Optimization Multi-Item Lot Sizing Model involve Transportation and Capacity Constraint under Stochastic Demand using Aquila Optimizer

ABSTRACTA unified framework coupling activity-based modelling and dynamic traffic assignment has recently been proposed. It formulates dynamic activity-travel assignment (DATA) in multi-state supernetworks as a dynamic user equilibrium. Choices of departure time, route, mode, activity sequence, and activity/parking location are determined endogenously, reflected in time-dependent activity-travel patterns (ATPs). However, capacity constraints associated with activities, parking, and public transit vehicles have not taken into account. This paper extends this approach by formulating these constraints and incorporating them into the DATA framework. Three numerical examples are presented to illustrate the effectiveness of the approach. It is shown that capacity constraints have significant effects on the choice facets.

We propose a decision support approach, called DESMILS, to solve multi-item lot sizing problems with a large number of items by using single-item multiobjective lot sizing models. This approach for making lot sizing decisions considers multiple conflicting objective functions and incorporates a decision maker’s preferences to find the most preferred Pareto optimal solutions. DESMILS applies clustering, and items in one cluster are treated utilizing preferences that the decision maker has provided for a representative item of the cluster. Thus, the decision maker provides preferences to solve the single-item lot sizing problem for few items only and not for every item. The lot sizes are obtained by solving a multiobjective optimization problem with an interactive method, which iteratively incorporates preference information and supports the decision maker in learning about the trade-offs involved. As a proof of concept to demonstrate the behavior of DESMILS, we solve a multi-item lot sizing problem of a manufacturing company utilizing their real data. We describe how the supply chain manager as the decision maker found Pareto optimal lot sizes for 94 items by solving the single-item multiobjective lot sizing problem for only ten representative items. He found the solutions acceptable and the solution process convenient saving a significant amount of his time.

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.

Competition, Collusion and Spatial Sales Patterns - Theory and Evidence

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.

In this paper, the joint production and recycling problem is investigated for a hybrid manufacturing and remanufacturing system where brand-new products are produced in the manufacturing plant and recycled products are remanufactured into as-new products in the remanufacturing facility. Both the brand-new products and remanufactured products are used to satisfy customer demands. Returns of used products that are recycled from customers are assumed to be stochastic and nonlinearly price-dependent. A mathematical model is proposed to maximize the overall profit of the system through simultaneously optimizing the production and recycling decisions, subject to two capacity constraints — the manufacturing capacity and the remanufacturing capacity. Based on Lagrangian relaxation method, subgradient algorithm and heuristic algorithm, a solution approach is developed to solve the problem. A representative example is presented to illustrate the system, and managerial analysis indicates that the uncertainties in demand and return have much influence on the production and recycling policy. In addition, twenty randomly produced examples are solved, and computational results show that the solution approach can obtain very good solutions for all examples in reasonable time.

The inventory model for deteriorating items with a stochastic demand rate is studied in our paper. Inventory models dealing with the deterioration of items have attracted considerable interests in recent decades since the deteriorating phenomenon is a crucial factor affecting the profits of a company. However, most of current inventory models considering deterioration assumes a certain or a constant demand function which is unreasonable in the prevailing market that conforms to our daily reality. Therefore, stochastic demand must be considered. Besides, shortage is allowed in the study. We provide approximating solutions for optimal ordering quantities for our model, and show that our optimal solutions from the assumed models give conditions and results very close to the optimal solutions obtained by computation. Further, these results illustrate the impact of various parameters on the optimal policy and the profit.KeywordsEOQ modelDeteriorating EOQ modelStochastic demand

This paper analyses the performance of Excel spreadsheet simulation analysis on supply chain. The spreadsheet was used to model the inventory control issue that developed in order to minimize the total cost of inventory, shortages and transportations for single supplier multi retailer problem who face a stochastic demand. Thus, the aim of this study is to identify the most appropriate inventory control parameters (by using can-order policy) for each of the retailers. The inventory position was periodically reviewed. In order to optimize the simulation model, the concept of Scatter Search and Tabu Search algorithms was used by implementing OptQuest software in spreadsheet. Two simulation models were set with different distribution of demand pattern in order to analyze the performance of the Optquest tool and compared with exact solution generated by brute-force approach. The result showed that the combination of inventory parameters produced by OptQuest close to the exact value obtained by brute force approach.

