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DSMAP for Demand-to-Supply Planning

  • Masayuki Matsui
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 202)

Abstract

The SCM age causes companies to produce excess inventories as well as long order fulfillment times. For the collaboration of the sales and production functions, a DSMAP is developed by using Matsui and Takahashi’s method. This map consists of a row for demand speed and a column for the smoothing factor, while the respective elements indicate the indices in economics and reliability on collaboration. This chapter presents a theory and an effective planning tool, called the planner, for collaborative demand-to-supply management based on the strategic demand-to-supply map. The planner consists of demand forecasting, aggregate planning, the strategic map, a scheduler, and progressive analysis. The effectiveness of the planner is demonstrated using a numerical example.

Keywords

Expect Return Demand Forecast Corporate Sustainability Expect Cost Progressive Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

8.1 Demand-to-Supply Planner: DSMAP

8.1.1 Introduction

In the so-called mass-production and mass-consumption age, because of long-term product life cycles and increasing demand, most companies recognized inventory to be a valuable corporate asset. In such a situation, balancing demand and supply plans in order to avoid excess inventory and improve corporate profit was not a critical issue because strong demand could absorb excess inventory in most cases.

However, today’s competitive and unforeseeable market requests shorten product life cycles and increase product variety. Therefore, excess production compared with market demand creates excess inventory, which needs to be valued at disposal cost in order to classify it into the correct inventory level.

In this chapter, collaborative demand-to-supply management is also called demand-to-supply management, while strategy is characterized as a set of parameters that formulates plans including sales and production plans. Under demand-to-supply management, sales and production functions work together to decide the integrated demand and supply strategy to be followed by the company.

To support demand-to-supply management, we have developed steps and mechanisms for formulating a collaborative demand-to-supply plan by using Matsui and Takahashi’s method [7]. This PC-based decision support software applies the steps and mechanisms that comprise the DSMAP [1] for post-ERP/SCM, also called the planner hereafter.

A numerical example of the planner is demonstrated next. In addition, we apply the planner as a tool for training and education to implement demand-to-supply management successfully in practice. Finally, we propose future development topics for investigating demand-to-supply management in the SCM age (see [1, 11]).

8.1.2 Demand-to-Supply Management Problem

The sales function in typical companies nowadays decides the sales strategy, which aims to maximize corporate-wide sales volume, while the production function decides on the production strategy, which aims to minimize production cost (see Fig. 8.1). In order to avoid lost sales opportunities because of stock shortages, the sales function’s strategy tends to make forecasts under the highest possible level of demand. By contrast, the production function’s strategy tends to take large-lot size production to reduce its cost. It cannot follow unexpected demand fluctuations because of the longer production lead-time.
Fig. 8.1

A simplified mechanism of excess inventory and stock shortage under non-collaborative strategies

In a stable demand situation, independent sales and production strategies can result in corporate-wide profit optimization. However, in today’s unstable and unforeseeable market, local optimization in each function may lead to the loss of sales opportunities and increased inventory cost [7].

To create a rational demand-to-supply management strategy from a corporate-wide standpoint and to increase corporate profit in today’s market, demand-to-supply management, where the sales and production functions work together by sharing information, is necessary.

As shown in Fig. 8.2, a collaborative demand-to-supply management strategy is based on information from both the sales function and the production function. The planned collaborative strategy is then returned to each function in the form of feedback in order for it to update its individual strategy and formulate its plan.
Fig. 8.2

A two-function model of the collaborative demand-to-supply problem

Since the mid-1990s, ERP [9] has been widely used as a core corporate information system. ERP is a software application that fully integrates core business functions, including transaction processing and management information. Most ERP packages, for example, can apply financial management, human resource management, marketing, sales, production management, and so on. Each ERP package has an original business process, unified enterprise database, and implementation methodology.

The business process is a standard process that ERP provides as a best practice to optimize the company. In other words, implementing ERP aims to reform the company based on the business process ERP provides. However, few ERP packages include the concept of demand-to-supply management. Although they are useful to integrate corporate information, they have few mechanisms for collaborative decision-making among different functions.

Most companies have recognized the importance of the demand-to-supply planning problem in today’s market. However, the sales and production functions still collaborate poorly [6]. In addition, research and practice are not enough to provide tools and methodologies applicable to collaborative demand-to-supply management.

