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Chapter 8Aggregate Planningin a Supply Chain

Supply Chain Management

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Outline

Role of aggregate planning in a supply chain The aggregate planning problem Aggregate planning strategies Implementing aggregate planning in practice

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Role of Aggregate Planning in a Supply Chain

Capacity has a cost, lead times are greater than zero Aggregate planning:

– process by which a company determines levels of capacity, production, subcontracting, inventory, stockouts, and pricing over a specified time horizon

– goal is to maximize profit

– decisions made at a product family (not SKU) level

– time frame of 3 to 18 months

– how can a firm best use the facilities it has?

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Role of Aggregate Planning in a Supply Chain

Specify operational parameters over the time horizon:– production rate– workforce– overtime– machine capacity level– subcontracting– backlog– inventory on hand

All supply chain stages should work together on an aggregate plan that will optimize supply chain performance

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The Aggregate Planning Problem

Given the demand forecast for each period in the planning 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 3-18 months) Specify the duration of each period Specify key information required to develop an

aggregate plan

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Information Needed foran Aggregate Plan

Demand forecast in each period (deterministic) Production costs

– labor costs, regular time ($/hr) and overtime ($/hr)– subcontracting costs ($/hr or $/unit)– cost of changing capacity: hiring or layoff ($/worker) and cost of adding or

reducing machine capacity ($/machine) Labor/machine hours required per unit Inventory holding cost ($/unit/period) Stockout or backlog cost ($/unit/period) Constraints: limits on overtime, layoffs, capital available,

stockouts and backlogs

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Outputs of Aggregate Plan Production quantity from regular time, overtime, and subcontracted

time: used to determine number of workers and supplier purchase levels Inventory held: used to determine how much warehouse space and

working capital is needed Backlog/stockout quantity: used to determine what customer service

levels will be Workforce hired/laid off: used to determine any labor issues that will be

encountered Machine capacity increase/decrease: used to determine if new

production equipment needs to be purchased A poor aggregate plan can result in lost sales, lost profits, excess

inventory, or excess capacity

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Aggregate Planning Strategies

Trade-offs available to a planner are between labor and machine capacity, inventory, backlog/lost sales

Chase strategy: synchronize production rate with demand rate. Time flexibility strategy: vary amounts of overtime and hours

worked in order to synchronize production and demand rates. Level strategy: keep stable machine usage/capacity and labor

force and meet demand with inventory Mixed strategy – a combination of one or more of the first three

strategies

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Chase Strategy(设备和人员数量变化 )

Production rate is synchronized with demand by varying machine capacity or hiring and laying off workers as the demand rate varies

However, in practice, it is often difficult to vary capacity and workforce on short notice

Expensive if cost of varying capacity is high Negative effect on workforce morale Results in low levels of inventory Useful when inventory holding costs are high and costs of

changing capacity are low

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弹性策略

总体思想：生产计划（包括人力与设备利用情况）的安排依照需求的变动而变动。

特征：生产量与需求量的变化保持同步。– 库存费用较低，但生产费用较高。– 员工的频繁雇佣和解雇不仅会增加成本，还会使员工士

气低落，不利于企业的长期稳定发展。– 适用于产品技术含量不高、而产品库存成本和存货风险

又较高的生产企业。

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Time Flexibility Strategy（设备和人员数量不变，但工作时间变化）

Can be used if there is excess machine capacity Workforce is kept stable, but the number of hours worked is

varied over time to synchronize production and demand Can use overtime or a flexible work schedule Requires flexible workforce, but avoids morale problems of

the chase strategy Low levels of inventory, lower utilization Should be used when inventory holding costs are high and

capacity is relatively inexpensive

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充足策略

总体思想：把设备及人员的生产能力作为一种资源进行储备，以满足需求量增大情况下，对生产能力增加的要求。

特征：同样追求生产量与需求量的变化的同步，但能够保持人力资源配置的相对稳定性。– 会降低设备和人员的平均利用率，导致生产成本的增

加。– 适合于产品的库存成本较高、设备和人力的固定费用

相对较低的情形。

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Level Strategy（设备和人员数量、工作时间均相对稳定）

