Manufacturing Operations Management: A Comprehensive Guide to Production Planning and Inventory Control
Chapter 1
Purpose
The purpose of this chapter is to introduce the student to a variety of strategic issues that arise in the manufacturing function of a firm.
Key Points
1. Manufacturing matters. This writer contends that the loss of the manufacturing base in the U.S. counters the argument that our evolution into a service economy is a natural and healthy thing.
2. Strategic dimensions. Along with cost and/or product differentiation, other dimensions along which firms distinguish themselves include (a) quality, (b) delivery speed, (c) delivery reliability, and (d) flexibility.
3. Classical view. The classical literature on manufacturing strategy indicates that strategy should be viewed in relation to one or more of the following issues: (a) time horizon, (b) focus, (c) evaluation, and (d) consistency.
4. Global competition. How do we measure our success and economic health on a global scale? National competitive advantage is a consequence of several factors (factor conditions, demand conditions, related and supporting industries, firm strategy structure, and rivalry), although productivity also plays an important role.
5. Strategic initiatives. We discuss several strategic initiatives that have allowed many companies to shine in their respective arenas. These include (a) business process reengineering, (b) just-in-time manufacturing and purchasing systems, (c) time-based competition, and (d) competing on quality.
6. Product and process life cycles. Most of us understand that products have natural life cycles: start-up, rapid growth, maturation, stabilization, or decline. A firm needs to match the phases of product and process life cycles to be the most successful in its arena.
7. Learning and experience curves. These are helpful in forecasting the decline in unit cost of a manufacturing process as one gains experience with the process. Learning curves are more appropriate when modeling the learning of an individual worker, and experience curves are more appropriate when considering an entire industry.
8. Capacity growth planning. Another important strategic issue in operations is determining the timing and sizing of new capacity additions. Simple models (make or buy problem) and more complex exponential growth models are explored in Section 1.11
Chapter 2
Purpose
To present and illustrate the most important methods for forecasting demand in the context of operations planning.
Key Points
1. Characteristics of forecasts.
- They are almost always going to be wrong.
- A good forecast also gives some measure of error.
- Forecasting aggregate units is generally easier than forecasting individual units.
- Forecasts made further out into the future are less accurate.
- A forecasting technique should not be used to the exclusion of known information.
2. Subjective forecasting. Refers to methods that measure either individual or group opinion. The better known subjective forecasting methods include:
- Sales force composites.
- Customer surveys.
- Jury of executive opinion.
- The Delphi method.
3. Objective forecasting methods (time series methods and regression). Using objective forecasting methods, one makes forecasts based on past history. Time series forecasting uses only the past history of the series to be forecasted, while regression models often incorporate the past history of other series. Based on the identified pattern, different methods are appropriate. An example would be predicting the start or end of a recession based on housing starts (housing starts are considered to be a leading economic indicator of the health of the economy).
4. Evaluation of forecasting methods. The forecast error in any period, et, is the difference between the forecast for period t and the actual value of the series realized for period t (et = Ft – Dt). Three common measures of forecast error are MAD (average of the absolute errors over n periods), MSE (the average of the sum of the squared errors over n periods), and MAPE (the average of the percentage errors over n periods).
5. Methods for forecasting stationary time series. We consider two forecasting methods when the underlying pattern of the series is stationary over time: moving averages and exponential smoothing. A moving average is simply the arithmetic average of the N most recent observations. Exponential smoothing forecasts rely on a weighted average of the most recent observation and the previous forecast. The weight applied to the most recent observation is α, where 0 α α. Both methods are commonly used in practice, but the exponential smoothing method is favored in inventory control applications—especially in large systems—because it requires much less data storage than does moving averages.
6. Methods for forecasting series with trend. When there is an upward or downward linear trend in the data, two common forecasting methods are linear regression and double exponential smoothing via Holt’s method. Linear regression is used to fit a straight line to past data based on the method of least squares, and Holt’s method uses separate exponential smoothing equations to forecast the intercept and the slope of the series each period.
