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Outline Chapter 8: AggregatePlanning in the Supply Chain Role of aggregate planning in a supply chain The aggregate planning problem Aggregate planning strategies Implementing aggregate planning in practice8-1

Role of Aggregate Planningin a Supply Chain Basic Assumptions:– Capacity has a cost– Lead times are greater than zero Aggregate planning:– Is the process by which a company determines levels of capacity,production, subcontracting, inventory, stockouts, and pricing over aspecified time horizon– goal is to maximize profit Or, if demand is effectively fixed for all thedecision we can make, we can just minimize costs– decisions made at a product family (not SKU) level– time frame of 3 to 18 months (What decision phase are we in?)» Too late to build another plant» Too early to get into daily/weekly production issues, SKU level detail– We need to answer: how can a firm best use the facilities it has?8-2

The Aggregate Planning Problem(and role in the Supply Chain) The Problem: Given the demand forecast for each period in theplanning horizon, determine the production level, inventory level,and the capacity level for each period that maximizes the firm’s(supply chain’s) profit over the planning horizon– Specify the planning horizon (typically 3 to 18 months)– Specify the duration of each period (typically 1 month for longer horizons)– Specify key information required to develop an aggregate plan All supply chain stages should work together on an aggregate planthat will optimize supply chain performance– For now we ignore transportation issues and costs and have single facility– Avoid sub-optimization by silo. We may need to incur more costs (ex.outsourcing production) in a function to maximize overall profit– Supply chains usually involve multiple firms. If these firms have close ties,it may be possible to optimize the efficiency of the entire chain8-3

Information Needed foran Aggregate Plan Demand forecast in each period Production costs–––– Machine costslabor costs, regular time ( /hr) and overtime ( /hr)subcontracting costs ( /hr or /unit)cost of changing capacity: hiring or layoff ( /worker) and cost of addingor reducing machine capacity ( /machine)Labor/machine hours required per unitMaterial requirements per unit, material cost and availabilityInventory holding cost ( /unit/period)Stock-out / backlog cost ( /unit/period)Constraints: physical or policy limits on overtime, layoffs,capital available, warehousing, stock-outs and backlogs8-4

Outputs of Aggregate Plan Production quantity from regular time, overtime, andsubcontracted time: used to determine number of workers andsupplier purchase levels Inventory held: used to determine how much warehouse spaceand working capital is needed Backlog/stock-out quantity: used to determine what customerservice levels can be– (i.e. do we short customers for a certain time- and how much/how long?) Machine capacity increase/decrease: used to determine if newproduction equipment needs to be purchasedA poor aggregate plan can result in lost sales, lost profits, excessinventory, or excess capacity8-5

Aggregate Planning Strategies There is typically a trade-off between optimizing forcapacity (machine labor), inventory, and backlog/lost sales– Chase strategy: sync production with demand, hiring and firing asneeded.– Time flexibility from workforce or capacity strategy: assumes laborpool can work variable hours (incl. overtime), has lower inventory&utilization,– Level strategy – keep capacity & labor usage constant, eitherstockpile inventory or short orders as needed– Mixed strategy – a combination of one or more of the first threestrategies 8-6

Tools for Creating Aggregate Plans Some companies have not created explicit aggregate plans, andrely only on orders from warehouses or DCs to drive productionschedules (pure pull system).– This is acceptable only if products are not capacity intensive, or ifmaintaining a plant with low utilization is inexpensive.– It also assumes material and labor inputs are flexible / available whenneeded For simple problems, it may be possible to produce a feasible planby guessing. (No guarantee of optimality) What tool is commonly used to produce an optimal aggregateplan?8-7

Linear Programming Inherently assumes costs are linear– Pure unit costs are the easiest– Increasing marginal costs (e.g. regular labor 20/hour, overtime 30/hour)– Economies of scale harder to model, but possible (ignored for this class) Difficulty of solving increases with degree of detail– Take a 1-year plan for a plant that monitors weekly production of 100different SKUs. How many variables?» have 100*52 over 5000 production decision variables Pi,t– If we could aggregate SKUs into 5 different product families, withmonthly time buckets, how many variables do we have now?» only have 5*12 60 decision variables for Pi,t– Industry aggregate plans often have 10,000 to 100,000 decision variables» In this class will keep our problem scales well below that of industry(under 200 decision variables, the limit of the built in Excel solver)8-8

