Production and changeover control policies of a class of failure prone buffered flow-shops

This article deals with a stochastic optimal control problem for a class of buffered multi-parts flow-shops manufacturing system. The involved machines are subject to random breakdowns and repairs. The flow-shop under consideration is not completely flexible and hence requires setup time and cost in order to switch the production from a part type to another, this changeover is carried on the whole line. Our objective is to find the production plan and the sequence of setups that minimise the cost function, which penalises inventories/backlogs and setups. A continuous dynamic programming formulation of the problem is presented. Then, a numerical scheme is adopted to solve the obtained optimality conditions equations for a two buffered serial machines two parts case. A complete heuristic policy, based on the numerical observations which describe the optimal policies in system states, is developed. It will be shown that the obtained policy is a combination of a KANBAN/CONWIP and a modified hedging corridor policy. Moreover, based on our observations and existent research studies extension to cover more complex flow-shops is henceforth possible. The robustness of such a policy is illustrated through sensitivity analysis.     

Energy-oriented bi-objective optimization for the tempered glass scheduling

This paper investigates a real life bi-objective hybrid flow shop scheduling problem in an energy-intensive manufacturing system, in which glass is produced successively in cutting, printing and tempering stages. The problem aims to simultaneously optimize makespan and the total electricity cost under a time-of-use electricity pricing policy. The glass production has to respect the following environments: (i) the cutting and printing operations are processed in parallel machine environments; (ii) the tempering operation is processed on a batch machine; (iii) machine eligibility and setup time have to be considered in the cutting and printing stages; (iv) the whole manufacturing system is under a time-of-use electricity pricing policy. For the problem, an integer programming model is firstly proposed and shown to be strongly NP-hard. Then a model-based heuristic is adopted and a bi-objective differential evolution algorithm (BODE) is devised based on problem features. Computational experiments on randomly generated instances demonstrated that the BODE outperforms the model-based heuristic in terms of computation time and solution quality. Moreover, with mild increase on computation burden, the BODE significantly outperforms the classic NSGA II in terms of solution quality.     

Acquisition Management Under Fluctuating Raw Material Prices

We study a continuous‐review acquisition problem, in which the raw material price follows a discrete‐state Markov process and demand is compound Poisson. We show that one optimal policy is of the order‐up‐to type. Under our mean reversion and time continuity conditions, we further show that the order‐up‐to levels are decreasing at the current price level. At the same time, our computational study verifies that both conditions are indispensable for the monotonicity result. The study also hints at the connection between discrete‐ and continuous‐state price processes.     

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent (s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.     

O(m2) ALGORITHMS FOR THE TWO AND THREE SUBLOT LOT STREAMING PROBLEM

Lot streaming is the process of splitting a job or lot into sublots to reduce its makespan on a sequence of machines. The goal in the lot streaming problem is to find the optimal size of each sublot that will minimize the makespan. The makespan is defined as the time the last sublot completes its processing on the last machine. If the sizes of these sublots are restricted to remain the same on all machines, the solution is called a consistent sublot solution. However, if the sizes of the sublots are allowed to vary, the solution is referred to as a nonconsistent or variable sublot solution. Also, if the machines must be in operation continuously from the first to the last sublot, the solution is a no idling solution. When setups are explicitly considered in the problem, there will be two cases. If setups on each machine require some portion of the first sublot be present by the machine, the problem is referred to as the attached setup time problem. If setups can be performed ahead of time before the first sublot reaches the particular machine, the corresponding problem is referred to as the detached setup problem. Finally, if the machines are allowed to be idle between the processing of sublots, the resultant solution is an intermittent idling solution. In this paper, the consistent sublot lot streaming problem with intermittent idling and no setups is discussed. The models developed also assume that the number of sublots are fixed and known. The m machine two sublot lot streaming problem is reviewed. An algorithm for the three sublot, m machine problem is derived using a network representation of the problem. The complexity of the algorithm is O (m²). Finally, using the insights from three sublot problem, a heuristic algorithm is provided for the m machine, n sublot problems. The results on the proposed heuristic are very encouraging; average percent deviation from optimal makespan is approximately at 0.76% on 155 randomly generated problems with different m and n values.     

