Replenishment Problem Research Articles

Optimizing multi-supplier multi-item joint replenishment problem for non-instantaneous deteriorating items with quantity discounts

This paper deals with a new joint replenishment problem, in which a number of non-instantaneous deteriorating items are replenished from several suppliers under different quantity discounts schemes. Involving both joint replenishment decisions and supplier selection decisions makes the problem to be NP-hard. In particular, the consideration of non-instantaneous deterioration makes it more challenging to handle. We first construct a mathematical model integrated with a supplier selection system and a joint replenishment program for non-instantaneous deteriorating items to formulate the problem. Then we develop a novel swarm intelligence optimization algorithm, the Improved Moth-flame Optimization (IMFO) algorithm, to solve the proposed model. The results of several numerical experiments analyses reveal that the IMFO algorithm is an effective algorithm for solving the proposed model in terms of solution quality and searching stableness. Finally, we conduct extensive experiments to further investigate the performance of the proposed model.

ATM cash replenishment under varying population coverage requirements

Inspired by an automated teller machine (ATM) cash replenishment problem involving population coverage requirements (PCRs) in the Netherlands, we propose the vehicle tour problem with minimum coverage requirements. In this problem, a set of minimum-cost routes is constructed subject to constraints on the duration of each route and the population coverage of the replenished ATMs. A compact formulation incorporating a family of valid inequalities and an efficient tour-splitting metaheuristic are proposed and tested on 77 instances derived from real-life data involving up to 98 ATMs and 237,604 citizens and on 144 newly generated synthetic instances. Our results for the real-life instances indicate significant cost differences in replenishing ATMs for seven major Dutch cities when the PCRs vary. Additionally, we illustrate the impact of different PCRs on the ATM replenishment costs for seven major cities in the Netherlands by presenting an aggregated cost evaluation of 11 PCRs involving 1,003,519 citizens, 338 ATMs, and 19 cash distribution vehicles.

A stochastic scheduling, allocation, and inventory replenishment problem for battery swap stations

Electric vehicles and drones promise to transform transportation systems and supply chains. However, long recharge times and battery degradation inhibit adoption. To overcome these barriers, swap stations enable quick battery exchange. We introduce a stochastic scheduling, allocation, and inventory replenishment problem which determines the charging, discharging, and replacement decisions at a swap station over time. The decisions are complex because recharging is necessary for short-term operation but causes degradation and the need for future replacement. We model the problem as a Markov Decision Process, solve it using backward induction, and show that the problem suffers from the curses of dimensionality. Hence, we propose two approximate methods, a heuristic benchmark policy and a reinforcement learning method, which provide high-quality solutions. Using a designed experiment, we deduce effective operational insights.

Bi-objective optimisation of the joint replenishment problem in a two-echelon supply chain

In this research, a bi-objective optimisation model for the joint replenishment problem (JRP) of a supply chain comprised of a single supplier and multiple retailers is developed, in which the retailers are assumed to be members of a unique distribution company. The mathematical model minimises the supplier's as well as the retailers' cost subject to some constraints. The constraints are the required storage spaces for any retailer, for any product, and for all the products. The benefit of using the JRP policy is shown based on minimising total cost of supplier and retailers. Since the developed model of the problem is NP-hard, the multi-objective meta-heuristic optimisation algorithm of non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the problem. Besides, since no benchmark is available in the literature to verify and validate the results obtained, a non-dominated ranking genetic algorithm (NRGA) is suggested to solve the problem as well. For further validation, the Pareto fronts are compared to lower and upper bounds obtained using a genetic algorithm employed to solve two single-objective problems separately.

An Optimization-Simulation Framework for Integrated Inventory and Cash Replenishment Problem of Automated Teller Machines in India

An Optimization-Simulation Framework for Integrated Inventory and Cash Replenishment Problem of Automated Teller Machines in India

An efficient approach for the Petrol Station Replenishment Problem: An Algerian case study

An efficient approach for the Petrol Station Replenishment Problem: An Algerian case study

Collaborative Multidepot Petrol Station Replenishment Problem with Multicompartments and Time Window Assignment

