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The purpose of this paper is to present a polynomial time algorithm which determines the lot sizes for purchase component in Material Requirement Planning (MRP) environments with deterministic time-phased demand with zero lead time. In this model, backlog is not permitted, the unit purchasing price is based on the all-units discount system and resale of the excess units is possible at the ordering time. The properties of an optimal order policy are argued and on the basis of them, a branch and bound algorithm is presented to construct an optimal sequence of order policies. In the proposed B&B algorithm, some useful fathoming rules have been proven to make the algorithm very efficient. By... 

Integrated supplier selection and order allocation is a complex problem that is important for both designing and operating supply chains. It becomes especially complicated when quantity discounts are considered at the same time. Under such circumstances, most studies often formulate the problem as a Multi-Objective Linear Programming problem (MOLP), and then transform it to a Mixed Integer Programming problem (MIP) to handle the inherited multi-objectives, simultaneously. But, objectives are not of equal importance and in this approach scaling and subjective weighting often are not considered. In addition, some of the studies that use weighting method to solve the MOLP, usually ignore to... 

While in multi-periodic inventory control problems the usual assumption are that the orders are placed at the beginning of each period (periodic review) or depending on the inventory level they can happen at any time (continuous review), in this research, we relax these assumptions and assume that the periods between two replenishments of the products are independent and identically distributed random variables. Furthermore, assuming the purchasing price are triangular fuzzy variables, the quantities of the orders are of integer-type and that there are space, budget and service level constraints, incremental discount is considered to purchase products and a combination of back-order and... 

The Newsboy problem has always been an important issue in inventory management. The multi-product newsboy problem with random yield and budget constraint named as the Gardener Problem is one of the novels and popular extensions of the newsboy problem. Different from the existing studies, this paper presents a multi-product gardener problem with reservation policy. Moreover, a discount rate is offered to those customers who are willing to make reservations. In addition to the demand from the original customers, extra demand is included in the model due to the motivation received by the discount rate. A solution algorithm namely the multi-product gardener problem with reservation policy... 

An optimal algorithm based on branch-and-bound approach is presented in this paper to determine lot sizes for a single item in material requirement planning environments with deterministic time-phased demand and constant ordering cost with zero lead time, where all-units discounts are available from vendors and backlog is not permitted. On the basis of the proven properties of optimal order policy, a tree-search procedure is presented to construct the sequence of optimal orders. Some useful fathom rules have been proven, which make the algorithm very efficient. To compare the performance of this algorithm with the other existing optimal algorithms, an experimental design with various... 

This paper presents an optimal algorithm based on Branch and Bound approach for determining lot sizes for purchased component in Material Requirement Planning (MRP) environments with deterministic time-phased demand and constant ordering cost with zero lead time. Backlog is not permitted and the unit purchasing price depends on the quantity of an order and resale of the excess is possible at the ordering time. We assume an all-units discount system with single price break point. Based on proven properties of an optimal order policy, a tree search procedure is designed to construct the sequences of orders and resales amount in optimal order policy. Some useful fathom rules have been proven to... 

In this paper, a multi-item multiperiod inventory control problem with all-unit and/or incremental quantity discount policies under limited storage capacity is presented. The independent random demand rates of the items in the periods are known and the items are supplied in distinct batch sizes. The cost consists of ordering, holding, and purchasing. The objective is to find the optimal order quantities of all items in different periods such that the total inventory cost is minimized and the constraint is satisfied. A mixed binary integer programming model is first developed to model the problem. Then, a parameter-tuned genetic algorithm (GA) is employed to solve it. Since there is no... 

In this paper, the joint replenishment-location problem of some distribution centers (DCs) with a centralized decision maker who is responsible for ordering and dispatching shipments of a single product is modeled. The warehouse spaces of the DCs are limited and the product is sold under an incremental discount policy. The model seeks to minimize the total cost of the supply chain under the joint replenishment policy along with minimizing the cost of locating the DCs in potential sites as the first objective. The second objective is to minimize the warehouse space of all DCs using the revisable approach. As the proposed model is a bi-objective integer non-linear optimization problem... 