PRODUCTION FLOW CONTROL FOR A MANUFACTURING SYSTEM WITH FLEXIBLE ROUTINGS

We study the dynamic routing problem for a flexible manufacturing system consisting of two unreliable machines and a finite buffer. One product-type is produced which requires two operations in sequence. The demand rate is assumed to be constant. Each machine is capable of performing both operations. The objective is to trace the demand while keeping the work-in-process low and the cycle-time short. An optimal control formulation is established for the dynamic routing problem. A production flow control algorithm is developed based on a combination of mathematical modeling and heuristics. The control policy is simulated and a comparison with the numerical optimal solution shows that it performs well for the instances under consideration.     

CAPACITY AND PRODUCTION DECISIONS IN STOCHASTIC MANUFACTURING SYSTEMS: AN ASYMPTOTIC OPTIMAL HIERARCHICAL APPROACH

We present a new paradigm of hierarchical decision making in production planning and capacity expansion problems under uncertainty. We show that under reasonable assumptions, the strategic level management can base the capacity decision on aggregated information from the shopfloor, and the operational level management, given this decision, can derive a production plan for the system, without too large a loss in optimality when compared to simultaneous determination of optimal capacity and production decisions. The results are obtained via an asymptotic analysis of a manufacturing system with convex costs, constant demand, and with machines subject to random breakdown and repair. The decision variables are purchase time of a new machine at a given fixed cost and production plans before and after the purchase. The objective is to minimize the discounted costs of investment, production, inventories, and backlogs. If the rate of change in machine states such as up and down is assumed to be much larger than the rate of discounting costs, one obtains a simpler limiting problem in which the random capacity is replaced by its mean. We develop methods for constructing asymptotically optimal decisions for the original problem from the optimal decisions for the limiting problem. We obtain error estimates for these constructed decisions.     

Inventory Rationing for Multiple Class Demand under Continuous Review

We consider how a firm should ration inventory to multiple classes in a stochastic demand environment with partial, class‐dependent backlogging where the firm incurs a fixed setup cost when ordering from its supplier. We present an infinite‐horizon, average cost criterion Markov decision problem formulation for the case with zero lead times. We provide an algorithm that determines the optimal rationing policy, and show how to find the optimal base‐stock reorder policy. Numerical studies indicate that the optimal policy is similar to that given by the equivalent deterministic problem and relies on tracking both the current inventory and the rate that backorder costs are accumulating. Our study of the case of non‐zero lead time shows that a heuristic combining the optimal, zero lead time policy with an allocation policy based on a single‐period profit management problem is effective.     

Revenue Management Through Dynamic Cross Selling in Call Centers

This paper models the cross‐selling problem of a call center as a dynamic service rate control problem. The question of when and to whom to cross sell is explored using this model. The analysis shows that, under the optimal policies, cross‐selling targets may be a function of the operational system state. Sufficient conditions are established for the existence of preferred calls, i.e., calls that will always generate a cross‐sell attempt. These provide guidelines in segment formation for marketing managers, and lead to a static heuristic policy. Numerical analysis establishes the value of different types of information, and different types of automation available for cross selling. Increased staffing for the same call volume is shown to have a positive and increasing return on revenue generation via cross selling, suggesting the need to staff for lower loads in call centers that aim to be revenue generators. The proposed heuristic leads to near optimal performance in a wide range of settings.     

Sequential Search and Selection Problem Under Uncertainty

This paper formulates and discusses a series of sequential decision problems of the following common structure: A decision alternative of multiple attributes‐that is, a job, an employee, or an investment alternative‐is to be selected within a certain fixed length of time. An unknown number of alternatives are presented sequentially, either deterministically or in a random manner. The decision maker can rank all the alternatives from best to worst without ties, and the decision to accept or reject an alternative is based solely on the relative ranks of those alternatives evaluated so far. The nonparametric sequential decision problem is first studied for a model involving a discrete time period and then generalized in terms of continuous time. Also considered is a variant of this problem involving a Bayesian estimation of (1) the uncertain probability of having an alternative at a given stage in the discrete‐time model and (2) the arrival rate of alternatives in the continuous‐time model. The optimal selection strategy that maximizes the probability of selecting the absolute best alternative is illustrated with the job search problem and the single‐machine job assignment problem.     

