A just-in-time three-level integrated manufacturing system for linearly time-varying demand process

This paper considers a just-in-time (JIT) manufacturing system in which a single manufacturer procures raw materials from a single supplier, process them to produce finished products, and then deliver the products to a single-buyer. The customer demand rate is assumed to be linearly decreasing time-varying. In the JIT system, in order to minimize the suppliers as well as the buyers holding costs, the supply of raw materials and the delivery of finished products are made in small quantities. In this case, both the supply and the delivery may require multiple installments for a single production lot. We develop a mathematical model for this problem, propose a simple methodology for solving the model, and illustrate the effectiveness of the method with numerical examples.     

Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers

This research addresses an optimal policy for production and procurement in a supply-chain system with multiple non-competing suppliers, a manufacturer and multiple non-identical buyers. The manufacturer procures raw materials from suppliers, converts them to finished products and ships the products to each buyer at a fixed-interval of time over a finite planning horizon. The demand of finished product is given by buyers and the shipment size to each buyer is fixed. The problem is to determine the production start time, the initial and ending inventory, the cycle beginning and ending time, the number of orders of raw materials in each cycle, and the number of cycles for a finite planning horizon so as to minimize the system cost. A surrogate network representation of the problem developed to obtain an efficient, optimal solution to determine the production cycle and cycle costs with predetermined shipment schedules in the planning horizon. This research prescribes optimal policies for a multi-stage production and procurements for all shipments scheduled over the planning horizon. Numerical examples are also provided to illustrate the system.     

Supply chain models for an assembly system with preprocessing of raw materials

In this paper, we investigate the material procurement and delivery policy in a production system where raw materials enter into the assembly line from two different flow channels. The system encompasses batch production process in which the finished product demand is approximately constant for an infinite planning horizon. Two distinct types of raw materials are passed through the assembly line before to convert them into the finished product. Of the two types of raw materials, one type requires preprocessing inside the facility before the assembly operation and other group is fed straightway in the assembly line. The conversion factors are assigned to raw materials to quantify the raw material batch size required. To analyze such a system, we formulate a nonlinear cost function to aggregate all the costs of the inventories, ordering, shipping and deliveries. An algorithm using the branch and bound concept is provided to find the best integer values of the optimal solutions. The result shows that the optimal procurement and delivery policy minimizes the expected total cost of the model. Using a test problem, the inventory requirements at each stage of production and their corresponding costs are calculated. From the analysis, it is shown that the rate and direction change of total cost is turned to positive when delivery rates per batch reaches close to the optimal value and the minimum cost is achieved at the optimal delivery rate. Also, it is shown that total incremental cost is monotonically increasing, if the finished product batch size is increased, and if, inventory cost rates are increased. We examine a set of numerical examples that reveal the insights into the procurement-delivery policy and the performance of such an assembly type inventory model.     

A single-period inventory placement problem for a supply system with the satisficing objective

Consider the inventory placement problem in an N-stage supply system facing a stochastic demand for a single planning period. Each stage is a stocking point holding some form of inventory (e.g., raw materials, subassemblies, product returns or finished products) that after a suitable transformation can satisfy demand. Stocking decisions are made before demand occurs. Unsatisfied demands are lost. The revenue, salvage value, ordering, transformation, and lost sales costs are proportional. There are fixed costs for utilizing stages for stock storage. The objective is to maximize the probability of achieving a given target profit level.     

A Model for Continuous Production Control with Warning Signals to Fault Occurrences

The advance of computer, automation and control technology has led to the adoption of continuous control and monitoring of production processes in high technology industries. By monitoring the state of the production process continuously, occurrence of any faults in the production process can be identified with zero or negligible detection delay. As a result, the costs of defective products, loss in yield and restoration are minimized. On the other hand, the sensitivity of the continuous monitoring system could result in very frequent repair and maintenance of the process, causing frequent disruptions of production. This paper addresses the question of the determination of the optimal level at which warning signals should be given of fault occurrences in a production system that is continuously monitored. A model is developed from which the expected total costs per time unit can be derived. A numerical example illustrates the determination of the optimal warning level under this framework.     

Notice

In a recent issue of this journal, Trypia presented a simple rule to determine the blending pattern and quantities for a multi‐product blending firm. This paper presents three variations of Trypia's model suitable for discussion in production management and mathematical modelling courses. First, it presents a generalized version of Trypia's problem leading to a linear programming formulation. Next a more realistic version of Trypia's problem including set‐up costs is presented together with a simple method for determining production sequence and quantities. Finally, the case of sequence dependent set‐up costs is discussed.     

