Finite-horizon operations planning for a lean supply chain system

This dissertation studies an operational policy for a lean supply chain system consisting of a manufacturer, multiple suppliers and multiple buyers. The manufacturer procures raw materials from the suppliers and converts them into finished products, which are then shipped in batches to the buyers at certain intervals of times. Three distinct but inseparable problems are addressed: single supplier and single buyer with fixed delivery size (FD), multiple suppliers and multiple buyers with individual delivery schedule (MD), and time dependent delivery quantity with trend demand (TD). The mathematical formulations of these supply systems are categorized as mixed-integer, nonlinear programming problems (MINLAP) with discrete, non-convex objective functions and constraints. The operations policy determines the number of orders of raw material, beginning and ending times of cycles, production batch size, production start time, and beginning and ending inventories. The goal is to minimize the cost of the two-stage, just-in-time inventory system that integrates raw materials ordering and finished goods production system. The policy is designed for a finite planning horizon with various phases of life cycle demands such as inception (increasing), maturity (level) and phasing out (declining). Analytical results that characterize the exact, optimal policy for the problems described above are devised to develop efficient and optimal computational procedures. A closed-form heuristic that provides a near-optimal solution and tight lower bound is proposed for the problem FD. A network model to represent the problems is proposed and network-based algorithms are implemented to solve the problems FD, MD and TD optimally. The computational complexities of the algorithms are Θ(N2) or O(N3) where N is the total number of shipments in the planning horizon. Numerical tests to assess the robustness and quality of the methods show that the present research provides superior results. Production and supply chain management play an important role in ensuring that the necessary amounts of materials and parts arrive at the appropriate time and place. A manager, using the models obtained in this research, can quickly respond to consumers\u27 demand by effectively determining the right policies to order raw materials, to deliver finished goods, and to efficiently manage their production schedule

Solving finite production rate model with scrap and multiple shipments using algebraic approach

This paper solves a finite production rate (FPR) model with scrap and multiple shipments using an algebraic method. Classic FPR model assumes a continuous inventory issuing policy to satisfy demand and perfect quality production for all items produced. However, in real life vendor-buyer integrated production-inventory system, multiple shipment policy is practically used in lieu of a continuous issuing policy and generation of defective items during production run is inevitable. In this study, it is assumed that all defective items are scrap and the perfect quality items can only be delivered to customers if the whole lot is quality assured at the end of the production run. A conventional approach for solving the FPR model is the use of differential calculus on the long-run average cost function with the need to prove optimality first. This paper demonstrates that optimal lot size and its overall costs for the aforementioned FPR model can be derived without derivatives. As a result, it enables students or practitioners who have little knowledge of calculus to understand and to handle with ease the real-life FPR model

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

Determining replenishment lot size and shipment policy for an extended EPQ model with delivery and quality assurance issues

AbstractThis paper derives the optimal replenishment lot size and shipment policy for an Economic Production Quantity (EPQ) model with multiple deliveries and rework of random defective items. The classic EPQ model assumes a continuous inventory issuing policy for satisfying demand and perfect quality for all items produced. However, in a real life vendor–buyer integrated system, multi-shipment policy is practically used in lieu of continuous issuing policy and generation of defective items is inevitable. It is assumed that the imperfect quality items fall into two groups: the scrap and the rework-able items. Failure in repair exists, hence additional scrap items generated. The finished items can only be delivered to customers if the whole lot is quality assured at the end of rework. Mathematical modeling is used in this study and the long-run average production–inventory-delivery cost function is derived. Convexity of the cost function is proved by using the Hessian matrix equations. The closed-form optimal replenishment lot size and optimal number of shipments that minimize the long-run average costs for such an EPQ model are derived. Special case is examined, and a numerical example is provided to show its practical usage

Optimal production-shipment decisions for the finite production rate model with scrap

This paper is concerned with the decision-making on the optimal production batch size and optimal number of shipments for a finite production rate model with random scrap rate. The classic finite production rate (FPR) model assumes a continuous inventory issuing policy for satisfying product demand and perfect quality for all items produced. However, in a real life vendor-buyer integrated production-inventory system, a multiple shipment policy is practically used in lieu of the continuous issuing policy, and it is inevitable to generate defective items during a production run. All nonconforming items produced are assumed to be scrap, and the finished (perfect quality) products can only be delivered to customers if the whole lot is quality assured at the end of the production run. The fixed-quantity multiple instalments of the finished batch are delivered to customers at a fixed interval of time. Mathematical modelling is employed and the renewal reward theorem is used to cope with the variable production cycle length. The long-run average cost for the proposed model is derived, and its convexity is proved by the use of the Hessian matrix equations. A closed-form optimal production-shipment policy for such an imperfect FPR model is obtained and a special case is discussed. Finally, a numerical example is provided to demonstrate the model’s practical usage