Maintain stable machine capacity and workforce levels with a constant output rate

Shortages and surpluses result in fluctuations in inventory levels over time

Inventories that are built up in anticipation of future demand or backlogs are carried over from high to low demand periods

Better for worker morale Large inventories and backlogs may accumulate Should be used when inventory holding and backlog costs are

relatively low

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稳定策略

总体思想：无论需求量增加或者降低，生产率总是保持在一个相对稳定的状态。

特征：员工的配置及其工作量的安排比较稳定。– 当需求量低于生产量时，多余的产品将被储存起来，

以备需求量高于生产量时的供应。– 有利于生产的平稳与连续性，避免员工的频繁雇佣和

解雇。– 会带来库存成本和库存风险的增加，适合于库存成本

和产品时效性较低的情形。

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弹性策略 --- 使用生产能力作为手段– 增减设备或雇佣 / 解雇员工

充足策略 --- 使用利用率作为手段– 需求高峰时工人加班或提高设备的利用率

稳定策略 --- 使用存货作为手段– 存货可满足未来的高需求

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弹性策略将导致低库存，以及生产能力和人力资源上的高度变动。

充足策略将导致低库存，但生产能力的平均利用率将降低。

稳定策略将导致高库存，但生产能力和人力的安排较为稳定。

企业应在确定所采取的基本策略后，再制定具体的生产供给规划。

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制定生产供给规划基本策略的原则

要明确企业的总体经营与发展策略，并结合生产与经营的实际情况，考虑人力资源、经营安全、企业信誉等因素及其指标，在企业的中长期发展战略下，制订生产供给规划要采纳的基本策略。– 弹性策略– 充足策略– 稳定策略– 混合策略

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可用优化模型与算法求解

制定生产供给规划的思路

决策变量

约束条件

目标函数

参数 利润最大化

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Red Tomato Tools

A gardening tool manufacturer Product highly seasonal, peaking in the spring How to use aggregate planning to deal with

seasonal demand and still make a profit? Options:

– Adding workers during the busy season

– Subcontracting out some of the work

– Building up inventory during the slow months

– Building up a backlog of orders to be delivered late

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Demand Forecast at Red Tomato Tools

Month Demand ForecastJanuary 1,600February 3,000

March 3,200April 3,800May 2,200June 2,200

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Aggregate Planning

Item CostMaterials $10/unitInventory holding cost $2/unit/monthMarginal cost of a stockout $5/unit/monthHiring and training costs $300/workerLayoff cost $500/workerLabor hours required 4/unitRegular time cost $4/hourOver time cost $6/hourCost of subcontracting $30/unit

Working/each day: 8 Working days/month: 20

No employee can work more than 10 hours of overtime/month

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Aggregate Planning (Define Decision Variables)