Supply planning models for a remanufacturer under just-in-time manufacturing environment with reverse logistics

We study a supply planning problem in a manufacturing system with two stages. The first stage is a remanufacturer that supplies two closely-related components to the second (manufacturing) stage, which uses each component as the basis for its respective product. The used products are recovered from the market by a third-party logistic provider through an established reverse logistics network. The remanufacturer may satisfy the manufacturer’s demand either by purchasing new components or by remanufacturing components recovered from the returned used products. The remanufacturer’s costs arise from product recovery, remanufacturing components, purchasing original components, holding inventories of recovered products and remanufactured components, production setups (at the first stage and at each component changeover), disposal of recovered products that are not remanufactured, and coordinating the supply modes. The objective is to develop optimal production plans for different production strategies. These strategies are differentiated by whether inventories of recovered products or remanufactured components are carried, and by whether the order in which retailers are served during the planning horizon may be resequenced. We devise production policies that minimize the total cost at the remanufacturer by specifying the quantity of components to be remanufactured, the quantity of new components to be purchased from suppliers, and the quantity of recovered used products that must be disposed. The effects of production capacity are also explored. A comprehensive computational study provides insights into this closed-loop supply chain for those strategies that are shown to be NP-hard.     

Deterministic hierarchical substitution inventory models

In this paper, we consider a deterministic nested substitution problem where there are multiple products which can be substituted one for the other, if necessary, at a certain cost. We consider the case when there are n products, and product j can substitute products j + 1,…,n at certain costs. The trade-off is the cost of storing products (for example, customised products) at a higher inventory holding stage versus the cost of transferring downwards from a lower inventory holding cost (generic product) stage. The standard approach to solving the problem yields an intractable formulation, but by reformulating the problem to determine the optimal run-out times, we are able to determine the optimal order and substitution quantities. Numerical examples showing the effect of various system parameters on the optimal order and substitution policy are also presented.     

A new approach towards integrated cell formation and inventory lot sizing in an unreliable cellular manufacturing system

This paper presents a comprehensive mathematical model for integrated cell formation and inventory lot sizing problem. The proposed model seeks to minimize cell formation costs as well as the costs associated with production, while dynamic conditions, alternative routings, machine capacity limitation, operations sequences, cell size constraints, process deterioration, and machine breakdowns are also taken into account. The total cost consists of machine procurement, cell reconfiguration, preventive and corrective repairs, material handling (intra-cell and inter-cell), machine operation, part subcontracting, finished and unfinished parts inventory cost, and defective parts replacement costs. With respect to the multiple products, multiple process plans for each product and multiple routing alternatives for each process plan which are assumed in the proposed model, the model is combinatorial. Moreover, unreliability conditions are considered, because moving from “in-control” state to “out-of-control” state (process deterioration) and machine breakdowns make the model more practical and applicable. To conquer the breakdowns, preventive and corrective actions are adopted. Finally, a Particle Swarm Optimization (PSO)-based meta-heuristic is developed to overcome NP-completeness of the proposed model.     

Production and Subcontracting Strategies for Manufacturers with Limited Capacity and Volatile Demand

We study a manufacturing firm that builds a product to stock to meet a random demand. If there is a positive surplus of finished goods, customers make their purchases without delay and leave. If there is a backlog, the customers are sensitive to the quoted lead time and some choose not to order if they feel that the lead time is excessive. A set of subcontractors, who have different costs and capacities, are available to supplement the firm's production capacity. We derive a feedback policy that determines the production rate and the rate at which the subcontractors are requested to deliver products. The performance of the system, when it is managed according to this policy, is evaluated.     

Lot-sizing two-echelon assembly systems with random yields and rigid demand

We consider a two-echelon assembly system producing a single final product for which the demand is known. The first echelon consists of several parallel stages, whereas the second echelon consists of a single assembly stage. We assume that the yield at each stage is random and that demand needs to be satisfied in its entirety; thus, several production runs may be required. A production policy should specify, for each possible configuration of intermediate inventories, on which stage to produce next and the lot size to be processed. The objective is to minimize the expected total of setup and variable production costs.We prove that the expected cost of any production policy can be calculated by solving a finite set of linear equations whose solution is unique. The result is general in that it applies to any yield distribution. We also develop efficient algorithms leading to heuristic solutions with high precision and, as an example, provide numerical results for binomial yields.     