Matsui et al. [7] propose a DSMAP, the planner, using a strategic map to show the performance of each combination of sales and production strategies. Such a strategic map is developed using a pair-matrix table [4]. Matsui et al. [8] modify the planner to be applicable to long-term business planning. The effectiveness of the application is demonstrated in a case study.

In this chapter, the planner is expanded to select a better strategy using production scheduling. In addition, a training and education system to educate demand-to-supply management staff using the planner is developed.

8.1.3 Overview of DSMAP

The planner formulates a collaborative plan that maximizes profit, called expected net return (EN). It consists of six major systems, as shown in Fig. 8.3. The planner defines future demand based on historical demand data in certain periods and designs a demand-to-supply strategic map (called the strategic map).
Fig. 8.3

Steps of DSMAP

The strategic map [5] is a two-dimensional matrix that consists of a demand strategy axis and a supply strategy axis, as explained in Sect. 8.1.4.2 in this chapter. The design of the strategic map defines the ranges of both axes.

Aggregate planning creates an aggregate plan that minimizes the expected cost (EC) of each combination of strategies. Because the expected return (ER), which can be defined by demand level, is already shown on the map, EN is obtained as EN = ER−EC. Then, the planner selects from the map the demand-to-supply plan that maximizes EN.

The selected plan is simulated in more detailed production conditions using production scheduling [10], and the strategy is modified to improve the accuracy of the plan as necessary. In addition, the plan is evaluated by progressive analysis. The planner returns the results of the evaluation to the aggregate planning or scheduling teams until an acceptable demand-to-supply plan for both the sales function and the production function has been created.

In the planner, demand forecasting is considered to be a strategy that reflects the sales function’s intensions, while the plan formulated by aggregate planning and scheduling is considered to be a strategy that reflects the production function’s intensions.

The strategic map is used to compare both functions’ strategies and find the optimum plan. Hence, we use the map as a tool for collaborative demand-to-supply management. The progressive analysis is used to find the potential directions for collaborative works between both functions.

In the following sections, the functions and methodologies used in the planner are explained.
  1. (i)

    Demand forecasting

     

The demand forecasting system in the planner forecasts monthly market demand for the target products based on historical demand data. In the current version, the planner uses the exponential smoothing method for demand forecasting. The numerical formula of the method is presented in Sect. 8.2.4.

Although different demand forecasting approaches can be applied in the system, the design of the demand-to-supply map may need to be modified.
  1. (ii)

    Design of the demand-to-supply strategic map

     
The strategic map represents the possible combinations of sales and production strategies, as shown in Fig. 8.4. The map consists of a row for expected demand, which is considered to be a sales function strategy, and a column for the smoothing factor of exponential smoothing, which considered to be a production function strategy. In the strategic map, each cell, which indicates the crossing point of a row and column, shows the objective’s indices in economics including expected net return (EN), expected return (ER), expected cost (EC), and expected lead-time at the N inventory level (ET(N*)).
Fig. 8.4

Example of a strategic map

The maximum ER for each strategy combination is also calculated based on demand and demand price. The mathematical model used to calculate ER is described in Sect. 8.1.4.1. The steps to create the strategic map are explained in Sect. 8.1.4.2 in detail.
  1. (iii)

    Aggregate planning

     
Aggregate planning uses linear programming to calculate the monthly production quantities that minimize EC including production cost and inventory cost, back order penalty cost, and the cost of idle resources. The monthly production quantity is provided by demand forecasting. The numerical formula to obtain an aggregate plan is shown in Sect. 8.1.4.
  1. (iv)

    Selection of a demand-to-supply plan

     

The strategic map visualizes the value of the objective functions as a matrix in order to find the optimum combination of sales and production strategies, as shown in Fig. 8.4. The strategic map is completed using the results from aggregate planning. The detailed steps to generate a map are shown in Sect. 8.1.4. The plan, where EN takes its maximum value, is recognized as the optimum strategy, consisting of a sales strategy and a production strategy.

In the steps to find the optimum strategy and its aggregate plan, the roles of the strategic map are to find the possible combinations of strategies for both functions and examine the expected performance of the selected aggregate plan in a comprehensive way. Because the value used to create the strategic map can be imprecise, more detailed performance is examined in the next scheduling step using more precise data and detailed conditions.
  1. (v)

    Scheduling

     

The scheduling step simulates the aggregate plan, selected from the strategic map using detailed production conditions including production sequence, machine speed, production lot size, the number of products and production volume of each product, setup time, and overtime work. Based on the scheduling results, the planner rebuilds the strategic map if expected production capacity is significantly different from the aggregate planning condition.