Single machine group scheduling to minimize mean flow time subject to due date constraints

This paper considers a single machine group scheduling problem. All jobs are classified into groups and the jobs within a group are processed contiguously on the machine. A sequence-independent setup time is incurred between each two consecutively scheduled groups. This paper presents a solution procedure which utilizes Smith's algorithm and a proposed modified Smith's algorithm to find an optimal job sequence and an optimal group sequence which minimizes the mean flow time of jobs subject to the constraint that no jobs are tardy. The complexity of the algorithm is shown to have a polynomial running time in the number of groups and jobs.     

Experimental Results Indicating Lattice‐Dependent Policies May Be Optimal for General Assemble‐To‐Order Systems

We consider an assemble‐to‐order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite‐horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice‐dependent base‐stock and lattice‐dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M‐system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state‐dependent base‐stock and state‐dependent rationing (SBSR) policy, and a fixed base‐stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.     

Scheduling in an assembly-type production chain with batch transfer

This paper addresses a three-machine assembly-type flowshop scheduling problem, which frequently arises from manufacturing process management as well as from supply chain management. Machines one and two are arranged in parallel for producing component parts individually, and machine three is an assembly line arranged as the second stage of a flowshop for processing the component parts in batches. Whenever a batch is formed on the second-stage machine, a constant setup time is required. The objective is to minimize the makespan. In this study we establish the strong NP-hardness of the problem for the case where all the jobs have the same processing time on the second-stage machine. We then explore a useful property, based upon which a special case can be optimally solved in polynomial time. We also study several heuristic algorithms to generate quality approximate solutions for the general problem. Computational experiments are conducted to evaluate the effectiveness of the algorithms.     

A Single‐Period Assortment Optimization Model

This paper studies a single‐period assortment optimization problem with unequal cost parameters. The consumer choice process is characterized by a Multinomial Logit (MNL) model. When the store traffic is a continuous random variable, we explicitly derive the structure of the optimal assortment. Our approach is to use a comprehensive measure–profit rate to evaluate the profitability of each variant and then determine which product should be offered. We demonstrate that the optimal assortment contains the few items that have the highest profit rate. When the store traffic is discrete, the optimal solution is difficult to obtain. We propose a “profit rate” heuristic, which is inspired by the result for the case of continuous store traffic. In a special case with equal cost parameters and normal demand distribution, the profit rate heuristic is indeed optimal. Using randomly generated data, we test the effectiveness of the heuristic and find that the average percentage error is less than 0.1% and that the hit rate is above 90%. Our research provides managerial insights on assortment planning and accentuates the importance of measuring the profitability of each product when the demand is random and cannibalization among different products exists.     

INFLATION STABILIZATION AND WELFARE: THE CASE OF A DISTORTED STEADY STATE

This paper considers the appropriate stabilization objectives for monetary policy in a micro‐founded model with staggered price‐setting. Rotemberg and Woodford (1997) and Woodford (2002) have shown that under certain conditions, a local approximation to the expected utility of the representative household in a model of this kind is related inversely to the expected discounted value of a conventional quadratic loss function, in which each period's loss is a weighted average of squared deviations of inflation and an output gap measure from their optimal values (zero). However, those derivations rely on an assumption of the existence of an output or employment subsidy that offsets the distortion due to the market power of monopolistically competitive price‐setters, so that the steady state under a zero‐inflation policy involves an efficient level of output. Here we show how to dispense with this unappealing assumption, so that a valid linear‐quadratic approximation to the optimal policy problem is possible even when the steady state is distorted to an arbitrary extent (allowing for tax distortions as well as market power), and when, as a consequence, it is necessary to take account of the effects of stabilization policy on the average level of output. We again obtain a welfare‐theoretic loss function that involves both inflation and an appropriately defined output gap, though the degree of distortion of the steady state affects both the weights on the two stabilization objectives and the definition of the welfare‐relevant output gap. In the light of these results, we reconsider the conditions under which complete price stability is optimal, and find that they are more restrictive in the case of a distorted steady state. We also consider the conditions under which pure randomization of monetary policy can be welfare‐improving, and find that this is possible in the case of a sufficiently distorted steady state, though the parameter values required are probably not empirically realistic. (JEL: D61, E52, E61)     

UNINSURED COUNTERCYCLICAL RISK: AN AGGREGATION RESULT AND APPLICATION TO OPTIMAL MONETARY POLICY

We consider an incomplete markets economy with capital accumulation and endogenous labor supply. Individuals face countercyclical idiosyncratic labor and asset risk. We derive conditions under which the aggregate allocations and price system can be found by solving a representative agent problem. This result is applied to analyze the properties of an optimal monetary policy in a New Keynesian economy with uninsured countercyclical individual risk. The optimal monetary policy that emerges from our incomplete markets economy is the same as the optimal monetary policy in a representative agent model with preference shocks. When price rigidity is the only friction the optimal monetary policy calls for stabilizing the inflation rate at zero.     

