A new solution method for the finite-horizon discrete-time EOQ problem

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Lost Sales Inventory Model in Finite Planning Horizon

This research will extends a previous Economic Order Quantity (EOQ) model with all-units quantity discount when the period is finite planning horizon into the analysis. Exact algorithms are developed for each quantity discount structure to compute optimal policies for models that will minimized total cost over an finite planning horizon. A practical approach and numerical examples are proposed to find the optimal solutions for a discrete quantity order and discrete number of order.The method prove that inventory policy or total cost value when using finite planning horizon always greater equal to inventory policy EOQ, but the difference is not too significant, so this method is good enough to be used

A two-storage model for deteriorating items with holding cost under inflation and Genetic Algorithms

A deterministic inventory model has been developed for deteriorating items and Genetic Algorithms (GA) having a ramp type demands with the effects of inflation with two-storage facilities. The owned warehouse (OW) has a fixed capacity of W units; the rented warehouse (RW) has unlimited capacity. Here, we assumed that the inventory holding cost in RW is higher than those in OW. Shortages in inventory are allowed and partially backlogged and Genetic Algorithms (GA) it is assumed that the inventory deteriorates over time at a variable deterioration rate. The effect of inflation has also been considered for various costs associated with the inventory system and Genetic Algorithms (GA). Numerical example is also used to study the behaviour of the model. Cost minimization technique is used to get the expressions for total cost and other parameters

Inventory Analytics

"Inventory Analytics provides a comprehensive and accessible introduction to the theory and practice of inventory control – a significant research area central to supply chain planning. The book outlines the foundations of inventory systems and surveys prescriptive analytics models for deterministic inventory control. It further discusses predictive analytics techniques for demand forecasting in inventory control and also examines prescriptive analytics models for stochastic inventory control. Inventory Analytics is the first book of its kind to adopt a practicable, Python-driven approach to illustrating theories and concepts via computational examples, with each model covered in the book accompanied by its Python code. Originating as a collection of self-contained lectures, Inventory Analytics will be an indispensable resource for practitioners, researchers, teachers, and students alike.

A Single Item Lot Sizing with Backorder and a Finite Replenishment Rate in MRP

There are the following characteristics in decision on lot size in material requirements planning (MRP) systems: multiple time periods, a finite time horizon, discrete demand, and time-varying costs etc. In MRP system there are several different types of lot size techniques, such as the economic order quantity (EOQ), lot-for-lot, periodic order quantity, Wagner-Whitin algorithm, Silver-Meal algorithm and part-period algorithm. Although these lot size approaches focus on controlling the cost of holding cost and order cost, none of them, with the exception of the Wagner-Whitin algorithm, assures an optimal or minimum cost solution for time-varying demand patterns and copes with quantity discount. And Zangwill(1966), Blackburn and Kunreuther (1974) et al extended the Wagner-Whitin algorithm by following demand to go unsatisfied during some period, provided it is satisfied eventually by production in some subsequent period. R. M. Hill (1997), Stanislaw Bylka, Ryszarda Rempala (2001) give dynamic programming formulation to decide lot sizing for a finite rate input process. But the Wagner-Whitin algorithm and its extensions commonly are criticized as being difficult to explain and compute because the algorithms are complicated dynamic programming algorithms. In this paper, we propose a series of inventory models in which backorder and a finite replenishment rate are considered according to the characteristics in MRP ordering and the optimal solutions can be obtained by using general-purpose linear program solver, like EXCEL, LINDO, etc

Operational planning of supply chains in a production and distribution center with just-in-time delivery

Purpose: A supply chain consists of raw material suppliers, manufacturers and retailers where inventory of raw materials and finished goods are involved, respectively. Therefore, it is important to find optimal solutions, which are beneficial for both supplier, manufacturer and retailer. Design/methodology/approach: This research focuses on a semi-continuous manufacturing facility by assuming that the production of succeeding cycle starts immediately after the production of preceding cycle. In reality, the inventory of a supply chain system may not be completely empty. A number of products may be left over after the deliveries are made. These leftover inventories are added to the next shipment after the production of required amount to make up a complete batch for shipment. Therefore, it is extremely important to search for an optimal strategies for these types production facilities where leftover finished goods inventory remains after the final shipment in a production cycle. Considering these scenarios, an inventory model is developed for an imperfect matching condition where some finished goods remains after the shipments. Findings: Based on the previous observation, this research also considers a single facility that follows JIT delivery and produces multiple products to satisfy customers’ demand. For this problem a rotational cycle model is developed to optimize the facility operations. Both problems are categorized as mixed integer non-linear programming problems which are to be solved to find optimum number of orders, shipments and rotational cycle policy for multiple products. Also, this solution will lead to estimate the optimum production quantity and minimum total system cost. Research limitations: This research considers the supply chain based on manufacturers point of view and it does not consider the transportation cost associated with supply chain. Next study will be focused on issues with joint decision making, information sharing, and transportation decision. Practical implications: This study will help the managers of refinery and paper industries in making their operation smooth by applying optimizing techniques and robust decision making. Originality/value: Based on the literature, no research was found on continuous production system supply chain and its optimization with JIT delivery. This research will definitely provide a direction for such problem to the researchers.Peer Reviewe

Static and dynamic inventory models under inflation, time value of money and permissible delay in payment

In this research a number of mathematical models were developed for static and dynamic deterministic single-item inventory systems. Economic factors such as inflation, time value of money and permissible delay in payment were considered in developing the models. Nonlinear optimization techniques were used to obtain the optimal policies for the systems.;First, a static single-item inventory model was considered in which shortages are allowed and a delay is permitted in payment. In this case, suppliers allow the customers to settle their accounts after a fixed delay period during which no interest is charged.;An extension of the model was then considered in which all cost components of the model are subject to inflation and discounting, with constant rates over the planning horizon. The mathematical model of the system was developed and a nonlinear optimization technique, Hooke and Jeeves search method, was used to obtain the optimal policies for the system.;A dynamic deterministic single-item inventory model was also considered in which the demand was assumed to be a linear function of time. Suppliers allow for a delay in payment and the cost components are subject to inflation and discounting with constant rates and continuous compounding. The Golden search technique was used to obtain the optimum length of replenishment cycle such that the total cost is minimized.;Computer applications using Visual Basic and Mathematics were developed and several numerical example were solved