SCHEDULES: FUNDAMENTALS, EXAMPLES, AND IMPLEMENTATION
3. A SYSTEM FOR MPS CREATION
• Often, a changeover time will incur every time a new product is to be made at a production line or work center. These changeover or setup times usually demand a non-negligible time, which varies from product to product and their production sequence. Sequence dependent setup times are then to be considered since a different production sequence can yield dramatic savings in the use of limited resources. In such cases, the MPS process should consider a changeover matrix.
• Avoidance of routing flexibility, that is, there is not only one production resource that can produce the product. This routing flexibility increases the complexity in the MPS process.
Even authors of renowned books in this area simplify the explanation of how complex the MPS process really is (VoUmann et al, 1992; Slack et al., 2001; and Gaither & Frazier, 2002).
The MPS constitutes one of the modules part of the production planning and control structure. There are not, however, a commonly adopted form for this structure. It is the result of several factors like promised delivery dates from suppliers, production capacity, strategies and objectives (e.g., minimum inventory levels), and considers information exchange between departments, such as between manufacturing and marketing - for the production and sales forecasting.
Master production scheduling becomes a very complex problem as the number of products, number of periods, and number of resources (production lines assembly lines, machines, production cells) increase. In fact, Garey & Johnson (1979) proved that production planning problems are NP-hard. Yet, setup times and overtime can make this problem even more complex. Moreover, as seen previously, production planning problems usually involve conflicting objectives, like minimizing inventory and maximizing service levels. Because of all this, use of heuristics or meta- heuristics is suggested for the resolution of these types of problems. Since absolute optimal solution finding might be extremely time consuming, a good, perhaps close to optimal, in reasonable computer time is preferred.
Several artificial intelligence meta-heuristics have been applied to optimization, among them, genetic algorithms, tabu search, ant colony, beam search and simulated annealing. Some of these techniques are explained in the following sections.
A clear definition of objectives and respective performance measure indicators (see Section 3.4). Multiple objectives may exist in an optimization approach, such as minimization of ending inventory levels and maximization of service levels. Coefficients specifying the importance - weight - of each one of the performance measure considered should also be defined.
Parameters to be used, like initial inventories, gross requirements, standard lot sizes, minimum or safety inventory levels (Sections 0 and 3.2).
Final adjustments by the master scheduler. No planning (scheduling) information system will generate a plan (schedule) that will perfectly fit the expectation of those responsible for this task in the industry. There are always annoyances that an experience person considers which are often not considered by standard software packages. There are also specificities and cultural aspects particular of an industry that such packages were not intended to deal with. For these reasons, the planner will generally have to make final adjustments to master plans generated by computer systems.
Resource planning
^ W
Detailed capacity
^ ^
Shop-floor systems
Production planning
i,
Master production
1
r
Detailed Material 1
r
Material and capacity
1
r
Vendor systems
^ ^
Demand management
Figure 7-2. Manufacturing Planning and Control System - simplified (Vollmann et ah, 1992)
Long-term (years)
Mid-term (6-18 months)
Short-term (several weeks to months)
Production Planning and Control Systems
Long-term capacity planning
Aggregate planning
Master Production Schedules
Production Planning and Control Systems
Inventory building
Inventory building
Inventory building
Inventory building
Figure 7-3. Manufacturing Production Planning (Gaither & Frazier, 2002) Three categories of parameters exist in a master production scheduling system, especially one based on an optimization (pseudo-optimization, heuristics, or meta-heuristics) approach. These are input parameters, output parameters, and objective function parameters. MPS parameters can also be categorized into updatable and non-updatable parameters. Updatable parameters can be manually altered by the scheduler while, as its name suggests, the non-updatable cannot. Examples for these parameters are given in the following sections.
3.1 Main input parameters
The following are some of the main input parameters often considered in the MPS process:
• Planning horizon: Usually weeks to a couple of months.
• Resources and products (SKUs).
• Gross requirements: mainly demand or production forecasts and customers orders. Usually, initial periods (time buckets) rely more on orders while further periods more on forecasts.
• Subcontracted: Quantity to be manufactured by third-party companies at a certain period of time.
• Standard lot size: The quantity to be manufactured should be a multiple of the standard lot size. It can be estimated based on costs, pallet sizes, minimum raw material (or components) purchase order size, number of parts per box.
• Minimum lot size: the minimum quantity to be scheduled.
• On-hand inventory: Represents the SKU inventory at the beginning of the planning horizon. Sometimes it is confused with beginning inventory (output parameter explained later).