Energy supply is an important system that affects the overall efficiency of urban transportation. To improve the system operational efficiency and reduce costs, we formulate and solve a collaborative multidepot petrol station replenishment problem with multicompartments and time window assignment by establishing a mixed-integer linear programming model. The hybrid heuristic algorithm composed of genetic algorithm and particle swarm optimization is used as a solution, and then the Shapley value method is applied to analyze the profit allocation of each petrol depot under different coalitions. The optimal membership sequence of the cooperation is determined according to the strict monotone path. To analyze and verify the effectiveness of the proposed method, a regional petrol supply network in Chongqing city in China is investigated. Through cooperation between petrol depots in the supply network, the utilization of customer clustering, time window coordination, and distribution truck sharing can significantly reduce the total operation costs and improve the efficiency of urban transportation energy supply. This approach can provide theoretical support for relevant government departments and enterprises to make optimal decisions. The implementation of the joint distribution of energy can promote the sustainable development of urban transportation.

Multi-Compartment Vehicle Routing Problem to Find the Alternative Distribution Route of Petroleum Product Delivery

Distribution is an activity that the firm has to do to deliver their product to the customers. The product has to deliver to the customers on the right condition, at the right time, and with the minimal cost of delivery. This paper focuses to solve the planning distribution problem on petrol product delivery or Petrol Station Replenishment Problem. One of the ways to solve the planning distribution is VRP (Vehicle Routing Problem). VRP aims to find the minimal total cost delivery with some constraints depend on the factory. In this research, VRP is used by the distribution center to find the optimal route of distribution of petrol products. Using Multi-Compartment Vehicle Routing Problem (MC-VRP) that considers the demand for the petrol product, tank-truck capacity, distribution cost, and the number of the compartment. In this work, a mathematical formulation for MC-VRP is developed in the Mixed Integer Linear Programming (MILP) model. Using Ilog Cplex with branch and bound algorithm to solve this distribution problem with the minimum total distribution cost. There are 10 customers with different distances, different time deliveries and different travel costs in this research. The mathematic formulation produces the best alternative that is Rp 1.898.584 to deliver products from depot to the customers.

Benders decomposition for a stochastic three-level lot sizing and replenishment problem with a distribution structure

We address a stochastic three-level lot sizing and replenishment problem with a distribution structure in a two-stage decision process. We consider one production plant that produces one type of item over a discrete and finite planning horizon. The items produced are transported to warehouses and then to retailers using direct shipments. Each retailer is linked to a unique warehouse and there are no transfers between warehouses nor between retailers. The stochasticity comes from the uncertainty in the demand at the retailer level and is modelled through scenarios. The setup decisions are made in the first stage and the production, transportation and inventory decisions are made in the second stage, once the demands are revealed. The objective is to minimize the sum of the fixed production and replenishment costs, and of the expected variable inventory holding costs among all scenarios. We also study an extension where we allow for lost sales at the retailer level. We use a Benders decomposition approach and develop a Benders-based branch-and-cut algorithm to efficiently solve the problem. We take advantage of the substructures identified in the decomposition and design efficient procedures to solve the subproblems obtained. We also propose computational enhancements to speed up the solution process. Finally, we perform extensive computational experiments to assess the performance of our decomposition approach and analyze the impact of the enhancements. The Benders-based branch-and-cut algorithm we propose clearly outperforms CPLEX.

Preservation effort effects on retailers and manufacturers in integrated multi-deteriorating item discrete supply chain model

This paper studies the multi-deteriorating item discrete supply chain to realize considerable savings by aggregating the replenishment. The present integrated replenishment policy has already been widely applied in a variety of industries. This study deals with an integrated multi-deteriorating item replenishment problem with preservation effort and discrete demand rate and discrete order quantity. Most existing studies about preservation effort focused on a single-item replenishment policy. However, integrated replenishment has been extensively applied in many industries to take advantage of economies of scale in preservation. Since it is difficult to solve this problem directly, the necessary and sufficient conditions with these properties are derived; a solution procedure and an algorithm using heuristic approach are developed to obtain the optimal solutions. Numerical examples, comparative analysis and sensitivity analyses are also provided and tested to elucidate the multi-deteriorating item discrete supply chain model with preservation efforts. The results reveal that the extensions of the model provide a wider and reasonable situation in practice, so that the annual channel profit can be maximized.

