Combining Monte Carlo simulation with heuristics for solving the inventory routing problem with stochastic demands

The inventory routing problem (IRP) combines inventory management and delivery route‐planning decisions. This work presents a simheuristic approach that integrates Monte Carlo simulation within a variable neighborhood search (VNS) framework to solve the multiperiod IRP with stochastic customer demands. In this realistic variant of the problem, our goal is to establish the optimal refill policies for each customer–period combination, that is, those individual refill policies that minimize the total expected cost over the periods. This cost is the aggregation of both expected inventory and routing costs. Our simheuristic algorithm allows to consider the inventory changes between periods generated by the realization of the random demands in each period, which have an impact on the quantities to be delivered in the next period and, therefore, on the associated routing plans. A range of computational experiments are carried out in order to illustrate the potential of our simulation–optimization approach.

We consider an inventory routing problem with stochastic demand where the demand is expressed in a probabilistic sense and it is dynamic in which the demand is gradually revealed at the end of each period. The problem is known as dynamic and stochastic inventory routing problem (DSIRP). DSIRP distribution network consists of a supplier and a set of retailers is considered. A limited number of single product is assumed to be produced by the supplier and a holding cost per unit product is incurred at both the supplier. The demand is assumed to follow the binomial probability distribution. We adopt an order-up-to level inventory policy and each unit of positive inventory at the retailer is incurred a holding cost, while the unmet demand (stock-out) is penalized. We assumed that the transportation of the product from supplier to the retailers is handled by a third party. The aim of DSIRP is to minimize the total expected cost which includes the inventory cost at supplier, inventory cost at retailers, stockout cost at retailers and transportation cost. The DSIRP is modeled as a Markov decision process (MDP) where the state in period t is represented as the inventory level for all retailers. A hybrid rollout algorithm where a Mixed Integer Linear Programming of the problem is used to obtain the control in each state. We also proposed an Artificial Bee Colony (ABC) algorithm to obtain a feasible and better controls. Computational experiments is conducted using an existing benchmark problem.

The inventory routing problem with stochastic demand includes the inventory control, product transportation and scheduling decisions, considering an estimation of customer demands. This problem appears in several real situations, playing a fundamental role in reducing costs and improving the efficiency and reliability of the service. In practice, there are often restrictions on the window, which corresponds to a certain period of the day on which deliveries can be made. Despite the great relevance of this type of constraint, there are no results in the literature that combine stochastic demand and time window constraints. In this work, we propose a system, using advanced techniques of operational research, to solve the inventory routing problem with stochastic demand, considering time window constraints, as well as additional constraints of maximum inventory capacities in both the client and the depot and individual confidence level of the customer service.

It presents a practical modeling and solution approach for VMI cyclic inventory routing problem (IRP) under constant customer demand rates. In VMI, the supplier takes the responsibility for replenishing his customers' inventories based on their consumption data, with the aim of optimizing the overall distribution and inventory costs throughout the supply chain. The objective of this IRP problem is to determine a distribution plan that minimizes average distribution and inventory costs without causing any stockout at the customers. Deterministic constant customer demand rates are assumed and therefore, a long-term cyclical approach is adopted, integrating fleet sizing, vehicle routing, and inventory management. Further, realistic side-constraints such as limited storage capacities, driving time restrictions and constant replenishment intervals are taken into account. A heuristic solution approach is proposed, analyzed and evaluated against a comparable heuristic. The heuristic solution approach is well capable of finding the appropriate cost trade-off under varying circumstances. Furthermore, when fleet sizing is not considered, the heuristic outperforms an existing heuristic in finding the two-way trade-off between distribution and inventory costs.

In today's business landscape, demand variability plays a crucial role in determining the success of companies across various industries. This article explores the concept of demand variability, encompassing both deterministic and stochastic demand patterns. We delve into the differences between these demand types and their implications for businesses. The article emphasizes the significance of accurate demand forecasting and its role in strategic decision-making. Deterministic demand, characterized by predictable patterns, allows businesses to forecast with certainty. On the other hand, stochastic demand introduces uncertainty, requiring statistical methods and probability theory for estimation and management. Furthermore, we explore the distinction between stochastic stationary demand and stochastic nonstationary demand. While the former maintains consistent statistical properties over time, the latter experiences fluctuations in its characteristics due to external factors. We highlight the challenges faced by businesses in forecasting and managing nonstationary demand and the need for adaptive forecasting methods. To successfully navigate today's dynamic market, companies must embrace advanced analytics and data-driven approaches. By leveraging historical data, statistical models, and forecasting techniques, businesses can gain valuable insights into demand patterns, optimize inventory management, and make informed strategic decisions. Ultimately, understanding and managing demand variability is paramount for businesses seeking to improve customer satisfaction, optimize operations, and enhance their competitive advantage. This article aims to provide a comprehensive understanding of demand variability and equip readers with insights and strategies to tackle the challenges posed by an ever-changing market landscape.