The scheduling result is assumed to show actual production capacity under the current production conditions. Therefore, the planner replaces the capacity parameters of aggregate planning and this creates a more accurate strategic map [14].

Scheduling enables us to examine the aggregate plan selected from the strategic map under detailed production conditions, and to generate a more accurate plan by comparing the results of scheduling with those of the aggregate plan.
  1. (vi)

    Progressive analysis

     

Progressive analysis, which is an application of progressive curve-based control [13], graphically depicts the cumulative figures of the input to and output from the production system. By using the figure, we can analyze the work in process, order fulfillment time, and their fluctuations.

In the planner, progressive analysis is used to compare the plans from the strategic map with those from scheduling. Based on the comparison results, this allows us to evaluate these plans and to understand how to improve the accuracy of the strategic map.

8.1.4 Model of the Planner

8.1.4.1 Mathematical Model

The objective function of the sales and production functions (i.e., expected return (ER) and expected cost (EC), respectively) is optimized mathematically by applying strategic parameters. The combination of a sales strategy and a production strategy leads to the expected net return (EN). The relationship between the objective function and strategic parameters is given as
$$ EN\left(N,d,\alpha \right)= ER\left(d,\alpha \right)- EC\left(N,d,\alpha \right)\to \max, $$
(8.1)
In this equation, N, d, and α, respectively, stand for the standard inventory level, expected demand quantity, and smoothing factor for demand forecasting. Here, ER is given as (8.2) and T stands for the planning horizon.
$$ ER={\displaystyle \sum_{t=1}^T{p}_t{D}_t/T\to \max }. $$
(8.2)
Further, D t stands for forecasted demand in the t-th period, obtained from historical demand data d t by Eq. (8.3):
$$ {D}_t=\alpha {d}_t+\left(1-\alpha \right){D}_{t-1}\kern2em \left(0\le \alpha \le 1\right), $$
(8.3)
P t stands for the price in the t-th period, given as (8.4):
$$ {p}_t={p}_0+\frac{p_0\left|{d}_0-d\right|}{ b\rho {d}_0}. $$
(8.4)

In addition, p 0, d 0, ρ, and b stand for, respectively, standard price, standard demand quantity, utilization rate, and price elasticity, which means demand sensitivity when the price changes.

Then, EC is expressed as (8.5), obtained using linear programming. The constraints are given as (8.6) and (8.7). Table 8.1 describes the nomenclature in each equation:
Table 8.1

Explanation of the variables and constants

 

Variables

X t

Regular production quantity

Y t

Overtime work production quantity

Z t

Outsourcing production quantity

I t

Inventory at the end of the t-th period

B t

Back order quantity

 

Constants

c 1

Cost of regular production

c 2

Cost of overtime work production

c 3

Cost of outsourcing production

c 4

Inventory holding cost

 

Back order cost (penalty)

c 6

Cost of idle resources

I 0

Inventory at the beginning of the planning

X max

Capacity of regular production

Y max

Capacity of overtime work production

Z max

Capacity of outsourcing production

$$ \begin{array}{l} EC={\displaystyle \sum_{t=1}^T\Big\{{c}_1{X}_t+{c}_2{Y}_t+{c}_3{Z}_t+{c}_4{I}_t}\\ {}+{c}_5{B}_t+{c}_6\left({X}_{\max }-{X}_t\right)\Big\}/T\to \min, \end{array} $$
(8.5)
where
$$ {I}_t-{B}_t={I}_{t-1}-{B}_{t-1}+{X}_t+{Y}_t+{Z}_t-{D}_t, $$
(8.6)
$$ {X}_t\le {X}_{\max },{Y}_t\le {Y}_{\max },{Z}_t\le {Z}_{\max }. $$
(8.7)
The objective function (8.5) can be modified to (8.8) in order to add the condition on N. In other words, in the objective function (8.8), penalty costs are defined as the gap between I t and N :
$$ \begin{array}{l} EC={\displaystyle \sum_{t=1}^T\Big\{{c}_1{X}_t+{c}_2{Y}_t+{c}_3{Z}_t+{c}_4N+}\\ {}\kern0.16em {c}_7{\left({L}_t-N\right)}^{+}+{c}_8{\left(N-{L}_t\right)}^{+}\Big\}/T\to \min, \end{array} $$
(8.8)

s.t. L t = I t B t , (a)+ = max(0, a),

where c 7 means penalty cost when L t is larger than N, and c 8 means penalty cost when L t is smaller than N.

