Multi-item EOQ inventory model with varying holding cost under two restrictions: A geometric programming approach

In this paper we provide a simple method to determine the inventory policy of multiple items having varying holding cost using a geometric programming approach. The varying holding cost is considered to be a continuous function of the order quantity. The EOQ inventory model with constant holding cost and the classical EOQ inventory model without constraints are derived.     

Constrained production lot-size model with trade-credit policy: 'A comparison geometric programming approach via Lagrange'

In this paper our main objective is to investigate a deterministic inventory production lot-size model with a permissible delay in payment under a restriction. We analyse our deterministic inventory model under a restriction which will be assumed as the average inventory level. In fact we use in our analysis two approaches: the geometric programming approach; and the Lagrange method. Then a comparison between these two approaches is performed, which is our aim. Finally we deduce some previously published works of other researchers as special cases.     

Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: A geometric programming approach

A multi-item inventory model with constant demand and infinite replenishment is developed under the restrictions on storage area, total average shortage cost and total average inventory investment cost. These restrictions may be precise or imprecise. Here, it is assumed that inventory costs are directly proportional to the respective quantities, and unit purchase/production cost is inversely related to the demand. Restricted shortages are allowed but fully backlogged. First, the problem is formulated in crisp environment taking the deterministic and precise inventory parameters. It is solved by both geometric programming (GP) and gradient-based non-linear programming (NLP) methods. Later, the problem is formulated with fuzzy goals on constraints and objectives where impreciseness is introduced through linear membership functions. It is solved using the fuzzy geometric programming (FGP) method. The inventory models are illustrated with numerical values and compared with the crisp results. A sensitivity analysis on the optimum order quantity and average cost is also presented due to the variation in the tolerance of total average inventory investment cost and total average shortage cost following Dutta et al., 1993, Fuzzy Sets and Systems, 55, 133-142.     

The resource constrained single-item inventory problem with demand-dependent unit cost

In this paper, we present an economic order quantity (EOQ) with both demand-dependent unit cost and restrictions. An analytical solution of the EQO is derived using a recent and simple method, which isthe geometric programming approach. The EOQ inventory model with demand-dependent unit cost without any restriction and the classical EOQ inventory model are obtained.     

Setup cost reduction a multi-stage order quantity model

In this paper, a single item, multi-stage serial order quantity (MSOQ) model with constant demand is discussed. The objective of the model is to minimize the total cost which includes the setup cost and the inventory holding cost. This paper examines and analyses the investment in a one-time cost to reduce the (current) setup level and adds a per unit item amortization of this cost to the other costs associated with the MSOQ model. We consider the setup cost to be decreased on each stage with the same rate and the cost of the joint setup cost reduction is a logarithmic cost function.     

The resource constrained multi-item inventory problem with price discount: a geometric programming approach

In this paper we present a geometric programming approach for determining the inventory policy for multiple items having price discount and a limit on the total average inventory of all the items. An example is solved to illustrate the method.     

An integrated production and inventory model for a whole manufacturing supply chain involving reverse logistics with finite horizon period

This paper proposes a model and solution method for coordinating integrated production and inventory cycles in a whole manufacturing supply chain involving reverse logistics for multiple items with finite horizon period. A whole manufacturing supply chain involving reverse logistic consists of tier-2 suppliers supplying raw materials to tier-1 suppliers, tier-1 suppliers producing parts, a manufacturer which manufactures and assembles parts from tier-1 suppliers into finished products, distributors distributing finished products to retailers, retailers selling products to end customers and a third party which collects the used finished products from end customers, dissembles collected products into parts, and feed the parts back to the supply chain. In this system, we consider a finite horizon period. A mathematical model for representing the behaviors of the system is developed. Solution methods based on decentralized and a combination of decentralized and centralized decision making process, referred to as the semi-centralized decision making process, are proposed to solve the model while the centralized decision making process is solved by a mixed integer nonlinear programming method. A numerical example is used to demonstrate the model and the solutions based on the three types of the coordination.     

Multi-site aggregate production planning with multiple objectives: A goal programming approach

This paper addresses the problem of aggregate production planning (APP) for a multinational lingerie company in Hong Kong. The multi-site production planning problem considers the production loading plans among manufacturing factories subject to certain restrictions, such as production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers' preferences, as well as production capacity, workforce level, storage space and resource conditions of the factories. In this paper, a multi-objective model is developed to solve the production planning problems, in which the profit is maximized but production penalties resulting from going over/under quotas and the change in workforce level are minimized. To enhance the practical implications of the proposed model, different managerial production loading plans are evaluated according to changes in future policy and situation. Numerical results demonstrate the robustness and effectiveness of the developed model.     

Postponement implementation in integrated production and inventory plan under deterioration effects: a case study of a juice producer with limited storage capacity

Abstract

The aim of this study is to develop a production and inventory plan for a fresh apple juice producer. During harvest season, the producer extracts premium juice from freshly picked apples and keeps an inventory of these premium apples in his temperature-controlled storage facility. The producer extracts also regular juice from regular apples purchased from third-party storages. To satisfy future demand, the producer carries inventories of juice and apple. The levels of apple inventories are constrained by the producer’s limited storage space, but he can replenish regular apples. To assist the producer in facing demand uncertainty and deterioration of apples, we develop a production and inventory plan that incorporates postponement to mitigate demand uncertainty. As postponement decisions are shaped by the cost structure of inventories, we integrate in one model the postponement decisions and the deterioration mitigation decisions that can alter the inventory costs. We build multi-period stochastic programming with recourse model to determine juice batch sizes and apple inventories that maximize the producer’s expected profit. The optimal solution illustrates the use of time and form postponements. We discuss the interactions between postponement implementation and decisions to mitigate apples deterioration. We compare the production and inventory plans with and without postponement and with and without apple deterioration. We also present sensitivity analyses for the plan under varying inventory cost and storage space.