISMT) using the case-based reasoning (CBR) and neural network (NN) techniques to select and benchmark suppliers. Since the current market and conditions are quite dynamic in nature, it is not possible for a vendor to strictly stick to a policy and follow it at every point of time. One has to regularly search out for the best possible option that is applicable in the current situation so that the supply chain cost can be reduced while maximizing the satisfaction level of the customer. Both the inventory holding and the logistics cost plays a significant role for decision making in a supply chain. In this paper four replenishment policies are developed, and their analysis is done on system dynamics.

First policy is a time replenishment policy. According to this policy norm, products are delivered to the retailers in every time interval. This policy is same as described by Zhang et al. (2006) that is Time based consolidation replenishment policy, in this policy a distributor will be sending his product delivering vehicle to every retailer in every time interval unit. The second policy is somewhat, slightly deviating from the concept of policy 1. In this policy the distributor will be sending his vehicle in every time interval but only to few retailers, on the basis of demands occurring from the end customers. In the third policy, a distributor will sent his vehicle to retailers only when the sum total of demands occurring at all the retailers in a time interval exceeds a total demand threshold. This demand threshold is based on the forecasting predictions. Fourth policy is build on the concepts of second and third policy i.e. product delivering vehicles will be sent to few retailers only in those time intervals when the total demand occurring at retailers is greater than the demand threshold.

Fig. 1 represents a generalized supply chain of product transfer from manufacturer to end customer via distributor and retailer. Each distributor will be sending the delivery vehicles to few fellow retailers, who are shortlisted according to the policy, followed by the retailers and associated distributor. A dynamic TSP is solved using ant colony optimization to find the shortest path that the vehicles will be following for distributing the product. For finding out the minimum routing path, an ant colony optimization algorithm, a popular meta-heuristic approach is used in this paper. Ant colony optimization method is a biologically inspired heuristic algorithm. Ants are social insects, live in a group. When ants leave their nest in search of food they leave behind pheromone trail, a volatile chemical substance which can be sensed by ants, so that other ants can follow the same path. Dorigo, Colorni, and Maniezzo (1996) integrated this typical behaviour of ants to propose the ant colony optimization algorithm. After his work of accolade, lot of researchers has proposed and improvised the ACO. Dynamic ant colony optimization (DACO) is a recently proposed meta-heuristic algorithm, inspired by ants with altering nodes. The word ‘dynamic’ here signifies that the numbers of nodes, i.e. the retailers to whom truck will be sent, are varying with time interval.

In the proposed approach, ACO has been utilized as a search mechanism due to high speed convergence. The movement of each ant depends upon the pheromone concentration and distance between various retailers and distributor. The pheromone concentration incline ants to follow the most visited path by them so far, whereas heuristic criteria encourages them to move towards the global optimum. Initially the nodes, retailers to whom the product is supplied in a time interval, are selected on the basis of governing policy rules. Now in every generation, each of m ants constructs a tour passing through the distributor and selected retailers. Starting at a randomly generated node, each ant on ith node will moves to next node j, depending on the pheromone concentration, denoted by $T_{\mathit{ij}}$, as well as on heuristic information, denoted by $n_{\mathit{ij}}$. The heuristic value $n_{\mathit{ij}}=1/d_{\mathit{ij}}$, where $d_{\mathit{ij}}$ is the distance between ith node and jth node.

An ant in a tour will move to the next node either by exploitation or exploration rule. Exploration rule describe that, an ant will move from node i with probability $q_0$, where $0<q_0<1$, to node j from the set S of cities not visited so far which maximizes $[T_{\mathit{ij}}{]}^{\mathit{alpha}}[n_{\mathit{ij}}{]}^{\mathit{beta}}$, where alpha and beta are constant. On contrary, exploitation rule describes that with probability $1-q_0$, an ant will choose next node on the basis of probability distribution over S determined by Eq. (1).

$$p_{\mathit{ij}}=\frac{[{\tau }_{\mathit{ij}}{]}^{\alpha }[{\eta }_{\mathit{ij}}{]}^{\beta }}{{\sum }_{h\in S}[{\tau }_{\mathit{ih}}{]}^{\alpha }[{\eta }_{\mathit{ih}}{]}^{\beta }}$$

The pheromone chemical is a volatile substance; therefore a local update scheme is applied to modify the pheromone according to Eq. (2).

$${\tau }_{\mathit{ij}}\mapsto (1-\rho )·{\tau }_{\mathit{ij}}$$

where p is the evaporation rate. A basic elitist strategy is followed to prefer the best route found in a generation. For updating the best route pheromone, a global update strategy called as Restart Strategy, proposed by Guntsch and Middendorf (2001) is represented by the Eq. (3).

$${\tau }_{\mathit{ij}}\mapsto (1-{\gamma }_i){\tau }_{\mathit{ij}}+{\gamma }_i\frac{1}{n-1}$$