7. Methods for forecasting seasonal series. A seasonal time series is one that has a regular repeating pattern over the same time frame. A seasonal factor of 1.25 for a given month means that the demand in that month is 25 percent higher than the mean monthly demand. Winter’s method is a more complex method based on triple exponential smoothing. Three distinct smoothing equations are used to forecast the intercept, the slope, and the seasonal factors each period.
Chapter 3
Purpose
To develop techniques for aggregating units of production, and determining suitable production levels and workforce levels based on predicted demand for aggregate units.
Key Points
1. Aggregate units of production. This chapter could also have been called Macro Production Planning, since the purpose of aggregating units is to be able to develop a top-down plan for the entire firm or for some subset of the firm, such as a product line or a particular plant. For a service, such as provided by a consulting firm or a law firm, billed hours would be a reasonable way of expressing aggregate units.
2. Aspects of aggregate planning. The following are the most important features of aggregate planning:
Smoothing. Costs that arise from changing production and workforce levels. Planning in anticipation of peak demand periods. If too short, sudden changes in demand cannot be anticipated. If too long, demand forecasts become unreliable. All the mathematical models in this chapter consider demand to be known, i.e., have zero forecast error. 3. Costs in aggregate planning.
Smoothing costs. The cost of changing production and/or workforce levels. Holding costs. The opportunity cost of dollars invested in inventory. Shortage costs. The costs associated with back-ordered or lost demand. Labor costs. These include direct labor costs on regular time, overtime, subcontracting costs, and idle time costs.
4. Solving aggregate planning problems. When solving problems graphically, the first step is to draw a graph of the cumulative net demand curve. If the goal is to develop a level plan (i.e., one that has constant production or workforce levels over the planning horizon), then one matches the cumulative net demand curve as closely as possible with a straight line. If the goal is to develop a zero-inventory plan (i.e., one that minimizes holding and shortage costs), then one tracks the cumulative net demand curve as closely as possible each period.
5. The linear decision rule. The aggregate planning concept had its roots in the work of Holt, Modigliani, Muth, and Simon (1960) who developed a model for Pittsburgh Paints (presumably) to determine their workforce and production levels. The model used quadratic approximations for the costs, and obtained simple linear equations for the optimal policies. This work spawned the later interest in aggregate planning.
Chapter 4
Purpose
To consider methods for controlling individual item inventories when product demand is assumed to follow a known pattern (that is, demand forecast error is zero).
Key Points
1. Classification of inventories
Raw materials. These are resources required for production or processing. Components. These could be raw materials or subassemblies that will later be included into a final product. Work-in-process (WIP). These are inventories that are in the plant waiting for processing. Finished goods. These are items that have completed the production process and are waiting to be shipped out.
2. Why hold inventory?
Economies of scale. It is probably cheaper to order or produce in large batches than in small batches. Uncertainties. Demand uncertainty, lead time uncertainty, and supply uncertainty all provide reasons for holding inventory. Speculation. Inventories may be held in anticipation of a rise in their value or cost. Transportation. Refers to pipeline inventories that are in transit from one location to another. Smoothing. As noted in Chapter 3, inventories provide a means of smoothing out an irregular demand pattern. Logistics. System constraints that may require holding inventories. Control costs. Holding inventory can lower the costs necessary to monitor a system. (For example, it may be less expensive to order yearly and hold the units than to order weekly and closely monitor orders and deliveries.)3. Characteristics of inventory systems
Patterns of demand. The two patterns are (a) constant versus variable and (b) known versus uncertain. Replenishment lead times. The time between placement of an order (or initiation of production) until the order arrives (or is completed). Review times. The points in time that current inventory levels are checked. Treatment of excess demand. When demand exceeds supply, excess demand may be either backlogged or lost.
