Mathematical modeling for a multiproduct manufacturing system featuring postponement, external suppliers, overtime, and scrap

Manufacturing firms operating in today’s competitive global markets must continuously find the appropriate manufacturing scheme and strategies to effectively meet customer needs for various types of quality of merchandise under the constraints of short order lead-time and limited in-house capacity. Inspired by the offering of a decision-making model to aid smooth manufacturers’ operations, this study builds an analytical model to expose the influence of the outsourcing of common parts, postponement policies, overtime options, and random scrapped items on the optimal replenishment decision and various crucial system performance indices of the multiproduct problem. A two-stage fabrication scheme is presented to handle the products’ commonality and the uptime-reduced strategies to satisfy the short amount of time before the due dates of customers’ orders. A screening process helps identify and remove faulty items to ensure the finished lot’s anticipated quality. Mathematical derivation assists us in finding the manufacturing relevant total cost function. The differential calculus helps optimize the cost function and determine the optimal stock-replenishing rotation cycle policy. Lastly, a simulated numerical illustration helps validate our research result’s applicability and demonstrate the model’s capability to disclose the crucial managerial insights and facilitate manufacturing-relevant decision making.

MULTIPRODUCT MANUFACTURING WITH DELAYED DIFFERENTIATION, OUTSOURCING, EXPEDITED RATE, AND REWORK STRATEGIES

This study examines the effect of delayed differentiation, outsourcing, expedited fabrication rate, and rework strategies on optimal cycle-time decisions for a multi-item manufacturing system. Today’s manufacturing firms must simultaneously deal with externally increasing client multi-item requirements with rapid lead-time and high-quality products and internally on a limited capacity. This study is aimed at assisting manufacturers in meeting client needs in conditions of restricted-capacity and minimum total operating expenses, and adopts a delayed differentiation two-stage multiproduct manufacturing scheme to manage the end products’ commonality. The first stage produces all required common components, and the second stage fabricates individual finished goods. In both stages, we adopt the reworking of the inevitable nonconforming items produced to assure product quality. Furthermore, we implemented partial outsourcing of common parts’ batch and expedited the manufacturing rate of finished products to effectively reduce the uptimes in both stages. We explicitly developed a model to describe the characteristics of the problem. Mathematical analyses with optimization proved the cost function’s convexity and determined the cost-minimization rotation cycle policy. Finally, we numerically validated our model’s and results’ applicability and capability with a simulated example. Apart from creating a useful decision model, this study makes another important contribution to the existing literature in that its revelation of collective/individual effect of the manufacturing-relevant methods on the problem’s best-operating cycle policy and crucial performance indices helps manufacturers have better control over their operations and make effective and efficient managerial decisions.

ABOUT THE PERFOMANCE MULTI-PRODUCT MANUFACTURING SYSTEMS

The multi-product type of modern machine-building production significantly complicates the definition and use of its indicators. Some of them have clear meaning for traditional types of production. However, it is not well defined for multi-product production. This fully applies to the wellknown concept of “productivity” in mechanical engineering. Productivity metrics have traditionally been used as measures of production efficiency. However, they are not formally defined for multiproduct manufacturing. The presented article shows that these systems are collections of separate, but interacting subsystems. They are determined by a multitude of realized technological connections. It can be used several different productivity estimates when analyzing each subsystem. Only the results of the operation of alternative production systems, similar in input and output variables, can be compared in productivity. The productivity of the system grows with an increase in the share of its productive work time in the total time fund of its equipment, which is characterized by the value of the coefficient of extensive equipment use

Ensuring economic efficiency of flexible fixtures in multiproduct manufacturing

The first-priority directions for modern engineering, especially for multiproduct manufacturing, include the intensification of manufacturing processes, increasing the efficiency of technological equipment, and reducing the time required to implement technological solutions. Fixture design is a complicated and time-consuming process that requires considering many parameters of the closed-loop technological system “machine tool — fixture — cutting tool — workpiece”. One machined part can have several fixture layouts corresponding to all specified parameters; however, their effectiveness differs depending on production conditions. Search for an optimal fixture for specified production conditions is an essential stage of production planning. It has been proved that the efficiency of a manufacturing process should be assessed using single economic indicator — the cost of machining, which considers the costs of time, the total costs for process realisation, and a batch of parts. The paper aims to substantiate the efficiency of manufacturing processes in machining complex parts using flexible fixtures by developing a mathematical model that considers the cost of time, the cost of implementing the manufacturing process, and the batch value of parts production. This approach estimates the efficiency of manufacturing processes for machining complex parts and choosing the flexible fixture layout that corresponds to specific production conditions. It was proved that flexible fixtures could be effectively used for machining small batches of parts with frequent readjustments to new workpieces and short-term machining. A tendency has been established that the higher number of nomenclature of parts contributes to expanding the scope of the effective use of flexible fixtures.