EFFECTS OF RANDOM SHIFTS OF TESTING EQUIPMENT ON PROCESS CONTROL SYSTEM DESIGN AND SELECTION OF PROCESS CONTROL POLICIES*

This paper studies issues associated with designing process control systems when the testing equipment is subjected to random shifts. We consider a production process with two states: in control and out of control. The process may shift randomly to the out‐of‐control state over time. The process is monitored by periodically sampling finished items from the process. The equipment used to test sampled items also is assumed to have two states and may shift randomly during the testing process. We formulate a cost model for finding the optimal process control policy that minimizes the expected unit time cost. Numerical results show that shifts of the testing equipment may significantly affect the performance of a process control policy. We also studied the effects of the testing equipment's shifts on the selection of process control policies.     

Managing a Remanufacturing System with Random Yield: Properties,Observations, and Heuristics

We study a remanufacturing system that involves the ordering of a serviceable product and the remanufacturing of multiple types of returned products (cores) into the serviceable product. In addition to random demand for the serviceable product and random returned quantities of different types of cores in each time period, the remanufacturing yield of each type of core is also uncertain. By analyzing a multi‐period stochastic dynamic program, we derive several properties of the optimal ordering/remanufacturing policy. In addition to some insights, these properties can be used to reduce the search effort of the optimal policy. We also demonstrate that some existing results derived from related models no longer hold in remanufacturing systems with random yield. Recognizing the optimal ordering/remanufacturing policy is highly complex, we examine three simple heuristics that can be efficiently solved and implemented in practice. Among these three heuristics, our numerical analysis suggests that the heuristic that captures most of the yield uncertainty and future system evolvement as well as some of the properties of the optimal ordering/remanufacturing policy outperforms the other two heuristics.     

Managing appointments with waiting time targets and random walk-ins

The random arrivals of walk-in patients significantly affect the daily operations of healthcare facilities. To improve the performance of outpatient departments, this paper attempts to make an appointment schedule by considering walk-ins and the waiting time target (WTT) for appointment patients. A stochastic programming model is proposed to solve this problem with the objective of minimizing the weighted patient waiting and makespan cost. A non-decreasing waiting cost function is used to capture the WTT fulfillment of appointment patients, whereas walk-ins incur a linear waiting cost. A finite-horizon Markov Decision Process model is formulated to establish the optimal real-time scheduling policy under a given appointment schedule. The appointment schedule is determined by a two-stage stochastic programming approximation and a local search improvement. Structural properties of the optimal appointment scheduling and real-time scheduling policies are established. In particular, it is shown that appointment overbooking is allowed only at the end of the regular session, and the optimal real-time scheduling policy is an easy-to-implement threshold policy with bounded sensitivity. Numerical experiments based on real data are performed to investigate the influence of different parameters and to compare different schedules. The optimal schedule demonstrates superior performance by allowing reasonable waiting times for appointment patients depending on their WTTs. Managerial insights are also provided to hospital managers. Finally, the basic model is extended by incorporating random service times and random arrivals of appointment patients. The latter includes the random number of patients that show up for service or call for appointments, and the random arrival time (unpunctuality). Appointment overbooking strategies are shown to have different structures under some stochastic factors.     

A note on a well-known dispatching rule to minimize total tardiness

The single machine tardiness problem is considered. We clarify and correct an earlier result related to the Modified Due Date (MDD) Rule of Baker and Bertrand and show that a heuristic does not always satisfy an optimal sequence. However, we present some interesting special cases of optimal sequences that do satisfy the MDD Rule. We believe this note is important because the MDD Rule is still considered to be one of the most efficient rules to minimize the single machine tardiness problem. Because of its dispatching nature and simplicity, the MDD Rule is found to be very practical. It is widely applied in both static and dynamic job shop and industrial settings where setup times if any are negligible or included in the job processing times and hence not an issue.