Integral Logistics Management — Operations Management and Supply Chain Management Within and Across Companies

3.6 Scenarios and Exercises

Intended learning outcomes: Elaborate an example of a location configuration with linear programming.


3.6.1 Location Configuration with Linear Programming

The Ironer Company, a manufacturer of ironing machines, has its facilities at one single location. The Ironer Company markets two different products in two regions. Once a year, the company performs rough-cut capacity planning based on sales forecasts. In addition, it must answer the following important question for marketing: With the given capacity situation, what quantity of what product should be offered in which market in order to maximize the contribution margin? While demand for New Product P1 is increasing sharply in Market M2, sales of Predecessor Product P2 are declining as the market becomes saturated (decline stage). Here the assumed market demand reflects the maximum saleable number of pieces. The contribution margins of the two markets differ, in part considerably, due to the differing cost and price structures. Figure 3.6.1.1 shows the details:

Fig. 3.6.1.1       Input data for the planning problem at the Ironer Company.

Ironer Company requires 4 hours to manufacture Product P1 and 2.4 hours to manufacture Product P2. The total capacity in a year is 15,000 hours. Please answer the following questions:

  1. What quantities of P1 and P2 should be put on the two markets in order to maximize the contribution margin?
  2. A consulting firm is proposing, by introducing lean-/just-in-time concepts (lean/ JIT), to increase the contribution margin by 5% and lower the capacity required for P1 by 60 minutes and the capacity required for P2 by 24 minutes. What should the maximum cost of introducing JIT concepts be? And how will this improve the company situation?
  3. In addition, the marketing department decides to increase market penetration of P1 and, to maximize profits, to intensify the decline of P2. To do this, sales of P2 in Market M1 must rise to 4,000, while for Market M2 complete product withdrawal is planned. What are the advantages and disadvantages of this strategy?

Proceed as follows:

  1. A) Define the decision variables. Possible solution:

X_Pi_Mj , 1  j  2, 1  i  2 stands for the number of products P1 that will be delivered to Market Mj

  1. B) Formulate the target function. Possibility: contribution margin = max!

= (DB_P1_M1 · X_P1_M1) + (DB_P1_M2 · X_P1_M2) + (DB_P2_M1 · X_P2_M1) + (DB_P2_M2 · X_P2_M2)

Figure 3.6.1.2 shows how you can perform these first steps utilizing MS Excel Solver, Microsoft Excel’s tool for solving linear optimization.

Fig. 3.6.1.2        Solver tool in MS Excel, part 1.

Formulate all side conditions:

(a.) Demand: Maximum coverage of market demands
  • X_P1_M1 maximum demand for Product P1 in Market M1=1000
  • X_P1_M2 maximum demand for Product P1 in Market M2=5000
  • X_P2_M1 maximum demand for Product P2 in Market M1=3000
  • X_P2_M2 maximum demand for Product P2 in Market M2=2000
(b.) Capacity: Restricted total capacity
  • X_P1_M1 · capacity requiredP1 + X_P1_M2 · capacity requiredP1
    + X_P2_M1 · capacity requiredP2 + X_P2_M2 · capacity requiredP2
    total capacity
(c.) Variable non-negativity
  • X_P1_M1 ³  0;   X_P1_M2  ³  0;   X_P2_M1  ³  0;   X_P2_M2  ³  0

Figure 3.6.1.3 shows how MS Excel Solver handles the formulation of side conditions. The constraint operators (e.g. ,  ³ ) were entered only as text, for purposes of clarity to the reader.

Figure 3.6.1.4 shows how you must actually enter the decision variables, target function, and side conditions using the Solver tool in MS Excel. Solutions:

Task 1):
  • Click Solve (see Figure 3.6.1.4) to display the results. If you have entered everything correctly, the maximum contribution margin achievable should be 356.500€, as it is in Figure 3.6.1.2.

Fig. 3.6.1.3        Solver tool in MS Excel, part 2.

Fig. 3.6.1.4        Solver tool in MS Excel, part 3.

Task 2), the introduction of JIT:
  • Start out from the basic case in Task 1, copying and pasting it into a new Excel spreadsheet. Now change the values accordingly.
  • Through the higher contribution margins and lower capacity required, the total contribution margin and service level for P1 can be increased.
  • If everything is set correctly, you can determine the cost ceiling for introducing the JIT concept as the contribution margin difference: 451.500€ - 356.500€ = 94.900€.
Task 3), the additional marketing measure:
  • Start out from the basic case in Task 2) (JIT), copying and pasting it into a new Excel spreadsheet. Now change the values accordingly.
  • By intensifying the decline of Product P2, the total contribution margin can be incre­ased even more, to 476.000€. The service level for P1, however, drops in compa­rison, since the available capacities produce Product P2 for Market M1. For this reason, it is necessary to consider to what extent the increase in the number of pieces of P1 will take place and the extent to which P1 will at best replace product P2.


Course sections and their intended learning outcomes

  • Course 3 – Supply Chain Design: Location Planning and Sustainability

    Intended learning outcomes: Produce design options for global production, distribution, service, and transportation networks. Describe location selection / configuration for a production network using qualitative / quantitative methods. Explain the concept of sustainability with reference to the triple bottom line. Disclose economic opportunities for social and environmental commitment as well as energy management concepts.

  • 3.1 Design Options for Integrated Production, Distribution, Service, and Transportation Networks

    Intended learning outcomes: Explain design options for global production networks, distribution networks, service networks, and transportation networks. Describe the network structure for decentralized distribution, and design options for retail networks. Disclose the integration of the portfolios.

  • 3.2 Location Selection and Location Configuration

    Intended learning outcomes: Differentiate between location selection and location configuration. Explain location selection using qualitative methods and factor rating. Describe location selection and location configuration with linear programming.

  • 3.3 Sustainable Supply Chains

    Intended learning outcomes: Explain the changing concept of sustainability with reference to the triple bottom line. Disclose economic opportunities for social commitment and for environmental commitment. Describe energy management concepts and measures for improved environmental performance. Produce an overview on the measurement of the environmental performance. Present social and environmental dimensions in industrial practice.




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