Comparison of Integer Linear Programming and Dynamic Programming Approaches for ATM Cash Replenishment Optimization Problem

With the automated teller machine (ATM) cash replenishment problem, banks aim to reduce the number of out-of-cash ATMs and duration of out-of-cash status. On the other hand, they want to reduce the cost of cash replenishment, as well. The problem conventionally involves forecasting ATM cash withdrawals, and then cash replenishment optimization based on the forecast. The authors assume that reliable forecasts are already obtained for the amount of cash needed in ATMs. The focus of the article is cash replenishment optimization. After introducing linear programming-based solutions, the authors propose a solution based on dynamic programming. Experiments conducted on real data reveal that the proposed approach can find the optimal solution more efficiently than linear programming.

A Multi-Item Replenishment Problem with Carbon Cap-and-Trade under Uncertainty

Recently, as global warming has become a major issue, many companies have increased their efforts to control carbon emissions in green supply chain management (GSCM) activities. This paper deals with the multi-item replenishment problem in GSCM, from both economic and environmental perspectives. A single buyer orders multiple items from a single supplier, and simultaneously considers carbon cap-and-trade under limited storage capacity and limited budget. In this case we can apply a can-order policy, which is a well-known multi-item replenishment policy. Depending on the market characteristics, we develop two mixed-integer programming (MIP) models based on the can-order policy. The deterministic model considers a monopoly market in which a company fully knows the market information, such that both storage capacity and budget are already determined. In contrast, the fuzzy model considers a competitive or a new market, in which case both of those resources are considered as fuzzy numbers. We performed numerical experiments to validate and assess the efficiency of the developed models. The results of the experiments showed that the proposed can-order policy performed far better than the traditional can-order policy in GSCM. In addition, we verified that the fuzzy model can cope with uncertainties better than the deterministic model in terms of total expected costs.

Technical Note: A Joint Pricing, Supplier Selection, and Inventory Replenishment Model Using the Logit Demand Function*

ABSTRACTWe revisit the joint pricing, supplier selection, and inventory replenishment problem for a single item in a two‐stage system examined by Adeinat and Ventura (2015) and use the logit function to model the price‐sensitive demand. This article provides a detailed analysis regarding the shape and properties of the logit demand function. In this context, we propose a two‐stage piecewise‐linear approximation technique to solve the integrated pricing, supplier selection, and inventory replenishment model. Besides, in this research, we provide sufficient justification for the selection of the logit demand function as well as a comparison with other demand functions. A numerical study further suggests the importance of using a precise demand curve to select the set of suppliers, coordinate inventory, and accurately optimize the profit function.

Inventory Auditing and Replenishment Using Point‐of‐Sales Data

Spoilage, expiration, damage due to employee/customer handling, employee theft, and customer shoplifting usually are not reflected in inventory records. As a result, records often report phantom inventory, that is, units of good not available for sale. We derive an optimal polynomial‐time algorithm for the auditing and replenishment problem with phantom inventory, under the assumption that inventory is known immediately after replenishment. Moreover, we numerically show that a service‐level threshold policy performs comparably to the optimal.

An integrated algorithm for solving multi-customer joint replenishment problem with districting consideration

This paper studies a multi-customer joint replenishment problem with districting consideration (MJRPDC) which is of particular importance to a company that outsources its transportation and delivery operations to a third-party logistics (3PL) service provider. To solve the problem, we first propose an innovative search algorithm for solving the traditional multi-customer joint replenishment problem in a given zone. Then we design a GA-based framework to handle the corresponding districting problem based on the performance of each district evaluated by using the proposed search algorithm. The proposed methodologies are demonstrated by using an example of solving MJRPDC for a bank.

Use of Proximal Policy Optimization for the Joint Replenishment Problem

Deep reinforcement learning has been coined as a promising research avenue to solve sequential decision-making problems, especially if few is known about the optimal policy structure. We apply the proximal policy optimization algorithm to the intractable joint replenishment problem. We demonstrate how the algorithm approaches the optimal policy structure and outperforms two other heuristics. Its deployment in supply chain control towers can orchestrate and facilitate collaborative shipping in the Physical Internet.