4. Relevant costs
Holding costs. These include the opportunity cost of lost investment revenue, physical storage costs, insurance, breakage and pilferage, and obsolescence. Order costs. These generally consist of two components: a fixed component and a variable component. The fixed component is incurred whenever a positive order is placed (or a production run is initiated), and the variable component is a unit cost paid for each unit ordered or produced. Penalty costs. These are incurred when demand exceeds supply. In this case excess demand may be back-ordered (to be filled at a later time) or lost. Lost demand results in lost profit, and back orders require record keeping and in both cases, one risks losing customer goodwill.
5. The basic EOQ model. It treats the basic trade-off between the fixed cost of ordering and the variable cost of holding. If h represents the holding cost per unit time and K the fixed cost of setup, then we show that the order quantity that minimizes costs per unit time is
where λ is the rate of demand. This formula is very robust for several reasons: (a) It is a very accurate approximation for the optimal order quantity when demand is uncertain (treated in Chapter 5),
6. The EOQ with finite production rate. This is an extension of the basic EOQ model to take into account that when items are produced internally rather than ordered from an outside supplier, the rate of production is finite rather than infinite, as would be required in the simple EOQ model. We show that the optimal size of a production run now follows the formula where h‘ = h(1 – λ / P) and P is the rate of production (P > λ). Note that since h‘ h, the batch size when the production rate is taken into account exceeds the batch size obtained by the EOQ formula.
7. Quantity discounts. We consider two types of quantity discounts: all-units and incremental discounts. In the case of all-units discounts, the discount is applied to all the units in the order, while in the case of incremental discounts, the discount is applied to only the units above the break point. The all-units case is by far the most common in practice, but one does encounter incremental discounts in industry. In the case of all-units discounts, the optimization procedure requires searching for the lowest point on a broken annual cost curve. In the incremental discounts case, the annual cost curve is continuous, but has discontinuous derivatives
9. EOQ models for production planning. Suppose that n distinct products are produced on a single production line or machine. Assume we know the holding costs, order costs, demand rates, and production rates for each of the items. The goal is to determine the optimal sequence to produce the items, and the optimal batch size for each of the items to meet the demand and minimize costs. The problem is handled by considering the optimal cycle time, T, where we assume we produce exactly one lot of each item each cycle. The optimal size of the production run for item j is simply Qj = λjT, where T is the optimal cycle time. Finding T is nontrivial, however.
Chapter 5
Purpose
To understand how one deals with uncertainty (randomness) in the demand when computing replenishment policies for a single inventory item.
Key Points
1. What is uncertainty and when should it be assumed? Uncertainty means that demand is a random variable. In practice, it is common to assume that demand follows a normal distribution. When demand is assumed normal, one only needs to estimate the mean, μ, and variance, σ2. What value, then, does the analysis of Chapters 3 and 4 have, where demand was assumed known? Chapter 3 focused on systematic or predictable changes in the demand pattern, such as peaks and valleys. Chapter 4 results for single items are useful if the variance of demand is low relative to the mean. In this chapter we consider items whose primary variation is due to uncertainty rather than predictable causes.
If demand is described by a random variable, it is unclear what the optimization criterion should be, since the cost function is a random variable as well. To handle this, we assume that the objective is to minimize expected costs. The law of large numbers guarantees that the arithmetic average of the incurred costs and the expected costs grow close as the number of planning periods gets large.
2. The newsboy model. Consider a news vendor that decides each morning how many papers to buy to sell during the day. Since daily demand is highly variable, it is modeled with a random variable, D. Suppose that Q is the number of papers he purchases. If Q is too large, he is left with unsold papers, and if Q is too small, some demands go unfilled. If we let co be the unit overage cost, and cu be the unit underage cost, then we show that the optimal number of papers he should purchase at the start of a day, say Q*, satisfies:
F(Q*) = cu / (cu + co)
where F(Q*) is the cumulative distribution function of D evaluated at Q* (which is the same as the probability that demand is less than or equal to Q*).
