Applying possibilistic linear programming to aggregate production planning

This work presents a novel interactive possibilistic linear programming (PLP) approach for solving the multi-product aggregate production planning (APP) problem with imprecise forecast demand, related operating costs, and capacity. The proposed approach attempts to minimize total costs with reference to inventory levels, labor levels, overtime, subcontracting and backordering levels, and labor, machine and warehouse capacity. The proposed approach uses the strategy of simultaneously minimizing the most possible value of the imprecise total costs, maximizing the possibility of obtaining lower total costs, and minimizing the risk of obtaining higher total costs. An industrial case demonstrates the feasibility of applying the proposed approach to real APP decision problems. Consequently, the proposed PLP approach yields an efficient APP compromise solution and overall degree of decision maker (DM) satisfaction with determined goal values. Particularly, several significant management implications and characteristics of the proposed PLP approach that distinguish it from the other APP decision models are presented.     

Reliability evaluation and adjustment of supply chain network design with demand fluctuations

This study focuses on supply chain network design problems by considering economies of scale and demand fluctuations. A reliability evaluation method is developed to evaluate the performance of plants under demand fluctuations. In addition, two mathematical programming models are developed to determine the optimal adjustment decisions regarding production reallocation among plants under different fluctuating demands. The judgments to adjust or to do-nothing are investigated by comparing the results if the adjustment is made or not made. Results show that making adjustments benefits the manufacturers by reducing total production cost and avoiding revenue loss, which outweighs the extra costs, especially for high value-added products. Results also suggest that the manufacturer should ignore a short period abnormal state, since the benefits to respond to it might not compensate the high allocation costs. The results of this study provide a reference for the manufacturer in their decision making process of network planning with demand fluctuations, when they have to cope with benefits and costs during abnormal states.     

Capacity flexibility allocation in an outsourced supply chain with reservation

We consider a contract manufacturer that serves a limited number of outsourcers (customers) on a single capacitated production line. The outsourcers have different levels of demand uncertainty and the contract manufacturer faces the question how to allocate the contractual capacity flexibility in an optimal way. The contractual capacity flexibility is a contract parameter that sets the amount of demand the contract manufacturer is obliged to accept from the outsourcers. We develop a hierarchical model that consists of two decision levels. At the tactical level, the contract manufacturer allocates the capacity flexibility to the different outsourcers by maximizing the expected profit. Offering more flexibility to the more uncertain outsourcer generates higher expected revenue, but also increases the expected penalty costs. The allocated capacity flexibilities (determined at the tactical level) are input parameters to the lower decision level, where the operational planning decisions are made and actual demands are observed. We perform a numerical study by solving the two-level hierarchical planning problem iteratively. We first solve the higher level problem, which has been formulated as an integer program, and then perform a simulation study, where we solve a mathematical programming model in a rolling horizon setting to measure the operational performance of the system. The simulation results reveal that when the acceptance decision is made (given the allocated capacity flexibility decision), priority is given to the less uncertain outsourcer, whereas when the orders are placed, priority is given to the most uncertain outsourcer. Our insights are helpful for contract manufacturers when having contract negotiations with the outsourcers. Moreover, we show that hierarchical integration and anticipation are required, especially for cases with high penalty cost and tight capacities.     

Integrating noncyclical preventive maintenance scheduling and production planning for a single machine

This paper deals with the problem of integrating noncyclical preventive maintenance and tactical production planning for a single machine. We are given a set of products that must be produced in lots during a specified finite planning horizon. The maintenance policy suggests possible preventive replacements at the beginning of each production planning period, and minimal repair at machine failure. The proposed model determines simultaneously the optimal production plan and the instants of preventive maintenance actions. The objective is to minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. The problem is solved by comparing the results of several multi-product capacitated lot-sizing problems. The value of the integration and that of using noncyclical preventive maintenance when the demand varies from one period to another are illustrated through a numerical example and validated by a design of experiment. The later has shown that the integration of maintenance and production planning can reduce the total maintenance and production cost and the removal of periodicity constraint is directly affected by the demand fluctuation and can also reduce the total maintenance and production cost.     

Competition under capacitated dynamic lot-sizing with capacity acquisition

Lot-sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot-sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies of scale arising from dynamic lot-sizing costs is developed. Each firm can replenish inventory at the beginning of each period in a finite planning horizon. Fixed as well as variable production costs incur for each production setup, along with inventory carrying costs. The individual production lots of each firm are limited by a constant capacity restriction, which is purchased up front for the planning horizon. The capacity can be purchased from a spot market, and the capacity acquisition cost fluctuates with the total capacity demand of all the competing firms. We solve the competition model and establish the existence of a capacity equilibrium over the firms and the associated optimal dynamic lot-sizing plan for each firm under mild conditions.     

