Bi-objective Inventory Routing Problem Research Articles

A new cooperative depot sharing approach for inventory routing problem

This paper addresses cooperative game theory based bi-objective inventory routing problem, where replenishment plans are assumed as a coalition structure. Particularly, a distribution system is a set of customers that may order a single product from unique wholesalers to satisfy their own demands. When the products are carried from one depot to customers, transportation and inventory costs are incurred and some of the customers have insufficient depot capacity to their order levels. Therefore, in this paper, customers are willing to cooperate for cost saving benefits, where the depots are cooperatively used by each other with additional cost. The cooperative inventory game is established. An application is performed in a furniture roving parts company with the Shapley value cost allocation methods. The main objective of the study is to make a new replenishment plan for the demand of the customers, while meet the demands by sharing each other's depots and inventory routing costs. In addition, an improvement of 1.67% is obtained in vehicle utilization. Moreover, the proposed distribution method makes it possible to satisfy all customers demand for their own period. It helps customers who do not satisfy the demand into the warehouse, the three other most free capacitive customers can take the excess orders into their warehouse which are included in the coalition. As a result, a new effective replenishment plan has been obtained that it is economical to bear the additional costs.

A bi‐objective inventory routing problem with interval grey demand data

PurposeThe purpose of this paper is to manage the demand uncertainty considered as lower and upper levels for a medium-scale industrial distribution planning problem in a biobjective inventory routing problem (IRP). In order to achieve this, the grey system theory is applied since no statistical distribution from the past data and incomplete information.Design/methodology/approachThis study is investigated with optimizing the distribution plan, which involves 30 customers of 12 periods in a manufacturing company under demand uncertainty that is considered as lower and upper levels for a biobjective IRP with using grey demand parameters as a grey integer programming model. In the data set, there are also some missing demand values for the customers. So, the seven different grey models are developed to eliminat the effects on demand uncertainties in computational analysis using a piece of developed software considering the logistical performance indicators such as total deliveries, total cost, the total number of tours, distribution capacity, average remaining capacity and solution time.FindingsResults show that comparing the grey models, the cost per unit and the maximum number of vehicle parameters are also calculated as the new key performance indicator, and then results were ranked and evaluated in detail. Another important finding is the demand uncertainties can be managed with a new approach via logistics performance indicators using alternative solutions.Practical implicationsThe results enable logistics managers to understand the importance of demand uncertainties if more reliable decisions are wanted to make with obtaining a proper distribution plan for effective use of their expectations about the success factors in logistics management.Originality/valueThe study is the first in terms of the application of grey models in a biobjective IRP with using interval grey demand data. Successful implementation of the grey approaches allows obtaining a more reliable distribution plan. In addition, this paper also offers a new key performance indicator for the final decision.

Fuzzy bi-objective inventory-routing problem for blood products in a hospital network during disasters: two multi-objective meta-heuristic approaches

Post-disaster inventory-routing problem consisting of a blood products' supplier and a set of hospitals is investigated. With respect to the different scenarios of roads' availability, the goal of the proposed model is to establish a trade-off between the minimisation of total costs and total delivery time of blood products. Due to the criticality of platelets and red blood cells in disasters, only these two perishable items are addressed. The shortage and wastage costs are predicted based on the conformity measures of patient and donator. The demands are considered as a set of fuzzy numbers due to the lack of sufficient precise data. The model is solved exactly using e-constraint; however, for large-sized problems, two meta-heuristics, i.e., NSGA-II and MOSA are developed. Comparing the results of NSGA-II and MOSA to those of e-constraint confirms the efficiency of solution algorithms. Moreover, NSGA-II outperforms MOSA regarding the solution quality; but, MOSA needs fewer computational efforts.