On the structure of capacitated assembly systems

This paper proposes a heuristic procedure to solve cyclical scheduling problems. Lot sizes for two or more items must be chosen simultaneously for several periods into the future, while recognizing capacity constraints at several work centres. Solving this problem is important in its own right. It also has transfer value to even more complicated situations, such as when the items have parent-component relationships. The proposed heuristic, though in the spirit of Mamie's formulation, has fewer production sequences for each item. The simplified formulation can be solved with a general linear programming code. Another advantage is its use of fixed ordering intervals, which seems to be preferred in practice. Experimental results suggest that the heuristic gives near optimal solutions and requires less computational time. Of particular interest is the heuristic's ability to satisfy capacity constraints when selecting item lot sizes.

Electric motors are one of the achievements of technology that is qualified, both in terms of development of science and socio-economic aspects. Electric motors are promising products as an alternative mode of transportation for people by utilizing electricity as an energy source. To ensure the reliability and sustainability of these products in order to enter the automotive industry market and avoid negative sentiments in the form of consumers' concerns to recharge when they run out of electricity in the middle of their journey, it is proposed for the establishment of Battery Exchange Station (BES) in several locations in order to meet the availability of electrical energy supply in the form of batteries that are ready to use. Through the battery swapping method, electric motor users will exchange batteries that will run out with a new battery that has been charged 100% (fully charged). This causes the supplier is responsible for distributing the electric battery so that a model is needed to minimize distribution costs while maintaining inventory levels at the customer. The inventory routing problem model by considering stochastic demand and recharging time on BES is designed to solve that vendor problem related to the distribution of electric batteries. This problem is approached by the Traveling Salesman Problem (TSP) to determine the delivery route with a minimum total distance and modeled with the Markov Chain to determine scheduling related to its replenishment. The result revealed that cost of transportation will be minimum by TSP and cost of distribution (replenishment unit and truck dispatching) will be minimum by Modified Markov Chain Model.

We consider a well-studied multi-echelon (deterministic) inventory control problem, known in the literature as the one-warehouse multi-retailer (OWMR) problem. We propose a simple and fast 2-approximation algorithm for this NP-hard problem, by recombining the solutions of single-echelon relaxations at the warehouse and at the retailers. We then show that our approach remains valid under quite general assumptions on the cost structures and under capacity constraints at some retailers. In particular, we present the first approximation algorithms for the OWMR problem with nonlinear holding costs, truckload discount on procurement costs, or with capacity constraints at some retailers. In all cases, the procedure is purely combinatorial and can be implemented to run in low polynomial time.

Delivery of goods is a transaction or agreement between the seller and the buyer that produces an item to be transported and sent to the buyer. This study found problems with the late delivery of goods, namely limited vehicle capacity which resulted in delays in delivery of goods by sellers, delays in receiving goods by customers, and expensive transportation costs as a result where customers became dissatisfied with delivery services, decreased number of purchases, decreased delivery of goods and losses incurred suffered by the company or the seller in terms of costs or profits. The k-nearest neighbor algorithm is a classification technique by choosing a distance based on the size of the shortest distance and a saving matrix method that will form a delivery route taking into account vehicle capacity and saving on transportation costs. And later it will be formed into several new routes that aim to facilitate the delivery of goods with the advantage of providing satisfaction to customers and being able to save on transportation costs. So this research was developed for the route of delivery of goods by taking into account the capacity and number of vehicles which in previous studies regarding delivery routes. The results of this study solve the problem quite optimally at 12.67% or Rp. 757,356 cost savings while the delivery of goods resulted in 6 shipping lines instead of 11 shipping lines which cut 5 shipping lines or 11.11% for a total of 1532.15 Km.

This paper studies a buyer sourcing a product from multiple suppliers under stochastic demand. The buyer uses a (Q, s) continuous review, reorder point, order quantity inventory control system to determine the size and timing of orders. Lead time is assumed to be deterministic and to vary linearly with the lot size, wherefore lead time and the associated stockout risk may be influenced by varying the lot size and the number of contracted suppliers. This paper presents mathematical models for a multiple supplier single buyer integrated inventory problem with stochastic demand and variable lead time and studies the impact of the delivery structure on the risk of incurring a stockout during lead time.

The replenishment policy of agri-products with stochastic demand in integrated agricultural supply chains