Lot sizes in a capacity constrained facility—a simulation study of stationary stochastic demand

This paper considers the scheduling of several different items on a single machine, in literature known as the economic lot scheduling problem, ELSP. One of the characteristics of this problem is that the demand rate is deterministic and constant. However, in a practical situation demand usually varies. In this paper we examine if a deterministic model can be used if demand is stationary stochastic. A dynamic programming approach from Bomberger (Manage. Sci. 12(11) (1966) 778) and a heuristic method from Segerstedt (Int. J. Production Econom. 59(1–3) (1999) 469) are used to calculate lot sizes for four items. The production of these items is simulated with different variations in demand rates. Our conclusion is that a deterministic model of this kind can be used in a practical situation where the demand rate is stationary stochastic, but the models must be complemented by a decision rule; which item to produce and when to produce it. In our tests the heuristic method and the dynamic programming approach perform rather similarly with respect to costs and inventory levels, but the dynamic programming approach results in more backorders when there is small variation in demand rates. This study indicates that the model used for determination of lot sizes is of less importance than the decision rule used for identification of the item to produce and when to produce it.     

Coordinated capacity migration and expansion planning for semiconductor manufacturing under demand uncertainties

Semiconductor industry is very capital intensive in which capacity utilization significantly affect the capital effectiveness and profitability of semiconductor manufacturing companies. Due to constant technology advance driven by Moore's Law in semiconductor industry, multiple production technologies generally co-exist in a wafer fabrication facility with utilization of a pool of common tools for multiple technologies and critical tools dedicated for a specific technology. Because part of the equipment is common for products of different technologies, production managers have limited flexibility to dynamically allocate the capacity among the technologies via capacity migration. The possibility of capacity migration and interrelationship among different technologies make capacity planning difficult under demand and product-mix uncertainties.This paper aims to develop a dynamic optimization method that captures the unique characteristics of rolling demand forecast mechanism to solve capacity expansion and migration planning problems in semiconductor industry. In semiconductor industry, demand forecasts are rolling and updated when the latest market and demand information is available. This demand forecast mechanism makes forecast errors in different time periods correlated. We estimate the validity and robustness of the proposed dynamic optimization method in an empirical study in a semiconductor manufacturing company in Taiwan. The results showed practical viability of this approach and the findings can provide useful guidelines for capacity planning process under rolling forecast mechanism.     

A local search algorithm for the optimization of the stochastic economic lot scheduling problem

This paper describes a model for the stochastic economic lot scheduling problem (SELSP) and a Local Search heuristic to find close to optimal solutions to this model. The SELSP considers multiple products, which have to be scheduled on a single facility with limited capacity and significant setup times and costs. The demand is modeled as a stationary compound renewal process. The objective is to find a schedule that minimizes the long-run average costs for setups and inventories while satisfying a given fill rate. We use a cyclic scheduling approach in which the individual cycle time of each product is a multiple of some basic period (fundamental cycle).For the deterministic version of the SELSP, efficient heuristics have been developed which guarantee the feasibility of the solution by adding an additional constraint to the problem. In our case this is not sufficient, because for the calculation of the average inventory levels and fill rates we need to develop a schedule with detailed timing of the lots. We present an efficient heuristic for this scheduling problem, which can also be used to check the feasibility of the solution. Thereby, the most time-consuming step (the calculation of average inventory levels and fill rates) is only performed for a limited set of candidates.The algorithm was tested on deterministic benchmark problems from literature and on a large set of stochastic instances. We report on the performance of the heuristic in both cases and try to identify the main factors influencing the objective.     

Coordinated supply chain scheduling

A mixed integer programming approach is proposed for a long-term, integrated scheduling of material manufacturing, material supply and product assembly in a customer driven supply chain. The supply chain consists of three distinct stages: manufacturer/supplier of product-specific materials (parts), producer where finished products are assembled according to customer orders and a set of customers who generate final demand for the products. The manufacturing stage consists of identical production lines in parallel and the producer stage is a flexible assembly line. The overall problem is how to coordinate manufacturing and supply of parts and assembly of products such that the total supply chain inventory holding cost and the production line start-up and parts shipping costs are minimized. A monolithic approach, where the manufacturing, supply and assembly schedules are determined simultaneously, is compared with a hierarchical approach. Numerical examples modeled after a real-world integrated scheduling in a customer driven supply chain in the electronics industry are presented and some computational results are reported.     