Aggregate Planning Example: RedTomato Tools, Inc. Red Tomato makes a single product, a garden tool that sells for 40 Red Tomato starts with 1000 of these tools in inventory and is expected to endwith at least 500 in stock Red Tomato can temporarily backlog demand for a cost, but at the end of the timehorizon, they require their backlog to be zero– This is an important constraint to remember- if we forget it, we will get strange results Production costs are based on parts and labor with no machine capacity issues– They start with 80 employees can hire or fire workers for a cost.– Workers get regular pay whether they are producing or not. There are 20 days ofproduction per month, each month.– We can have workers work overtime (no more than 10 hrs/mo per worker) for extra – We can also subcontract production out and pay a flat fee (in lieu of labor materials) Red Tomato would like to generate a 6 month plan that maximizes profits(revenue net of costs)– For now we can just minimizing costs, if we have no influence over demand8-9

Aggregate Planning atRed Tomato ToolsHere’s the demand that the book gives us- see the emand Forecast1,6003,0003,2003,8002,2002,2008-10

Aggregate Planning- CostsItemMaterialsInventory holding costMarginal cost of a stockoutHiring and training costsLayoff costLabor hours requiredRegular time costOver time costCost of subcontractingCost 10/unit 2/unit/month 5/unit/month 300/worker 500/worker4/unit 4/hour 6/hour 30/unitNote: subcontracting costs includes all materials and laborTime to bring up Excel .8-11

Aggregate Planning(Define the Decision Variables)Wt Workforce size for month t, t 1, ., 6Ht Number of employees hired at start of month t, t 1, ., 6Lt Number of employees laid off at start of month t, t 1, ., 6Pt Production in month t, t 1, ., 6It Inventory at the end of month t, t 1, ., 6St Number of units stocked out (backlogged) at end of month t, t 1, ., 6Ct Number of units subcontracted for month t, t 1, ., 6Ot Number of overtime hours worked in month t, t 1, ., 68-12

Aggregate Planning(Define Objective Function)66t 1t 1Min 640W t 300 H t666t 1t 1t 1 500 Lt 6 O t 2 I t666t 1t 1t 1 5 S t 10 Pt 30 C tApologies to any Finance gurus but we do not consider NPV here8-13

Aggregate Planning (Constraints) Aside from the conditions for the ending level ofinventory and the ending backlog being 0, wewill have 4 other types of constraints to consider:1.2.3.4.Balance of workersProduction limitBalance of inventoryOvertime limit8-14

Aggregate Planning (DefineConstraints Linking Variables) Workforce size for each month is based on hiring and layoffs(# workers employed end of Month 1 # workers employedat the start of Month 2)– May end up with fractional # workers, e.g. 73.4, which could beacceptable if we allow for part-time (Also, even if not with largernumbers like this, we can get away with approximating for integer)– Is a Balance constraint. No spontaneous creation or destruction ofworkers outside of the hiring and layoff processesW t W t 1 H t Lt, orW t W t 1 H t Lt 0for t 1,.,6, where W 0 80.8-15

Links Between Periods? Why not create 6 different LPs, each with 1 period of a month?It would be easier* for the computer to solve, after all! Why not solve several 1-month problems sequentially? At endpoints, such as #workers left at the end of the month 1 andthen use that as the starting #workers for month 2?* A computer trivial aside from this class: as N increases, the inherent complexity andrequired solution time goes up by order of N3 or more)8-16

Aggregate Planning (Constraints) Production for each month cannot exceed capacity(hence, have a limit rather than balance constraint)Pt 40W t Ot 4 , or40W t Ot 4 Pt 0,for t 1,.,6.8-17