3. Lot size–reorder point systems. The newsboy model is appropriate for a problem that essentially restarts from scratch every period. For these cases we use an approach that is essentially an extension of the EOQ model of Chapter 4.
The lot size–reorder point system relies on the assumption that inventories are reviewed continuously rather than periodically. The system consists of two decision variables: Q and R. Q is the order size and R is the reorder point. That is, when the inventory of stock on hand reaches R, an order for Q units is placed. The model also allows for a positive order lead time, . Let D represent the demand over the lead time, and let F(t) be the cumulative distribution function of D. Cost parameters include a fixed order cost K, a unit penalty cost for unsatisfied demand p, and a per unit per unit time holding cost h. Interpret λ as the average annual demand rate (that is, the expected demand over a year). Then we show in this section that the optimal values of Q and R satisfy the following two simultaneous nonlinear equations:
1 – F(R) = Qh / pλ.
The solution to these equations requires a back-and-forth iterative solution method. We provide details of the method only when the lead time demand distribution is normal. A quick and dirty approximation is to set Q = EOQ and solve for R in the second equation. This will give good results in most cases.
4. Service levels in (Q, R) systems. We assume two types of service: Type 1 service is the probability of not stocking out in the lead time and is represented by the symbol α. Type 2 service is the proportion of demands that are filled from stock (also known as the fill rate) and is represented by the symbol β. Finding the optimal (Q, R) subject to a Type 1 service objective is very easy. One merely finds R from F(R) = α and sets Q = EOQ. Unfortunately, what one generally means by service is the Type 2 criterion, and finding (Q, R) in that case is more difficult. The solution requires using standardized loss tables, L(z), which are supplied in the back of the book. As with the cost model, setting Q = EOQ and solving for R will usually give good results if one does not want to bother with an iterative procedure.
In this chapter, we consider the link between inventory control and forecasting, and how one typically updates estimates of the mean and standard deviation of demand using exponential smoothing. The section concludes with a discussion of lead time variability, and how that additional uncertainty is taken into account.
5. Periodic review systems under uncertainty. In this case the form of the optimal policy is known as an (s, S) policy. Let u be the starting inventory in any period. Then the (s, S) policy is
If u ≤ s, order to S (that is, order S – u).
If u > s, don’t order.
Unfortunately, finding the optimal values of (s, S) each period is much more difficult than finding the optimal (Q, R) policy, and is beyond the scope of this book. We also briefly discuss service levels in periodic review systems.
6. Multiproduct systems. Virtually all inventory control problems occurring in the operations planning context involve multiple products. Their inventory levels should be reviewed often, and they should carry a high service level. B items do not need such close scrutiny, and C items are typically ordered infrequently in large quantities.
Chapter 7
Purpose
To understand the push and pull philosophies in production planning and compare MRP and JIT methods for scheduling the flow of goods in a factory.
Key Points
1. Push versus pull. There are two fundamental philosophies for moving material through the factory. A push system is one in which production planning is done for all levels in advance. A pull system is one in which items are moved from one level to the next only when requested. Materials requirements planning (MRP) is the basic push system. Based on forecasts for end items over a specified planning horizon, the MRP planning system determines production quantities for each level of the system. The earliest of the pull systems is kanban developed by Toyota, which has exploded into the just-in-time (JIT) and lean production movements. Each of the methods has particular advantages and disadvantages.
2. MRP basics. The MRP explosion calculus is a set of rules for converting a master production schedule (MPS) to a build schedule for all the components comprising the end product. It is derived from the forecasts of demand adjusted for returns, on hand inventory, and the like. The simplest production schedule at each level is lot-for-lot (L4L), which means one produces the number of units required each period. However, if one knows the holding and setup cost for production, it is possible to construct a more cost efficient lot-sizing plan. Three heuristics we consider are (1) EOQ lot sizing, (2) the Silver–Meal heuristic, and (3) the least unit cost heuristic
MRP as a planning system has advantages and disadvantages over other planning systems. Some of the disadvantages include (1) forecast uncertainty is ignored; (2) capacity constraints are largely ignored; (3) the choice of the planning horizon can have a significant effect on the recommended lot sizes; (4) lead times are assumed fixed, but they should depend on the lot sizes; (5) MRP ignores the losses due to defectives or machine downtime; (6) data integrity can be a serious problem; and (7) in systems where components are used in multiple products, it is necessary to peg each order to a specific higher-level item.