Another lead-time (LT) in a year is set as
$$ LT=\left\{{\displaystyle \sum_{t=1}^{12}\left({I}_t-{B}_t\right)/{D}_t}\right\}/T. $$
(8.9)

8.1.4.2 Steps for Creating Strategic Map

The strategic map is a matrix that consists of a smoothing factor (derived from the exponential smoothing method) and expected demand. The smoothing factor relates to fluctuations in production volume in each period, which affects the capacity of the production function. The simplified steps for generating the map are shown in Fig. 8.3, while an example of the map is shown in Fig. 8.4.

In the first step, demand data as well as the minimum and maximum values of α, d, and N are defined. Then, the intermediate values between the minimum and maximum values of α, d, and N are defined, respectively. The strategic map represents the objective functions (i.e., EN, ER, and EC) of all the combinations of α, d, and N. The number of intermediate values defines the degree of detail in the strategic map.

The values of α and d are set to be each minimum value at the beginning and increase at each iteration of the steps shown in Fig. 8.3. The EN, ER, and EC of each combination of α and d are calculated based on demand forecasting and aggregate planning.

The strategic map, therefore, is composed in a systematic fashion by changing the combination of α and d. For the same combination of α and d, the strategic map shows the values of EN, ER, and EC that maximize EN regarding N.

8.2 Example of DSMAP Performance

8.2.1 Operating Example of DSMAP

In this section, we present a numerical example of the planner. Table 8.2 shows sample demand data for 12 planning periods. In demand forecasting, historical data are adjusted by using Eq. (8.3), while average demand is set as expected demand (d).
Table 8.2

Demand data

t

d t

t

d t

1

284

7

314

2

268

8

253

3

253

9

275

4

252

10

264

5

271

11

238

6

325

12

292

  1. (i)

    Demand forecasting

     
For this example, we calculate exponential smoothing for a range of α from 0.1 to 1.0 with increments of 0.1. d ranges from 100 to 280 with increments of 20 and N from 40 to 200 with increments of 20. Therefore, 900 strategies can be derived from the combinations of α, d, and N in this example.
  1. (ii)

    Design of the demand-to-supply strategic map

     

The strategic map for the example can be obtained from the following steps for the DSMAP operation. Let us skip toward the next steps.

8.2.2 Steps for DSMAP Operation

  1. (iii)
    Aggregate planning by using linear programming, and (iv) selection of a demand-to-supply plan
    Table 8.3

    Values of the constants for linear programming

    Constants

    Value

    Constants

    Value

    c 1

    100

    P 0

    130

    c 2

    107

    d 0

    270

    c 3

    115

    b

    2

    c 4

    5

    I 0

    0

     

    270

    X max

    200

    c 6

    80

    Y max

    20

    c 7

    200

    Z max

    30

    c 8

    300

      
     

Table 8.3 shows the values of the constants of the linear programming, which was described in Sect. 8.1.4.1 as being used to obtain the optimum aggregate plan under the constraints, N, and the forecasted demand of each strategy.

Table 8.4 presents the aggregate plan selected using linear programming, which maximizes EN among the combinations of α, d, and N. The constraints of the selected plan are as follows:
Table 8.4

The aggregate plan selected by the planner

t

D t

X t

Y t

Z t

I t

B t

1

194

200

34

0

40

0

2

195

195

0

0

40

0

3

189

189

0

0

40

0

4

186

186

0

0

40

0

5

193

193

0

0

40

0

6

219

200

19

0

40

0

7

225

200

25

0

40

0

8

201

200

1

0

40

0

9

201

200

1

0

40

0

10

196

196

0

0

40

0

11

183

183

0

0

40

0

12

201

200

1

0

40

0

Total

2,382

2,342

81

0

Smoothing factor (α): 0.6,

Expected demand (d): 200,

Normal inventory quantity (N): 40.

Forecasted demand (D t ) is less than the data shown in Table 8.2 because demand data are adjusted with d.