Cement transportation planning via fuzzy linear programming

The mining of more than ten million tons of limestone for cement production in western Taiwan will be prohibited by the end of 1997 and hence almost half of the cement production will move toward eastern Taiwan. Since the supply and demand will be separated by the Central Ridge, the planning of transportation networks and facilities for limestone and cement appears urgent. This research resolves the cement transportation planning problem using fuzzy linear programming methods. Three types of fuzzy linear programming models are used to determine the optimal transportation amount and the capacity of new facilities. The emphasis is also on how to formulate a transportation planning problem where the port capacity, demand fulfillment, trans-shipping operation capacity and traffic congestion constraints are included.     

Optimal Capacity,Product Substitution,Linear Demand Models,and Uncertainty

We study the capacity, pricing, and production decisions of a monopolist producing two substitutable products with flexible capacity. Although the capacity decision needs to be made ex ante, under demand uncertainty, pricing and production decisions can be postponed until after uncertainty is resolved. We show how key demand parameters (the nature of uncertainty, market size, and market risk) impact the optimal capacity decision under the linear demand function. In particular, we show that if the demand shock is multiplicative, then in terms of the “invest or not” decision, the firm will be immune to forecast errors in parameters of the underlying demand distribution. Furthermore, incorrectly modeling the demand shock as additive, when, in fact, it is multiplicative, may lead to overinvestment. On the other hand, although the concept of a growth in market size leads to similar conclusions under both additive and multiplicative demand shocks, how market risk affects the optimal capacity decision depends critically on the form of the demand shock as well as its correlation structure. Our analysis provides insights and principles on the optimal capacity investment decision under various demand settings.     

A hierarchical process industry production–distribution planning model

Global and multinational companies are subject to government regulations in addition to other international uncertainties due to operation in diverse geographic locations. Such government regulations often affect the cost of raw materials adversely which in turn creates adverse impact on product cost and forces the decision makers to re-evaluate current production–distribution plan. This paper presents an integrated supply chain model for simultaneous strategic and operational planning of a strategic business unit (SBU) in a global supply chain affected by government regulations. The model incorporates impact of changes in cost of inputs on expected product cost and solves for an optimal strategic and operational plan for the entire supply chain. In addition, the model includes exchange rates, border crossing costs and solves a multi-period model with due consideration of uncertainties in demand and transportation time.     

A memetic algorithm for a multistage capacitated lot-sizing problem

We present a heuristic approach to solve a complex problem in production planning, the multistage lot-sizing problem with capacity constraints. It consists of determining the quantity to be produced in different periods in a planning horizon, such that an initially given demand forecast can be attained. We consider setup costs and setup times. Due the complexity to solve this problem, we developed methods based on evolutionary metaheuristics, more specifically a memetic algorithm. The proposed heuristics are evaluated using randomly generated instances and well-known examples in the literature.     

Dynamic lot sizing problem with continuous-time Markovian production cost

This paper develops a polynomial algorithm for obtaining dynamic economic lot sizes in a single product multiperiod production system with the objective of minimizing total production and inventory costs over T periods. It is assumed that production costs are linear, inventory costs are concave, setup costs are zero and backlogging is not permitted in all periods. Moreover, the unit production cost is a stochastic variable, which is evolved according to a continuous-time Markov process over the planning horizon. The model is formulated as a stochastic dynamic programming (DP) optimization with the state variable being unit production cost. Then, it is solved using the backward dynamic programming approach. To justify the application of the proposed model, two practical cases are presented.     

Development of a Network-location-model for the Economic Optimization of Local Heating Systems in Urban Chile

Cogeneration of heat and electricity is an important pillar of energy and climate policy. To plan the production and distribution system of combined heat and power (CHP) systems for residential heating, suitable methods for decision support are needed. For a comprehensive feasibility analysis, the integration of the location and capacity planning of the power plants, the choice of customers, and the network planning of the heating network into one optimization model are necessary. Thus, we develop an optimization model for electricity generation and heat supply. This mixed integer linear program (MILP) is based on graph theory for network flow problems. We apply the network location model for the optimization of district heating systems in the City of Osorno in Chile, which exhibits the “checkerboard layout” typically found in many South American cities. The network location model can support the strategic planning of investments in renewable energy projects because it permits the analysis of changing energy prices, calculation of break-even prices for heat and electricity, and estimation of greenhouse gas emission savings.     