3. JIT basics. The JIT philosophy grew out of the kanban system developed by Toyota. Production cannot commence until production ordering kanbans are available. This guarantees that production at one level will not begin unless there is demand at the next level. Information flows can be controlled more efficiently with a central information processor than with cards.
4. Comparison of JIT and MRP. JIT has several advantages and several disadvantages when compared with MRP as a production planning system. Some of the advantages of JIT include (1) reduce work-in-process inventories, thus decreasing inventory costs and waste, (2) easy to quickly identify quality problems before large inventories of defective parts build up, and (3) when coordinated with a JIT purchasing program, ensures the smooth flow of materials throughout the entire production process. Advantages of MRP include (1) the ability to react to changes in demand, since demand forecasts are an integral part of the system (as opposed to JIT which does no look-ahead planning); (2) allowance for lot sizing at the various levels of the system, thus affording the opportunity to reduce setups and setup costs; and (3) planning of production levels at all levels of the firm for several periods into the future, thus affording the firm the opportunity to look ahead to better schedule shifts and adjust workforce levels in the face of changing demand.
Chapter 8
Purpose
To gain an understanding of the key methods and results for sequence scheduling in a job shop environment.
Key Points
1. The job shop scheduling problem. A job shop is a set of machines and workers who use the machines. The relevant characteristics of the sequencing problem include
- The pattern of arrivals.
- Number and variety of machines.
- Number and types of workers.
- Patterns of job flow in the shop.
- Objectives for evaluating alternative sequencing rules.
2. Sequencing rules. The sequencing rules that we consider in this section include.
First come first served (FCFS). Schedule jobs in the order they arrive to the shop. Shortest processing time (SPT) first. Schedule the next job with the shortest processing time. Earliest due date (EDD). Schedule the jobs that have the earliest due date first. Critical ratio (CR) scheduling. The critical ratio is (due date – current time)/ processing time. Schedule the job with the smallest CR value next.
3.Sequencing results. A common criterion for evaluating the effectiveness of sequencing rules is the mean flow time. The flow time of any job is the amount of time that elapses from the point that the job arrives in the shop to the point that the job is completed. The mean flow time is just the average of all the flow times for all the jobs. The main result of this section is that SPT scheduling minimizes the mean flow time. Another result of interest is that if the objective is to minimize the maximum lateness, then the jobs should be scheduled by EDD. Moore’s algorithm minimizes the number of tardy jobs, and Lawler’s algorithm is used when precedence constraints are present (that is, jobs must be done in a certain order). All the preceding results apply to a single machine or single facility.
4. Sequence scheduling in a stochastic environment. The problems alluded to previously assume all information is known with certainty. In that case, the job times, say t1, t2, . , tn, are assumed to be independent random variables with α known distribution function. The optimal sequence for a single machine in this case is very much like scheduling the jobs in SPT order based on expected processing times. When the objective is to minimize the expected makespan (that is, the total time to complete all jobs), it turns out that the longest expected processing time (LEPT) first rule is optimal.
5. Line balancing. Another problem that arises in the factory setting is that of balancing an assembly line. While line balancing is not a sequence scheduling problem found in a job shop environment, it is certainly a scheduling problem arising within the plant. Assume we have an item flowing down an assembly line and that a total of n tasks must be completed on the item. The problem is to determine which tasks should be placed where on the line. Optimal line balances are difficult to find. We consider one heuristic method, which gives reasonable results in most circumstances.
circumstances.