An Optimization of (

Addressing the problems of a health care center which produces tailor-made clothes for specific people, the paper proposes a single product continuous review model and establishes an optimal policy for the center based on (Q,r) control policy to minimize expected average cost on an order cycle. A generic mathematical model to compute cost on real-time inventory level is developed to generate optimal order quantity under stochastic stock variation. The customer demands are described as compound Poisson process. Comparisons on cost between optimization method and experience-based decision on Q are made through numerical studies conducted for the inventory system of the center

Optimising replenishment policy in an integrated supply chain with controllable lead time and backorders-lost sales mixture

This paper aims to optimize the inventory replenishment policy in an integrated supply chain consisting of a single supplier and a single buyer. The system under consideration has the features such as backorders-lost sales mixture, controllable lead time, stochastic demand, and stockout costs. The underlying problem has not been studied in the literature. We present a novel approach to formulate the optimization problem, which is able to satisfy the constraint on the number of admissible stockouts per time unit. To solve the optimization problem, we propose two algorithms: an exact algorithm and a heuristic algorithm. These two algorithms are developed based on some analytical properties that we established by analysing the cost function in relation to the decision variables. The heuristic algorithm employs an approximation technique based on an ad-hoc Taylor series expansion. Extensive numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms

Efficient near-optimal procedures for some inventory models with backorders-lost sales mixture and controllable lead time, under continuous or periodic review

This paper considers a number of inventory models with backorders-lost sales mixture, stockout costs, and controllable lead time. The lead time is a linear function of the lot size and includes a constant term that is made of several components. These lot-size-independent components are assumed to be controllable. Both single- and double-echelon inventory systems, under periodic or continuous review, are considered. To authors knowledge, these models have never been previously studied in literature. The purpose of this paper is to analyse and optimize these novel inventory models. The optimization is carried out by means of heuristics that work on an ad hoc approximation of the cost functions. This peculiarity permits to exploit closed-form expressions that make the optimization procedure simpler and more readily applicable in practice than standard approaches. Finally, numerical experiments investigate the efficiency of the proposed heuristics and the sensitivity of the developed models

Optimal policy for multi-item systems with stochastic demands, backlogged shortages and limited storage capacity

Producción CientíficaIn this paper, an inventory model for multiple products with stochastic demands is developed. The scheduling period or inventory cycle is known and prescribed. Demands are independent random variables and they follow power patterns throughout the inventory cycle. For each product, an aggregate cycle demand is realized first and then the demand is released to the inventory system gradually according to power patterns within a cycle. These demand patterns express different ways of drawing units from inventory and can be a good approach to modelling customer demands in inventory systems. Shortages are allowed and they are fully backlogged. It is assumed that the warehouse where the items are stored has a limited capacity. For this inventory system, we determine the inventory policy that maximizes the expected profit per unit time. An efficient algorithmic approach is proposed to calculate the optimal inventory levels at the beginning of the inventory cycle and to obtain the maximum expected profit per unit time. This inventory model is applicable to on-line sales of a wide variety of products. In this type of sales, customers do not receive the products at the time of purchase, but sellers deliver goods a few days later. Also, this model can be used to represent inventories of products for in-shop sales when the withdrawal of items from the inventory is not at the purchasing time, but occurs in a period after the sale of the products. This inventory model extends various inventory systems studied by other authors. Numerical examples are introduced to illustrate the theoretical results presented in this work.Ministerio de Ciencia, Innovación y Universidades - Fondo Europeo de Desarrollo Regional (project MTM2017-84150-P

Distribution-free approach for stochastic joint-replenishment problem with backorders-lost sales mixtures, and controllable major ordering cost and lead times

In this paper, we study the periodic-review Joint-Replenishment Problem (JRP) with stochastic demands and backorders-lost sales mixtures. We assume that lead times aare made of two major components: a common part to all items and an item-specific portion. We further suppose that the item-specific component of lead times and the major ordering cost are controllable. To reflect the practical circumstance characterized by the lack of complete information about the demand distribution, we adopt the minimax distribution-free approach. That is, we assume that only the mean and the variance of the demand can be evaluated. The objective is to determine the strict cyclic replenishment policy, the length of (the item-specific component of) lead times, and the major ordering cost that minimize the long-run expected total cost. To approach this minimization problem, we present a first optimization algorithm. However, numerical tests highlighted how computationally expensive this algorithm would be for a practical application. Therefore, we then propose two alternative heuristics. Extensive numerical experiments have been carried out to investigate the performance of the developed algorithms. Results have shown that the proposed alternative heuristics are actually efficient and seem therefore promising for a practical application

Decentralized and centralized supply chains with trade credit option

The notion of a trade credit period is a common business practice, where a supplier allows a buyer a specified period to make a payment in full for a purchase made. The objective of this thesis is to explore the role of such a credit payment option in supply chain management. Towards this end, a two-echelon supply chain, consisting of a single supplier (e.g. manufacturer) and the cases of both a single and multiple buyers (e.g. retailers) is examined under decentralized (independent) and centralized (coordinated) decision making scenarios. The major emphasis of this research is limited to the case of a single product with price-sensitive deterministic, as well as stochastic market demand.The conditions under which a trade credit period should be offered and its appropriate length are determined from the supplier’s perspective under the decentralized case. Under the centralized decision scenario, the efficacy of a trade credit policy as a supply chain coordination mechanism is thoroughly analyzed and guidelines for pricing, production and delivery decisions are developed. The concepts developed in this study are illustrated via a number of numerical examples, in conjunction with thorough sensitivity analyses involving some selected problem parameters.The major contribution of this thesis is that we incorporate the pricing and inventory issues in supply chains with an endogenous credit payment period. This is the first study that examines the efficacy of trade credit option as a coordination mechanism. We propose a coordination mechanism that coordinates the supply chain, when a trade credit by itself is not sufficient to serve such a purpose, while preserving the benefits of a trade credit option. Also, this study is the first to examine the issues concerning trade credit under price sensitive stochastic demand. Another first for this work is the exploration of the implications of a trade credit policy in supply chains consisting of multiple competing retailers. The effects of the extent of competition and the market size on trade credit policy are evaluated. Our analyses lead to some important practical implications, to serve as managerial guidelines.Ph.D., Decision Sciences -- Drexel University, 201