We consider the coordinated capacitated lot-sizing problem (CCLSP) with stochastic non-stationary demand. Although the CCLSP with deterministic demand and the uncoordinated CLSP (UCLSP) with stochastic demand have been addressed in the literature, there is no published research on the CCLSP with stochastic demand. Motivated by the case of Stokke, we developed the formulation and solution method for a special case of the CCLSP. Our model is tested in the settings of stochastic and deterministic demand. The stochastic model out-performed the deterministic model with significantly lower total cost, leading to a reduction in inventory costs and to a slight increase in use of emergency supplies.

In this paper, we present a new mass-flow based Mixed Integer Linear Programming (MILP) formulation for the Inventory Routing Problem (IRP) with explicit energy consumption. The problem is based on a multi-period single-vehicle IRP with one depot and several customers. Instead of minimizing the distance or inventory cost, the problem takes energy minimization as an objective. In this formulation, flow variables describing the transported mass serve as a link between the inventory control and the energy estimation. Based on physical laws of motion, a new energy estimation model is proposed using parameters like vehicle speed, average acceleration rate and number of stops. The solution process contains two phases with different objectives: one with inventory and transportation cost minimization as in traditional IRP, the other with energy minimization. Using benchmark instances for inventory routing with parameters for energy estimation, experiments have been conducted. Finally, the results of these two solution phases are compared to analyse the influence of energy consumption to the inventory routing systems.

Comparing the value of information sharing under different inventory policies in construction supply chain

Energy efficiency is becoming an important criteria for the inventory systems. Our aim is to explicitly integrate the energy into the existing Inventory Routing Problem (IRP). The problem is based on a multi-period single-vehicle IRP with one depot and several customers. An energy estimation model is proposed based on vehicle dynamics. A mass-flow based Mixed Integer Linear Programming (MILP) formulation is presented. Instead of minimizing the distance or inventory cost, energy minimization is taken as an objective. Benchmark instances for inventory routing are adapted for energy estimation and experiments are conducted. The results are compared with those of the distance/inventory cost minimization.

In This Issue

Optimal control of a dual service rate M/M/1 production-inventory model

ILY Pharmaceutical is one of the pharmaceutical industry in Bandung that produces various type of medicines. In managing the raw materials for production, ILY Pharmaceutical is not using any standardize calculation for the inventory policy of the raw materials. That condition caused the raw materials to be overstocked and made the total inventory cost to be higher. The objective of this research is to minimize the total inventory cost in ILY Pharmaceutical by giving an inventory policy proposal. Based on the classification of the raw materials using ABC analysis, two inventory policy will be used. Periodic review (R, s, S) for A category and periodic review (R, S) for B and C category. The proposed inventory policy able to reduce the total inventory cost by 42% from $12.194,98 to $7.029,29. The reduced cost is mainly caused by the quantity of the raw materials that is stored in the warehouse is smaller than the existing condition. Even though the frequency of the order is increased thus increasing the order cost but the quantity ordered is smaller because in the proposed condition, there are a maximum inventory level so, the quantity ordered cannot exceed that level.

Inventory control is an important issue which must be considered by every company. The occurrence of overstock or excess inventories led to an increase in inventory cost the same as if the stockout. PT Perkebunan Nusantara VII Distrik Banyuasin is a company engaged in agriculture and processing of agricultural products such as palm oil , tea and rubber. Products covered is controlling tea products in the warehouse because of the problems that often occur in tea products . Kinds of tea products discussed namely BOP, BOPF, PF, DUST, BP, BT, PF II, DUST II, BP II, BT II, DUST III, FANN II, DUST IV. PT Perkebunan Nusantara VII Distrik Banyuasin has re- ordering method is less precise so that the reorder point should be calculated. To determine the fluctuating demand in the next year with forecasting is carried WinQsb program based on the pattern of sales data. Pattern sales data for 33 months is a seasonal pattern . The total cost incurred by the company during this time with a reservation made is Rp 385 506 418 , - . Therefore , we need a method that can control the supply so as to meet the demand for timely and can reduce the total cost of inventory . The method used is Multi Item EOQ method that produces a total cost of inventory Rp 414 195 905 ,-. Because the total cost of inventory with EOQ method Multi Item is greater than the method used by the company that carried out the study with Lagrange method taking into account capacity constraints warehouse and inventory costs which resulted in a total cost of inventories Rp 257 524 800 ,- which is smaller than the methods of the company . With the Lagrange method can save a total inventory cost Rp 127 981 619 , - with a percentage of 33.2 % .

Modeling a green inventory routing problem with a heterogeneous fleet

A multi-period mixed integer programming model is presented in this paper to reduce the overall cost of coal purchasing and transport in large-scale power generation group with the consideration of the stochastic coal demand. Mixed integer liner programming is used in problem formulation considering inherent connection between purchasing and inventory routing, and scenario tree method is applied to represent the uncertainty of demand. The objective is to minimize the purchase and transport costs, inventory costs and expected penalty costs across the entire scheduling cycle. Due to the stochastic feature of the coal demand and the unbearable stock-out, supplement coal purchasing is regarded as a mean to avoid shortage of coal. The berth constrain is taken into account to prevent time clashes. Numerical tests are performed for a power generation group and the result shows that the overall system costs can be saved by 17 million ¥ when taking the stochastic demand into consideration, and supplement quantity can be further reduced when transport plan is implemented with time flexibility.