The problem of allocating heterogeneous fleet of vehicles to the existing distribution network for dispensing products fro. manufacturing firm t. set of depots is considered. It is assume. heterogeneous fleet of vehicles with the given capacities and total costs consisting o. discounted fixed cost an. variable cost proportional to the amount shipped is employed for handling products. To minimize the total transportation costs, the problem is modeled i. form of the nonlinear mixed integer program. Due to the NP hard complexity of the mathematical model, three prioritized K-mean clustering hybrid GAs, by incorporating two new heuristic algorithms, are proposed. The efficiency of the algorithms... 

In this paper, the joint replenishment-location problem of some distribution centers (DCs) with a centralized decision maker who is responsible for ordering and dispatching shipments of a single product is modeled. The warehouse spaces of the DCs are limited and the product is sold under an incremental discount policy. The model seeks to minimize the total cost of the supply chain under the joint replenishment policy along with minimizing the cost of locating the DCs in potential sites as the first objective. The second objective is to minimize the warehouse space of all DCs using the revisable approach. As the proposed model is a bi-objective integer non-linear optimization problem... 

In this paper we consider a newsvendor problem in which the suppliers offer quantity discounts. We assume that the initial inventory at the beginning of the period is a random variable. This assumption, among other applications, may apply to the case where the decision about the order quantity must be made at a time long before the start of the period and the available inventory may decrease due to several factors, such as deterioration, consumption, etc. up to the start of the period. In this paper, we obtain the optimal order quantity that maximizes the total profit for this model  

The goal of this research is to formulate an inventory control problem of a single item with variable demand dependent on displayed stock level and selling price of the commodity. The item deteriorates based on a three-parameter Weibull distribution and advance payment is needed to purchase the item with the all-unit discount policy. Shortages are allowed partially and backlogged with the rate dependent on the length of customers' waiting time. The corresponding problem is formulated as a profit maximisation model. For solving this problem, four different variants of particle swarm optimisation (PSO) are utilised. Then, the application of the model is illustrated with the help of a numerical... 

We propose an efficient optimal algorithm for determining the lot sizes for purchase component in Material Requirement Planning (MRP) environments with deterministic time-phased demand and zero lead time. In this model, backlog is not permitted, the unit purchasing price is based on the all-units discount system with single price break point and resale of the excess units is acceptable at the ordering time. The problem is divided into the sub-plans with specific properties by the dynamic programming (DP) method already presented. By modifying the main structure of the DP method, we present a branch-and-bound algorithm to obtain the optimal ordering policy for each sub-plans. Furthermore, we... 

In this paper we develop a stochastic programming approach to solve a multi-period multi-product multi-site aggregate production planning problem in a green supply chain for a medium-term planning horizon under the assumption of demand uncertainty. The proposed model has the following features: (i) the majority of supply chain cost parameters are considered; (ii) quantity discounts to encourage the producer to order more from the suppliers in one period, instead of splitting the order into periodical small quantities, are considered; (iii) the interrelationship between lead time and transportation cost is considered, as well as that between lead time and greenhouse gas emission level; (iv)... 

A resource investment problem with discounted cash flows (RIPDCF) is a project-scheduling problem in which (a) the availability levels of the resources are considered decision variables and (b) the goal is to find a schedule such that the net present value of the project cash flows optimizes. In this paper, the RIPDCF in which the activities are subject to generalized precedence relations is first modeled. Then, a genetic algorithm (GA) is proposed to solve this model. In addition, design of experiments and response surface methodology are employed to both tune the GA parameters and to evaluate the performance of the proposed method in 240 test problems. The results of the performance... 

We study contracts between a single retailer and multiple suppliers of two substitutable products, where suppliers have fixed capacities and present the retailer cost contracts for their supplies. After observing the contracts, the retailer decides how much capacity to purchase from each supplier, to maximize profits from the purchased capacity from the suppliers plus his possessed inventory (endowment). This is modeled as a noncooperative, nonzero-sum game, where suppliers, or principals, move simultaneously as leaders and the retailer, the common agent, is the sole follower. We are interested in the form of the contracts in equilibrium, their effect on the total supply chain profit, and...