• Safety (or minimum) inventory: Quantity of inventory kept to deal with uncertainties, usually when demand surpasses forecast.
• Maximum inventory: Maximum quantity the company can carry in a time period. This is particularly important for perishable products, where maximum shelf-life is an important issue. It can also be given in terms of maximum inventory coverage, meaning that inventory should not cover more than a given period.
• Production rate: How much a resource can manufacture of a product per time unit. The reciprocal would be how much time the production of one unit consumes of capacity. (A value equal to zero means that a product cannot be made at the resource.)
• Changeover (or setup) time: Time needed to prepare a production resource (it is usually assumed that this time consumes capacity from the resource, also known as internal setup). It can depend on product type sequence (sequence dependent setup) or not (sequence independent setup).
• Backlogging: Maximum quantity of a product (derived from customer orders) that can not be made at the desired time bucket but can be manufactured in future periods.
• Capacity: Regular capacity available from a resource. Usually number of hours or days.
• Overtime: Maximum number of hours (or days) that can be used as overtime per time period per resource. (Usually, government rules specify a maximum number of hours a worker can do in overtime.)
3.2 Main output parameters
The following are some of the main output parameters:
• Beginning inventory: Quantity of a product available at the beginning of a time period. In the first time bucket, it equals the on-hand inventory;
for the remaining periods, it equals the ending inventory of the previous period.
• Ending inventory: Quantity of products available at the end of a time period.
• Net requirements: Represents what should be manufactured. It will be in fact manufactured if there is enough available capacity. It is directly calculated from gross requirements, initial inventory levels, maximum inventory, subcontracted, minimum lot size, and standard lot size. This can be approximated with the following expression:
Minimum {Multiple {Maximum {Maximum {Gross Requirements - Initial Inventory - Subcontracted; 0}; Minimum Lot Size}; Standard Lot Size}; Maximum Lot Size}.
• Master production schedule (MPS) row: Contains the final result with the product quantities to be manufactured, by which resources, through the planning horizon. When more than one resource is to be used, there will be several MPS rows, one for each resource used, and a "Total MPS"
row.
• Used capacity: For each resource, it shows the capacity used by the MPS at each period of time. It can also be given in relation to the total available capacity (% used capacity).
• Requirements met: Shows in absolute terms how much of the gross requirements will be met by the master plan.
• Requirements not met: Shows in absolute terms how much of the gross requirements will not be met by the master plan. This quantity can become backlogging and be transferred to future periods, if allowed by the scheduler.
• Service level: A percentage representing how much of the gross requirements (demand and orders) will be met by the MPS. In other words, it is the ratio between requirements met and gross requirements.
One can see that planning horizon, resources and products, gross requirements, subcontracted, standard lot size, minimum lot size, safety inventory, maximum inventory, on-hand inventory, production rate, changeover time, backlogging, capacity, overtime, and the MPS row are updatable parameters, while beginning inventory, ending inventory, net requirements, total MPS row, used capacity, % used capacity, requirements met, requirements not met, and service level are non-updatable parameters.
Most output parameters result from the calculation of input parameters and, therefore, are non-updatable. Other parameters, especially those related to costs (holding inventory, production and backlogging costs), also are part of an industrial master production scheduling system.
Table 7-1. Example of item and resource tables.
Item-table:
Product AAA
Resource- table:
Line XYZ
On-hand
Beginning inventory Gross requirements Standard lot size
Safety stock Net requirements
MPS Service level Ending inventory
Production rate
Line XYZ
Week 2
Week 3
Week 4
^^:'.:S\
Month 2
L}v>/ \ Month
3
' IX'-I}" Regular capacity
Used capacity
% Used capacity
Overtime allowed
Week 2
Week 3
Week 4
Month 2
Month 3
3.3
Item and resource tables
In a master production scheduling system, parameters can be grouped in two types of tables. Here, they are called "item-table" and "resource-table,"
as illustrated for a fictitious product and production resource {Product AAA and Production Line XYZ, respectively) shown at Table 7-1.
All products and resources are grouped in these tables, as shown on later examples.
3.4 The multi-objective function
In production planning and scheduling, optimization regards maximizing profits, e.g., "maximize { revenues - costs }." Since usually maximizing revenues is left to the sales and marketing personnel, the manufacturing
focuses more on the costs side of the function, that is to minimize costs:
"minimize { costs }." However, the approach described here considers both of them. Costs are easily understood by the parameters shown below, however, maximizing revenues is indirectly attained, by "minimizing requirements not met" as explained below.