Wt = Workforce size for month t, t = 1, ..., 6

Ht = Number of employees hired at the beginning of month t, t = 1, ..., 6

Lt = Number of employees laid off at the beginning of month t, t = 1, ..., 6

Pt = Production in month t, t = 1, ..., 6

It = Inventory at the end of month t, t = 1, ..., 6

St = Number of units outstocked out at the end of month t, t = 1, ..., 6

Ct = Number of units subcontracted for month t, t = 1, ..., 6

Ot = Number of overtime hours worked in month t, t = 1, ..., 6

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Objective Function

6

1

6

1

6

1

6

1

6

1

6

1

6

1

6

1

30105

26500

300*4*8*20

tt

tt

tt

tt

tt

tt

tt

tt

CPS

IOL

HWMin

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目标函数——成本最小化

6

1

6

1

6

1

6

1

6

1

6

1

6

1

6

1

301052

5003006640

tt

tt

tt

tt

tt

tt

tt

tt

CPSI

LHOWMin

正常工时和加班成本

：

聘用和解雇成本库存和

缺货成本物料和

外包成本

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Workforce Constraints

Workforce size for each month is based on hiring and layoffs

.80,6,...,1

0

,

0

1

1

WwheretforLHWW

orLHWW

tttt

tttt

初始值t 期员工人

数 t 期新雇佣的人数

t 期解雇的人数

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Capacity Constraints

Production for each month cannot exceed capacity

.6,...,1

,0440

,440

tforPOW

OWP

ttt

ttt

一个员工每月正常工作可以生产的产品数量

期 t加班生产的产品数量

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Inventory Balance Constraints

Inventory balance for each month

.500,0

,000,1,6,...,1

,

60

0

11

ISI

SISDCPI

and

wheretforttttttt

初始库存

期末库存期 t产品拥有量

期 t需求汇总

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Overtime Constraints

No employee can work more than 10 hours of overtime/month

.6,...,1

,10

tforWO tt

员工每月最多的加

班时数

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约束条件（ 5 ） 每个决策变量均为非负数

？还缺什么限制

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可根据实际情况和基本策略，加入其他限制，如– 限制每个月外包生产的产品数量– 限制每个月聘用或解雇员工的数量– 限制产品缺货的拖延时间– 限制每个月最多的产品库存数量

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步骤 6 ：模型求解

Excel/工具 / 规划求解 计算结果：规划期间总成本 =$422,275 也可以使用其它各种优化软件包：Lindo,AMSS,Lingo,Matlab等

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计算结果期间 

雇佣人数

解雇人数

人力规模

加班时数

存货量

缺货量

外包量

总产量

0 0 0 80 0 1000 0 0  

1 0 15 65 0 1983 0 0 2583

2 0 0 65 0 1567 0 0 2583

3 0 0 65 0 950 0 0 2583

4 0 0 65 0 0 267 0 2583

5 0 0 65 0 117 0 0 2583

6 0 0 65 0 500 0 0 2583

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计算结果分析

计算结果表明：– 在 1 月初解雇了 15名员工，之后员工的数量保持不变，

– 在整个规划期间没有外包，– 只有 4 月份有缺货，其他月份都有存货。

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误差估计及处理方法

可采用情景分析（ Scenery Analysis ）的方法：– 首先，考虑规划模型中各种参数的可能取值，以及变量之间、变

量与参数之间的各种可能关系，并将这些不同的情形的发生称为“情景”，分析这些情景发生的可能性；

– 其次，考虑不同情景下的决策结果，以及这些决策结果之间的偏离关系；

– 最后，对不同情景下的可能结果进行综合分析，从而对最初得到的决策结果进行必要的修正。

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可以用安全库存或安全生产能力来处理– 安全库存是为满足不确定需求而存有的、高于预测值的存货量。– 安全产能是为满足不确定需求而准备的、高于预测值的生产能力。

使用情景分析可从可能遇到的情形中寻找最合理的解决方案

修正方法

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Aggregate Planning in Practice

Think beyond the enterprise to the entire supply chain Make plans flexible because forecasts are always

wrong Rerun the aggregate plan as new information emerges Use aggregate planning as capacity utilization

increases

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Summary of Learning Objectives What types of decisions are best solved by aggregate

planning? What is the importance of aggregate planning as a

supply chain activity? What kinds of information are needed to produce an

aggregate plan? What are the basic trade-offs a manager makes to

produce an aggregate plan? How are aggregate planning problems formulated and

solved using Microsoft Excel?

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作业

根据所提供的 Excel 求解数学规划模板，制定具有以下需求情形时的供给规划

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Table 8.4 Demand Forecast with Higher Seasonal Fluctuation

Month Demand ForecastJanuary 1,000February 3,000

March 3,800April 4,800May 2,000June 1,400