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

Replenishment policies for a tree-type three echelon supply chain system

One of the common goals which most companies have is to maximize profits. There are two way to increase profit: increasing revenue or reducing cost. Lacking of ability to keep the cost down could potentially drive the companies out of the business. In recent years, many researchers have been paying more attention on improving supply chain system due to high potential of creating cost savings. The supply chain network considered in this research is a tree-type, three-echelon single producer, multiple distributors, and multiple retailers system. The goal of this research is to develop a replenishment policy which satisfies customers’ demand and minimizes the total production-inventory system cost. Three inventory models are developed here. First, tree-type, three-echelon distribution (producer, distributor and retailers) model with end customers’ backorders (TDB) at retailer’s level is developed. Second, the variation of downstream holding cost (DHV) is studied and a model is developed to investigate the effect downstream holding cost structure. Third, a model is developed to improve the retailer’s service rate (ISR). This model combines the features of TDB and DHV models together (allowable backorder and reduced delivery interval at retailer’s level). Operational schedules of TDB are constructed and the limitations of DHV model are established. The improvement in the ISR model is confirmed and demonstrated through numerical examples. Significance and conclusions of this research are highlighted along with an indication of future research

Effect of variable shipping frequency on production-distribution policy in a vendor-buyer integrated system

This paper investigates the effect of variable shipping frequency on production-distribution policy in a vendor-buyer integrated system. In a recent article Chiu et al. [1] derived the optimal replenishment lot size for an economic production quantity problem with multi-delivery and quality assurance, based on an assumption that the number of shipment is a given constant. However, in a vendor-buyer integrated system in supply chain environment, joint determination of replenishment lot size and number of shipments may help such a system to gain significant competitive advantage in terms of becoming a low-cost producer as well as having tight linkage to customer. For this reason, the present study extends the work of Chiu et al. [1] by considering shipping frequency as one of the decision variables and incorporating customer’s stock holding cost into system cost analysis. Hessian matrix equations are employed to certify the convexity of cost function that contains two decision variables, and the effect of variable shipping frequency on production-distribution policy is investigated. A numerical example is provided to demonstrate practical usage of the research result

Stochastic make-to-stock inventory deployment problem: an endosymbiotic psychoclonal algorithm based approach

Integrated steel manufacturers (ISMs) have no specific product, they just produce finished product from the ore. This enhances the uncertainty prevailing in the ISM regarding the nature of the finished product and significant demand by customers. At present low cost mini-mills are giving firm competition to ISMs in terms of cost, and this has compelled the ISM industry to target customers who want exotic products and faster reliable deliveries. To meet this objective, ISMs are exploring the option of satisfying part of their demand by converting strategically placed products, this helps in increasing the variability of product produced by the ISM in a short lead time. In this paper the authors have proposed a new hybrid evolutionary algorithm named endosymbiotic-psychoclonal (ESPC) to decide what and how much to stock as a semi-product in inventory. In the proposed theory, the ability of previously proposed psychoclonal algorithms to exploit the search space has been increased by making antibodies and antigen more co-operative interacting species. The efficacy of the proposed algorithm has been tested on randomly generated datasets and the results compared with other evolutionary algorithms such as genetic algorithms (GA) and simulated annealing (SA). The comparison of ESPC with GA and SA proves the superiority of the proposed algorithm both in terms of quality of the solution obtained and convergence time required to reach the optimal/near optimal value of the solution

On the inventory routing problem with stationary stochastic demand rate

One of the most significant paradigm shifts of present business management is that individual businesses no longer participate as solely independent entities, but rather as supply chains (Lambert and Cooper, 2000). Therefore, the management of multiple relationships across the supply chain such as flow of materials, information, and finances is being referred to as supply chain management (SCM). SCM involves coordinating and integrating these multiple relationships within and among companies, so that it can improve the global performance of the supply chain. In this dissertation, we discuss the issue of integrating the two processes in the supply chain related, respectively, to inventory management and routing policies. The challenging problem of coordinating the inventory management and transportation planning decisions in the same time, is known as the inventory routing problem (IRP). The IRP is one of the challenging optimization problems in logis-tics and supply chain management. It aims at optimally integrating inventory control and vehicle routing operations in a supply network. In general, IRP arises as an underlying optimization problem in situations involving simultaneous optimization of inventory and distribution decisions. Its main goal is to determine an optimal distribution policy, consisting of a set of vehicle routes, delivery quantities and delivery times that minimizes the total inventory holding and transportation costs. This is a typical logistical optimization problem that arises in supply chains implementing a vendor managed inventory (VMI) policy. VMI is an agreement between a supplier and his regular retailers according to which retailers agree to the alternative that the supplier decides the timing and size of the deliveries. This agreement grants the supplier the full authority to manage inventories at his retailers'. This allows the supplier to act proactively and take responsibility for the inventory management of his regular retailers, instead of reacting to the orders placed by these retailers. In practice, implementing policies such as VMI has proven to considerably improve the overall performance of the supply network, see for example Lee and Seungjin (2008), Andersson et al. (2010) and Coelho et al. (2014). This dissertation focuses mainly on the single-warehouse, multiple-retailer (SWMR) system, in which a supplier serves a set of retailers from a single warehouse. In the first situation, we assume that all retailers face a deterministic, constant demand rate and in the second condition, we assume that all retailers consume the product at a stochastic stationary rate. The primary objective is to decide when and how many units to be delivered from the supplier to the warehouse and from the warehouse to retailers so as to minimize total transportation and inventory holding costs over the finite horizon without any shortages