The Team Orienteering Problem with Overlaps: An Application in Cash Logistics

The team orienteering problem (TOP) aims at finding a set of routes subject to maximum route duration constraints that maximize the total collected profit from a set of customers. Motivated by a real-life automated teller machine cash replenishment problem that seeks for routes maximizing the number of bank account holders having access to cash withdrawal, we investigate a generalization of the TOP that we call the team orienteering problem with overlaps (TOPO). For this problem, the sum of individual profits may overestimate the real profit. We present exact solution methods based on column generation and a metaheuristic based on large neighborhood search to solve the TOPO. An extensive computational analysis shows that the proposed solution methods can efficiently solve synthetic and real-life TOPO instances. Moreover, the proposed methods are competitive with the best algorithms from the literature for the TOP. In particular, the exact methods can find the optimal solution of 371 of the 387 benchmark TOP instances, 33 of which are closed for the first time.

The fuel replenishment problem: A split-delivery multi-compartment vehicle routing problem with multiple trips

The Fuel Replenishment Problem (FRP) is a multi-compartment, multi-trip, split-delivery VRP in which tanker trucks transport different types of petrol, separated over multiple vehicle compartments, from an oil depot to petrol stations. Large customer demands often necessitate multiple deliveries. Throughout a single working day, a tanker truck returns several times to the oil depot to resupply. A solution to the FRP involves computing a delivery schedule of minimum duration, thereby determining for each vehicle (1) the allocation of oil products to vehicle compartments, (2) the delivery routes, and (3) the delivery patterns. To solve FRP efficiently, an Adaptive Large Neighborhood Search (ALNS) heuristic is constructed. The heuristic is evaluated on data from a Chinese petroleum transportation company and compared against exact results from a MILP model and lower bounds from a column generation approach. In addition, we perform sensitivity analysis on different problem features, including the number of vehicles, products, vehicle compartments and their capacities. Computational results show that the ALNS heuristic is capable of solving instances with up to 60 customers and 3 different products in less than 25 minutes with an average optimality gap of around 10%. On smaller instances, the heuristic finds optimal solutions in significantly less time than the exact MILP formulation.

A stochastic multi-item replenishment and delivery problem with lead-time reduction initiatives and the solving methodologies

With the intensification of time-based competition, the importance of reducing lead-time by rapidly delivering multi-orders has been underscored in the process of replenishment-storage-transportation. This perception has prompted enterprises to increase expenditure on purchasing modern time-tracing technologies (e.g. RFID), and equipping facilities for item fast movement (e.g. high-rack automatic shelves) to retain customers. In this study, we explore a novel extension of the multi-item joint replenishment problem (JRP) with lead-time compressing initiatives. By assuming controllable lead-time, we construct a stochastic periodic-review joint replenishment and delivery (JRD) model to investigate impacts of capital investment in lead-time reduction to the decisions of multi-item joint replenishment and delivery. To solve the proposed JRD, two heuristics and a differential evolutionary algorithm are presented based on the model property analyses. The experimental results reveal the performance differences (e.g., searching speed, robustness and searching effectiveness) of three algorithms. Furthermore, our findings have managerial implications that proper investment in lead-time reduction not only helps shorten replenishment time and cut major ordering cost, but can also reduce the system cost.

Inventory Management under Storage and Order Restrictions

Inventory management in most practical settings faces challenges due to various restrictions on storage and replenishment of products. These restrictions may be posed by budget availability, different production/supply schedules for different products, and limited storage space shared by a number of products—very common in retail, food, and the pharmaceutical industry. Motivated by this, we investigate in this study how simultaneous restrictions on shared storage capacity and product‐specific order capacities impact optimal replenishments in a multi‐product system. We formulate the inventory replenishment problem as a multi‐period stochastic dynamic program, where products face stochastic demand with general distributions and excess demand is lost or fulfilled by emergency orders. We first fully characterize the optimal replenishment policy for two‐product systems, and provide a methodology to compute optimal replenishment quantities, which can be described as a dynamic priority‐based replenishment rule. Our results show that for each product, the optimal replenishment priority as well as quantity depends on the inventory levels of both products and all available capacities. More interestingly, the results show that capacity restrictions can flip the stocking priorities of products. Based on the optimal policy for two‐product systems, we develop a heuristic for multi‐product systems whose complexity scales linearly with the number of products. Under moderate storage capacities, our heuristic significantly outperforms the naive heuristics that ignore dynamic priority assignment, and closely captures the benefits of the optimal policy for systems with large number of products.