Therefore, for the search of a good master production schedule, an objective function should consider the minimization of, at least, the following aspects:
• Ending inventory;
• Requirements not met (remember that demand is mainly given by customer orders and forecasts and service level is directly related to demand met);
• Overtime;
• Setup time;
• Risk of not meeting requirements when operating under safety inventory levels (in other words, risk of stockouts).
Since these variables operate in quite different ranges, the objective function should consider them in a common scale, or, in other words, they need to be normalized. There exist some standard normalization procedures on the literature. This study considers the following approach. Consider three variables A, B, and C that operate under minimum and maximum values given by (MinA, MaxA), (MinB, MaxB), (MinC, MaxC), respectively.
Other parameters that need to be considered regard the importance or weighting of these performance measures used in the objective function.
This work considers five weighting coefficients, one for each performance measure that can be used (CI, C2, C3, C4, and C5). These coefficients set the importance of each factor to the MPS quality to be created. Their appropriate definition is fundamental and depends on each company's own interests.
The multi-objective function can then be generically stated as:
Minimize { Ci[inventory] + C2[requirements not met] + C3[overtime]
+ C4[setup time] + C5[operating below safety levels]}
With this objective function, there are only five adjustable parameters (Ci, C2, C3, C4, and C5), which facilitate its use and, at the same time, allow one to use different policies by varying the weighting combination.
3.5 A generic MPS process
Gaither & Frazier (2002) mention that a master production schedule horizon has four sections. The first section includes the first few planning weeks and is referred to as thQ frozen section. The following section, also having a few weeks, is called thQ firm section. Third section, having weeks to a few months, is the fidll section. The last section, also lasting weeks to months, is called the open section. These sections can actually be simplified into only two: the fi^ozen and open sections. Basically, the planner can not, except on very rare and extraordinary situations, change the contents on the fi-ozen part of the planning horizon - since resources have already been
allocated, material prepared, and people on the shop-floor are practically working on the plan. The planner actually works on the open section, which is much longer then the frozen horizon.
The MPS process is usually updated weekly, which means that the week that just ended is removed from the beginning of the planning horizon and another week is added to its end, and requirements (demands and forecasts) related to the whole MPS are estimated again. The first week of the old open section is then set to fi^ozen. This is called "rolling-horizon" procedure.
Therefore, the first step in an MPS process is, whenever appropriate, to roll the horizon. Then, the master scheduler should read (update) the MPS input information, such as gross requirements, on-hand inventory levels, expected material arrival, maximum number of overtime allowed (if any), costs and setups - in case these have been changed.
Roughly, the rest of the execution logic is this: starting from the first time bucket in the open planning horizon, an MPS system calculates net requirements based on gross requirements, initial inventories, lot sizes, minimum and maximum inventory levels. Then, based on capacity constraints, it calculates the master production row. If capacity is readily available, the MPS row will equal net requirements (NR), otherwise, MPS will be lower than NR. In this case, if backlogging is permitted, requirements not met can be transferred to later periods. This idea repeats to the following periods. The system can also build inventory in advance to meet future demand in periods of high demand. This requires the system to repeat the above steps several times until it reaches an acceptable plan.
After a plan is proposed and the scheduler makes final adjustments, some periods should be frozen.
When different resources can be chosen and, at the same time, different setup times and production rates are involved, the system will need to be intelligent enough to make appropriate allocations: How much of ending inventory, service level, overtime, or setup time is acceptable? What would be the best alternative (plan)? That is, given penalties or cost values for
performance indicators - like those just mentioned - how can the system define a good schedule? Imagine, for instance, that just for one period, ten different SKUs need to be scheduled to one of four possible - but different - production lines and that, depending on the line chosen, different changeover times can incur? What if these lines have different processing rates? What if some products cannot be scheduled simultaneously because the use same tools, pallets or fixtures? What if some products should be scheduled only after others? Consider in this scenario that even with these four lines, the shop floor cannot yet manufacture all the requirements - which products should the system schedule first? Expand these questions to a scenario with three hundred different SKUs, forty production lines, and a planning horizon with fifteen time buckets - what do you do? How many different solutions can exist? Based on importance weights, can a system find the best (optimal) solution - a solution that maximizes profits?
These are just some of the dilemmas involved in the master scheduling process that an MPS information system must consider - especially if some optimization is desired. One of the following sections mentions some techniques that can be used in an master production scheduling system - focusing and exemplifying on the use of two artificial intelligence techniques: genetic algorithms (GA) and simulated annealing (SA).