Bi-objective inventory routing problem with backhauls under transportation risks: two meta-heuristics

ABSTRACTThis paper considers a multi-period and product inventory-routing problem. This model involves two levels, namely, a distributor and several retailers. This problem is modeled with the aim of minimizing bi-objectives, namely, the total cost of the system (including start-up, distribution, and maintenance costs) and risk-based transportation. Products are delivered to retailers by some heterogeneous vehicles with specific capacities through a direct delivery strategy, and inventory shortage is assumed to be impermissible. To validate this new bi-objective model, the ε-constraint method is used to solve problems. Because problems without distribution planning are very complex to solve optimally, the problem considered in this paper is also Non-deterministic Polynomial (NP-hard). Therefore, a nondominated sorting genetic algorithm (NSGA-II) and a multi-objective imperialist competitive algorithm (MOICA) are used and developed to solve a number of test problems. Furthermore, the computational results are compared and the performance of the foregoing algorithms is analyzed.

A new model for multi-period bi-objective inventory routing problem with stochastic demand, inventory holding, shortage and customer satisfaction

This paper presents a new multi-period, bi-objective inventory routing problem model with stochastic demand in two echelon network supply chain including some suppliers with several vehicles to satisfy customers' demands. Reducing the number of vehicles is also considered when each vehicle belongs to one route. The difference between this paper and the others is that the shortages and inventory holdings are kept at the customers' parts not in distribution centres. Customers' review of records costs and customer satisfaction and its relationship with shortage and inventory holding are the objective functions. The customer satisfaction increased by decreasing inventory holdings and shortage amount. The goal is to determine the delivery quantities to customers taking account of shortage and inventory holding amount per period. The objective of this paper is to minimise transportation routing costs, customers' review of records costs, inventory holding costs and shortage costs, and maximise customer satisfaction. The presented model is analysed by e-constraint method and run in GAMS software.

A new model for multi-period bi-objective inventory routing problem with stochastic demand, inventory holding, shortage and customer satisfaction

A new model for multi-period bi-objective inventory routing problem with stochastic demand, inventory holding, shortage and customer satisfaction

New mathematical model for the bi-objective inventory routing problem with a step cost function: A multi-objective particle swarm optimization solution approach

• Transportation costs are assumed to behave as a step cost function. • A novel bi-objective mathematical model is proposed to consider this assumption. • Despite this assumption, this type of function is not considered in the IRP. • An efficient multi-objective particle swarm optimization algorithm is presented. • The algorithm's efficiency compared with the augmented ε-constraint method. Inventory management and satisfactory distribution are among the most important issues considered by distribution companies. One of the key objectives is the simultaneous optimization of the inventory costs and distribution expenses, which can be addressed according to the inventory routing problem (IRP). In this study, we present a new transport cost calculation pattern for the IRP based on some real cases. In this pattern, the transportation cost is calculated as a function of the load carried and the distance traveled by the vehicle based on a step cost function. Furthermore, previous methods usually aggregate the inventory and transportation costs to formulate them as a single objective function, but in non-cooperative real-life cases, the inventory-holding costs are paid by retailers whereas the transportation-related costs are paid by the distributor. In this study, we separate these two cost elements and introduce a bi-objective IRP formulation where the first objective is to minimize the inventory-holding cost and the second is minimizing the transportation cost. We also propose an efficient particle representation and employ a multi-objective particle swarm optimization algorithm to generate the non-dominated solutions for the inventory allocation and vehicle routing decisions. Finally, in order to evaluate the performance of the proposed algorithm, the results obtained were compared with those produced using the augmented ε-constraint method, thereby demonstrating the practical utility of the proposed multi-objective model and the proposed solution algorithm.

Grouping genetic algorithms for a bi-objective inventory routing problem

Inventory routing problems (IRPs) is one of the versions of vehicle routing problems (VRPs), which retains the attention of the researchers. The main idea is to coordinate the distribution plan with the inventory management in a same model. The problem studied is to determine the multi-tours of a homogeneous fleet of vehicles covering a set of sales-points and minimising the distribution and inventory cost per hour. Of course no stock-outs are acceptable at the sales-points. In this paper, we analyse this problem like a bi-objective inventory routing problem in which the transportation cost and the delivery cost are considered separately. Two approaches are proposed to approximate the Pareto front of this bi-objective problem. Both methods are an adaptation of the hybrid grouping genetic algorithm (HGGA) that we proposed for the single objective problem in which a grouping genetic algorithm is combined with a local search. Computational experiments are reported using eight instances for four groups: (25, 50,100 and 200 sales points).