Figure 8.5 shows a part of the strategic map . In this figure, the maximum EN is located between the minimum EC and the maximum ER. This phenomenon is described by the ellipse-cross theory [7], which usually appears in the strategic map. This theory is useful to identify how to improve the demand-to-supply management strategy.
Fig. 8.5

A part of the strategic map

  1. (v)

    Scheduling using the ASPROVA tool

     
After an aggregate plan has been selected, the scheduling step examines the plan under detailed production conditions. The planner modifies the plan based on the scheduling results as necessary in order to improve the accuracy of the plan. Figure 8.6 shows the scheduling model in this example.
Fig. 8.6

A scheduling model. Production lot size: 5 units/lot, Setup time for every resource: 120 min

We assume that a job shop lot production system is employed. In the model, the production system makes two kinds of products. Setup time is required for any production process to change between products. In this example, we set lot size to be five units per lot and setup time as 120 min for every production process.

In the current version of the planner, we use ASPROVA (http://www.asprova.jp/), a commercial scheduler employed worldwide, as the production scheduler. ASPROVA can build a scheduling model based on practical conditions as well as provide scheduling algorithms to solve complex scheduling problems. Therefore, the planner can be applied to complex production systems in practical problems.
  1. (vi)

    Progressive analysis of performance

     
The differences between scheduling and the aggregate plan are visualized by the progressive curves shown in Fig. 8.7. In the figure, the scheduling result indicates that the aggregate plan has insufficient production capacity to supply products. The scheduling step therefore evaluates several scenarios to increase production capacity.
Fig. 8.7

Progressive curve

Figure 8.8 shows the inventory that results from the scheduling step. In this case, the production system for the first scheduling has insufficient capacity to satisfy demand; therefore, it cannot maintain the standard inventory level. In this situation, overtime work capacity is expanded to provide enough supply capacity to satisfy demand. The scheduling result after changing capacity is labeled second scheduling in Fig. 8.8.
Fig. 8.8

Change in inventory in the scheduling step

  1. (vii)

    Collaborative feedback for decision-making

     

The evaluation of the plans obtained from the strategic map and the scheduling is different because the assumed production conditions in the scheduling are more detailed than the plan in the strategic map. For example, production lot size, product variety, and setup time are not considered in the plans of the strategic map.

Therefore, we need to provide more accurate information about the aggregate plan in order to rebuild the strategic map, as necessary. The points included in this feedback are production capacity, lot size, and setup frequency.

8.2.3 Toward A Sustainable Company

One of the ultimate goals of demand-to-supply management is to improve corporate sustainability in today’s uncertain and unforeseeable market conditions. The overall demand-to-supply management framework can be depicted as shown in Fig. 8.9.
Fig. 8.9

An overall framework for demand-to-supply management in a sustainable company

The planner described in this chapter covers a short-term strategic perspective. A medium-term strategic perspective would generate a supply system plan including capacity expansion and outsourcing decisions. It also formulates a demand development plan including marketing and pricing strategies in order to improve corporate profit.

From a long-term strategic perspective, however, business life cycles based on core products should be considered. Any business has a life cycle. Hence, all companies must decide the right time to withdraw their mature products from the market. A long-term strategic perspective supports decisions on product releases and revisions as well as the management of the optimum product portfolio to improve corporate sustainability.

In the future, systems for generating medium- and long-term strategic perspectives should be developed [8]. In addition, the planner should be integrated with those systems in order to improve corporate sustainability.

The flexibility of the planner should also be increased to be applicable to diversified demand-to-supply problems in practice. For example, a generalized strategic map, which is applicable to many demand forecasting methods, could be developed. In addition, progressive analysis methodologies need to be improved. Progressive analysis evaluates the plan and indicates directions for its improvement. Therefore, the methodologies used in progressive analysis are critical to search for the optimum plan in the planner.

Regarding the education system [2], more trial classes are required to evaluate its effectiveness. In particular, it should be applied to corporate and learning staff to evaluate the system from several practitioners’ points of view [3, 12]. In addition, more case studies should be prepared to increase exercise variety.

Footnotes

  1. 1.

    The Japanese version of DSMAP is recently uploaded at the Repository of UEC Tokyo.

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  • Masayuki Matsui
    • 1
    • 2
  1. 1.The University of Electro-CommunicationsChofuJapan
  2. 2.Department of Industrial Engineering and Management Faculty of EngineeringKanagawa UniversityYokohamaJapan

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