CVP-analysis in the conditions of multiproduct manufacturing as a tool of operational controlling

CVP-analysis in the conditions of multiproduct manufacturing as a tool of operational controlling The peculiarities of CVP analysis in conditions of multiproduct manufacturing are revealed, comparing methods of its implementation are carried out. The possibilities of application the results of analysis when making managerial decisions in the operating system are determined. The problem of distribution of general constant retained expenses on separate types of products by various methods, as well as the definition of a break-free level of production and realization of certain types of products based on weighted average margin profits, are investigated. The impact on the profit of changing the level of constant costs and specific variables of expenses through an operating lever within the production enterprise is investigated. Keywords: CVP analysis, variable costs, fixed costs, marginal profit, break-even point, operational analysis, operational controlingl.

Incorporating Outsourcing Strategy and Quality Assurance into a Multiproduct Manufacturer–Retailer Coordination Replenishing Decision

This study explores the multiproduct manufacturer-retailer coordination replenishing decision featuring outsourcing strategy and product quality assurance. Globalization has generated enormous opportunities. Consequently, transnational firms now face tough competition in global markets. To stay competitive, a firm should meet the client’s multi-item and quality requirements under capacity constraints and optimize the intra-supply chain system to allow the timely distribution of finished goods under minimum system cost. The outsourcing option is considered to release machine loadings and reduce cycle time effectively. All items fabricated are screened for quality, and reworkable and scrap items are separated. Any reworked items that fail the quality reassurance screening are discarded, whereas all outsourced products are quality-guaranteed by the provider. A fixed-quantity multi-shipment plan is used when the whole finished lot is quality-ensured to help present-day transnational firms gain competitive advantage by making efficient and cost-effective multiproduct manufacturing and delivering decisions. Mathematical modeling is built to portray the system’s characteristics, and conventional differential calculus is used to solve and derive the optimal operating policy for the proposed problem. Simultaneously, we find the optimal delivery frequency and common cycle time for the problem mentioned above. A simulated numerical example and sensitivity analysis demonstrate the research result’s capability and applicability. Our precise analytical model can reveal/highlight the impact of deviations in quality- and outsourcing-related features on the optimal operating policy and several performance indicators that help managerial decision-making.

The Collective Influence of Component Commonality, Adjustable-Rate, Postponement, and Rework on Multi-Item Manufacturing Decision

The present study explores the collective influence of component commonality, adjustable-rate, postponement, and rework on the multi-item manufacturing decision. In contemporary markets, customer demand trends point to fast-response, high-quality, and diversified merchandise. Hence, to meet customer expectations, modern manufacturers must plan their multiproduct fabrication schedule in the most efficient and cost-saving way, especially when product commonality exists in a series of end products. To respond to the above viewpoints, we propose a two-stage multiproduct manufacturing scheme, featuring an adjustable fabrication rate in stage one for all needed common parts, and manufacturing diversified finished goods in stage two. The rework processes are used in both stages to repair the inevitable, nonconforming items and ensure the desired product quality. We derive the cost-minimized rotation cycle decision through modeling, formulation, cost analysis, and differential calculus. Using a numerical illustration, we reveal the collective and individual influence of adjustable-rate, rework, and postponement strategies on diverse critical system performances (such as uptime of the common part and/or end products, utilization, individual cost factor, and total system cost). Our decision-support model offers in-depth managerial insights for manufacturing and operations planning in a wide variety of contemporary industries, such as household merchandise, clothing, and automotive.

Technological Assurance of Manufacturing Effectiveness on CNC Machining Centers

The chapter is devoted to the solving of the problem of increasing the efficiency of lever-type parts machining due to the introduction of flexible fixtures ensuring multi-axis machining. The relationship between the design and technological parameters of the parts were discovered, which is the fundamentals for the analysis of parts and the search for the fixture layout for the given production conditions. An innovative approach to the design of technological processes for lever-type parts machining is proposed, which is based on the principle of intensification of machining processes, design and technological features of the parts, functional and technological capabilities of modern metal-cutting machine tools. A mathematical model of machining accuracy of parts depending on the level of fixture flexibility is obtained. It is analytically and experimentally proved the feasibility of using flexible fixtures for multi-axis machining of lever-type parts in multiproduct manufacturing.