Supply optimization for the production of raw sugar

Based on a case study from Venezuela, the production of raw sugar is investigated. Ideally, sugar mills operate at a constant production rate. However, safety stocks of the raw material cannot be maintained as sugar cane quality deteriorates very rapidly. Sugar cane is therefore continuously sourced in diverse quantities and qualities from hundreds of geographically dispersed haciendas and supplied to the milling process. Furthermore, due to weather conditions changing throughout the year, tight time windows must be observed for harvesting.The approach presented in this paper aims at preserving a constant supply while minimizing the associated costs. The entire planning problem is structured in a hierarchical fashion: (1) cultivation of the haciendas, (2) harvesting, and (3) dispatching of the harvesting crews and equipment. The corresponding optimization models and solution procedures are introduced and applied to the case study problem.     

Production planning of a hybrid manufacturing-remanufacturing system under uncertainty within a closed-loop supply chain

This paper deals with the production planning and control of a single product involving combined manufacturing and remanufacturing operations within a closed-loop reverse logistics network with machines subject to random failures and repairs. While consumers traditionally dispose of products at the end of their life cycle, recovery of the used products may be economically more attractive than disposal, while remanufacturing of the products also pursues sustainable development goals. Three types of inventories are involved in this network. The manufactured and remanufactured items are stored in the first and second inventories. The returned products are collected in the third inventory and then remanufactured or disposed of. The objective of this research is to propose a manufacturing/remanufacturing policy that would minimize the sum of the holding and backlog costs for manufacturing and remanufacturing products. The decision variables are the production rates of the manufacturing and the remanufacturing machines. The optimality conditions are developed using the optimal control theory based on stochastic dynamic programming. A computational algorithm, based on numerical methods, is used for solving the optimal control problem. Finally, a numerical example and a sensitivity analysis are presented to illustrate the usefulness of the proposed approach. The structure of the optimal control policy is discussed depending on the value of costs and parameters and extensions to more complex reverse logistics networks are discussed.     

Production lot sizing with a secondary outsourcing facility

An extended economic production quantity (EPQ) model under stochastic demand is investigated in this paper, where a fixed lot sizing policy is implemented to reduce the complexity of production planning and inventory control, and outsourcing with a secondary facility is used to supplement the lot sizing policy and to cope with the random demand. The considered cost includes: setup cost for the batch production, inventory carrying cost, backorder cost when the demand cannot be met immediately during the production period, and outsourcing cost when the total demand is greater than the lot size in one replenishment cycle. Under some mild conditions, the expected cost per unit time can be shown to be convex. Extensive computational tests have illustrated that the average cost reduction of the proposed model is significant when compared with that of the classical lot sizing policy. Significant cost savings can be achieved by deploying the production lot sizing policy with an outsourcing strategy when the mean demand rate is high.     

TECHNIQUES OF TRANSPORT PLANNING by John R. Meyer,Editor

This case study is an evaluation of actual alternatives for capacity expansion of an electrical power company. A systematic analysis of the important parameters of this complex problem is described to illustrate how multiple attribute decision analysis can be utilized to include the monetary and nonmonetary aspects of such a real world capacity expansion problem. The service cost data utilized is the type generated routinely by utilities and/or regulatory staffs. However, the use of outage costs and socio-economic coats demonstrates that the readily available service coats data can be expanded and combined into a framework that allows a more detailed analysis of the complex, capacity planning problem. The information reported here has been altered to the extent necessary to conceal the identity of the utility.     

Modified critical fractile approach for a class of partial postponement problems

This paper studies a single period partial postponement problem, which is motivated by an inventory planning problem encountered in Reebok NFL replica jersey supply chain. We consider a group of regular products each facing a random demand. There are two stocking options. One is to procure the regular products. The other is to stock a common component which can be customized later to any one of the regular products, after demand realization.We obtain an insightful interpretation of the optimality conditions for this class of problems, and use it to obtain rules of thumb that practitioners can incorporate into their inventory models to determine the stocking levels to minimize the supply chain cost. Instead of proposing a numerical procedure to obtain the optimal solution, we propose an adaptation of the classical critical fractile approach for this class of partial postponement problem. The closed-form formula obtained are surprisingly effective. Our numerical results suggest that this simple approach to inventory planning often comes close to the performance of the optimal solution obtained from numerical method.