Optimisation of integrated reverse logistics networks with different product recovery routes

The awareness of importance of product recovery has grown swiftly in the past few decades. This paper focuses on a problem of inventory control and production planning optimisation of a generic type of an integrated Reverse Logistics (RL) network which consists of a traditional forward production route, two alternative recovery routes, including repair and remanufacturing and a disposal route. It is assumed that demand and return quantities are uncertain. A quality level is assigned to each of the returned products. Due to uncertainty in the return quantity, quantity of returned products of a certain quality level is uncertain too. The uncertainties are modelled using fuzzy trapezoidal numbers. Quality thresholds are used to segregate the returned products into repair, remanufacturing or disposal routes. A two phase fuzzy mixed integer optimisation algorithm is developed to provide a solution to the inventory control and production planning problem. In Phase 1, uncertainties in quantity of product returns and quality of returns are considered to calculate the quantities to be sent to different recovery routes. These outputs are inputs into Phase 2 which generates decisions on component procurement, production, repair and disassembly. Finally, numerical experiments and sensitivity analysis are carried out to better understand the effects of quality of returns and RL network parameters on the network performance. These parameters include quantity of returned products, unit repair costs, unit production cost, setup costs and unit disposal cost.     

Marine inventory routing: shipments planning

This paper addresses a shipments-planning problem faced by producers of large volume liquid bulk products. Producing origins with limited tank storage capacity supply multiple products by ships (or barges) to consuming destinations that also have limited storage capacity. Timing, origin, destination, and product quantities of shipments have to be determined in a manner that minimizes costs and does not violate storage capacity constraints at both ends (neither stopping production at the origins, nor running out of stock at the destinations). A mixed integer-programming model is used to derive cost effective solutions within a few minutes. A cost-based heuristic algorithm is used to assure that acceptable solutions are obtained quickly.     

Cooperation in assembly systems: The role of knowledge sharing networks

Process improvement plays a significant role in reducing production costs over the life cycle of a product. We consider the role of process improvement in a decentralized assembly system in which a buyer purchases components from several first-tier suppliers. These components are assembled into a finished product, which is sold to the downstream market. The assembler faces a deterministic demand/production rate and the suppliers incur variable inventory costs and fixed setup production costs. In the first stage of the game, which is modeled as a non-cooperative game among suppliers, suppliers make investments in process improvement activities to reduce the fixed production costs. Upon establishing a relationship with the suppliers, the assembler establishes a knowledge sharing network – this network is implemented as a series of meetings among suppliers and also mutual visits to their factories. These meetings facilitate the exchange of best practices among suppliers with the expectation that suppliers will achieve reductions in their production costs from the experiences learned through knowledge sharing. We model this knowledge exchange as a cooperative game among suppliers in which, as a result of cooperation, all suppliers achieve reductions in their fixed costs. In the non-cooperative game, the suppliers anticipate the cost allocation that results from the cooperative game in the second stage by incorporating the effect of knowledge sharing in their cost functions. Based on this model, we investigate the benefits and challenges associated with establishing a knowledge sharing network. We identify and compare various cost allocation mechanisms that are feasible in the cooperative game and show that the system optimal investment levels can be achieved only when the most efficient supplier receives the incremental benefits of the cost reduction achieved by other suppliers due to the knowledge transfer.     

Modified base-stock policies for semiconductor production system with dependent yield rates

We consider a two-stage production system faced by semiconductor manufacturing which produces a hierarchy of multiple grades of outputs. In the first stage, a single type of input (wafer) is used to produce multiple types of semi-finished parts with dependent yield rates, and in the second stage, each type of semi-finished parts can be transformed into a corresponding type of final products, or downgraded to a type of lower grade final products. Random customer demands are faced on the final products, and demands of different types of final products are not allowed to be substituted. The advantage of this production system is that it can prevent unhealthy ordering from customers who intentionally send out false demand signals for high grade products and revise the orders to lower grade products when the delivery time is close, which was observed in semiconductor manufacturing. The objective of the study is to plan the quantity of the input at the first stage and the respective downgrade quantities at the second stage so as to meet the required service level at the minimum cost. With some common assumptions, we propose a modified base-stock policy for this two-stage production system and show that the occurrence of nil excess inventory above the base-stock level follows a renewal process. We further extend the modified base-stock policy to a better policy that invokes risk pooling over multiple grade products. The performance of these two polices are evaluated via simulation to provide managerial insights.     