Aggregate Planning (Constraints) Inventory balance for each month.Inventory levels change if we a) produce (P) or sub-contract (C)more units than we have demand for, either from this period (t) orthe prior one (t-1). It may help to think about what is a “debit”and a “credit” to the level of inventory .It 1 Pt C t Dt S t 1 I t S tFor t 1 to 6We can then rearrange the terms to reflect standard form (allvariables on one side). What happens at t 0?It 1 Pt C t Dt S t 1 I t S t 08-18

Aggregate Planning (Constraints) Over-time limit for each month, reflecting policythat no one worker can put in more than 10 hoursof overtime for the month.Ot 10W t, or10W t Ot 0,for t 1,.,6.8-19

Further Conditions All of the variables are inherently non-negative We have a starting balance of– 80 workers– 1000 tools– 0 backlogThus, the variables associated with these are going to need to beinitialized (put in a value for time period 0) Reminder: have been told that we are not allowed to haveany backlog and must have at least 500 tools in stock atthe end of the planning horizon8-20

LP Formulation We now take a brief digression and look at the formulation inExcel, including the LP Solver configuration and the reports Some things to think about:1. How many variables will we have?2. Which variables have “memory”- and why do we care?3. How many different types of constraints (aside from nonnegativity and certain beginning/end conditions)? Howmany total constraint equations?4. What is our overall goal? Why can we take a “shortcut”8-21

LP Formulation8-22

LP Formulation: Solver Decision variables are indexed to 1 thru 6, tp0 exists only for initialization We have 4 types of constraints, plus 2 ending conditions Technically we should require variables to be integers (no laying off .2people or making .3 tools) but for now will leave as linear.– Real industry LPs have numbers like 300K and 3M, so this is less of an issue Assume linear model and non-negativity both checked in Options8-23

What-if Scenarios Planners often run re-run their models to see how the planmight change if parameter values are different than expected Here are some potentially realistic changes that would resultin changes our previously optimal plan at Red Tomato:1. Increase the seasonal swings in demand (Example 8-1)2. Raise holding costs (from 2 to 6) (Example 8-2)8-24

Increased Demand mand Forecast1,0003,0003,8004,8002,0001,400For chapter 8, we are assuming that demandis beyond our control to influence.Demand is still 16000 within the total planning period8-25

Solution: Comparison of What-IfScenario 1 –vs.- Base Case Major changes– Increases total Costs by 10,583» Changes come from» Base Case costs:» Larger seasonal fluctuations:Inventory and Stock-out 10,233 1,333 12,400 9,750 Caveat: The book treats beginning and end periods differently when calculatingthe average inventory position (see p. 218, p.220). This is overkill: we can justuse a simple average if we are interested in the inventory position.– Should I ask you to calculate this on a test, either method is correct, but mymethod is easier!– I will focus on minimizing the total inventory COST over the planninghorizon rather than inventory LEVELS at any point in time- ultimately,inventory levels are measured because of their associated costs8-26

What-If Scenario #2: IncreaseInventory Costs from 2 to 6 Major changes- costs increase over base case . In what way? Reduce inventory carried by .– engaging in more ”workforce reductions” as pre-building inventory forpeak periods is no longer as cost effective– subcontracting some demand out in peak periods We switch from what type of strategy to what?8-27

More Thoughts on RedTomato’s Planning Problem1. What if our aggregate demand forecasts are incorrect?– Review/ Reminder: How often are real forecasts 100% accurate?2. What if demand is greater than anticipated?– What are some ways we can prepare for extra (either in terms of SafetyStock or Safety Capacity?)3. What if demand is less than anticipated- what will happen?– What is one way to keep costs lower if demand is greatly reduced andexpected to stay low for awhile?8-28

Managing Supply: Some PossibleTools to Consider Managing capacity–––––Time flexibility from workforceUse of a seasonal workforceUse of subcontractingUse of dual facilities – dedicated and flexibleDesigning product flexibility into production processes Managing inventory– Using common components across multiple products– Building up inventory of high demand or predictable demandproducts– Inventory strategies are discussed in detail in Chapters10-129-30

Aggregate Planning in Practice If possible, think beyond your enterprise to the entire supplychain* Make plans flexible because forecasts are always wrong– Sensitivity Anal