A single-period inventory placement problem for a supply chain with the expected profit objective

Consider the expected profit maximizing inventory placement problem in an N-stage, supply chain facing a stochastic demand for a single planning period for a specialty item with a very short selling season. Each stage is a stocking point holding some form of inventory (e.g., raw materials, subassemblies, product returns or finished products) that after a suitable transformation can satisfy customer demand. Stocking decisions are made before demand occurs. Because of delays, only a known fraction of demand at a stage will wait for shipments. Unsatisfied demand is lost. The revenue, salvage value, ordering, shipping, processing, and lost sales costs are proportional. There are fixed costs for utilizing stages for stock storage. After characterizing an optimal solution, we propose an algorithm for its computation. For the zero fixed cost case, the computations can be done on a spreadsheet given normal demands. For the nonnegative fixed cost case, we develop an effective branch and bound algorithm.     

Optimal production run time for a deteriorating production system under an extended inspection policy

A deteriorating production system is subjected to random deterioration from an in-control state to an out-of-control state with a general shift distribution. In order to reduce the defective items, part inspection policy, under which production inspections are performed only at the end of the production run, and full inspection policy are both considered in the literature. Moreover, the former dominates the latter. Since the product produced towards the end of a production cycle are more likely to be defective, it can further economize the inspection costs that they are directly reworked without inspection. In this paper, we propose an extended product inspection policy for a deteriorating production system. Product inspections are performed in the middle of a production cycle, and after the inspection, all products produced until the end of the production run are fully reworked. Based on the model, we show that there exists a production run time and a corresponding unique inspection policy such that the expected total cost per item per cycle is minimized. Finally, numerical examples are provided to illustrate our extended inspection policy, and indicate that such product inspection model will reduce the quality-related cost than part inspection does.     

Two-stage generalized age maintenance of a queue-like production system

In general, the initiation of preventive maintenance should be based on the technical state as well as the operating state of a production system. Since the operating state of a production system is often subject to fluctuations in time, the planning of preventive maintenance at preset points in time (e.g. age/block replacement) cannot be optimal. Therefore, we propose a so-called two-stage maintenance policy, which - in a first stage - uses the technical state of the production system to determine a finite interval [t, t + At] during which preventive maintenance must be carried out, and - in a second stage - uses the operating state of the production system to determine the optimal starting time t̂ for preventive maintenance within that interval. A generalized age maintenance policy optimizing both t and At is formulated in the first stage. To this end, the actual starting time of preventive maintenance is modelled in terms of a uniform distribution over the maintenance interval. Moreover, the expected costs of preventive maintenance are modelled as a decreasing function of the interval size. An efficient algorithm is developed to demonstrate the optimal strategy for a queue-like production system, via numerical results that offer useful insights.     

A two-bottleneck system with binomial yields and rigid demand

This study considers multistage production systems where production is in lots and only two stages have non-zero setup costs. Yields are binomial and demand, needing to be satisfied in its entirety, is “rigid”. We refer to a stage with non-zero setup cost as a “bottleneck” (BN) and thus to the system as “a two-bottleneck system” (2-BNS). A close examination of the simplest 2-BNS reveals that costs corresponding to a particular level of work in process (WIP) depend upon costs for higher levels of WIP, making it impossible to formulate a recursive solution.For each possible configuration of intermediate inventories a production policy must specify at which stage to produce next and the number of units to be processed. We prove that any arbitrarily “fixed” production policy gives rise to a finite set of linear equations, and develop algorithms to solve the two-stage problem. We also show how the general 2-BNS can be reduced to a three-stage problem, where the middle stage is a non-BN, and that the algorithms developed can be modified to solve this problem.     

Modeling and analysis of a supply–assembly–store chain

We consider a supply–assembly–store chain with produce-to-stock strategy, which comprises a set of component suppliers, a mixed-model assembly line with a constantly moving conveyor linking a set of workstations in series, and a set of product storehouses. Each supplier provides components of a specified family, which are assembled at a corresponding workstation. Units belonging to different models of products are sequentially fed onto the conveyor, and pass through the workstations to generate finished products. Each storehouse stores finished products belonging to a specific model for satisfying customer demands. The suppliers deliver components according to a just-in-time supply policy with stochastic leadtimes. Customer demands for a particular model of products arrive at the corresponding storehouse according to a Poisson stream. The paper conducts a modeling and performance analysis in the design stage of the system in the sense of “long-term-behavior”. A rolling technique is constructed for analyzing stationary probability distributions of the numbers of components. A two-dimensional Markov chain with infinite states is introduced for analyzing stationary probability distributions of inventories of finished products. Based on these distributions, performance measures of the system, such as work-in-process of components, inventory amounts of finished products, as well as service levels for customers, can be easily obtained. Managerial insights are obtained from both analytical and numerical results.