APM case Solution, session 7 uge 11 PDF

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APM ContainerMarch 3, 2020In July 2020, Thomas Young, regional manager of APM (see Infobox??), and his colleagues were looking for a new strategy to allocate containers for transportation from Korea and China to the Middle East. Challenged by top management, which had urged all business departmentst...

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APM Container

March 3, 2020

In July 2020, Thomas Young, regional manager of APM (see Infobox ??), and his colleagues were looking for a new strategy to allocate containers for transportation from Korea and China to the Middle East. Challenged by top management, which had urged all business departments to optimize their revenues and profit, Young wondered whether he could improve pricing or apply other revenue management techniques to enhance revenues. Container transportation was the core business of global shipping companies (see Infobox ??), and APM was no exception. APM shipped on trans-Pacific routes, to Europe and the Mediterranean, and around Asia. A major growth area for APM was the container trade from Korea and China to the Middle East. Korea/China to Middle East shipments In the 1990s, APM started shipping containers from Korea and China to the Middle East to take advantage of the booming trade between these countries. Dubai, in particular, was playing a very important role as the transshipment hub port for the region. APM had gained a strong reputation for having the fastest transit time from Asia to the Middle East. Consequently, for many years, several big companies, such as Sony, Nike, Epson and LG, had used APM for their shipping needs. Shipping on these routes was now the most profitable part of APM’s business. APM had dedicated a fleet of five container vessels to the Asia-Middle Eastern routes, each with a maximum container capacity of 2,000 TEU and a weight limit of 24,000 tons. When westbound, vessels called on ports in Asian countries where cargo was loaded, and the loaded vessels then sailed to Dubai. After unloading at the Dubai container hub, the containers were shipped to their final destinations by local carriers. The peak season for APM began in April and ended in the fall, when the Islamic holiday of Ramadan slowed trade. Ramadan was the most important festival in Islamic countries and lasted for one month, where people slowed down. The slack season was observed from Ramadan through March and was characterized by huge drops in demand. The main goods shipped from Asia to the Middle East were electronics, furniture, toys, tiles and clothing. Given that the maximum load weight was 24 tons for a 20-foot container and 30 tons for a 40-foot container, 40-foot containers were used for less dense cargo, such as toys and furniture. Given a vessel sailing, Table 1 shows the typical demand for container cargo at each season. Moreover, the average weights and prices for each origin are also given. Most container shipments were not particularly time-sensitive and could be delayed until the next vessel sailed without great consequences. However, a small amount of premium traffic was always accommodated on the first available vessel. Sometimes this premium freight arrived unexpectedly at the last minute; consequently, during the peak season, APM planned to load its vessels (excluding premium freight) to a maximum of 95 per cent of weight or TEU capacity (22,800 tons or 1,900 TEU). During the slack season the planned load factor was 90 per cent. The average weight of a 40-foot container was much less than the average weight of two 20-foot containers

1

APM Container - Logistics & Optimization

Spring 2020

High season Port of Origin Unit Japan China Hong Kong Indonesia India Korea Malaysia Singapore Taiwan Thailand

Low season

Weight

Price ($/TEU)

Demand (TEU)

20’ (Cont.)

40’ (Cont.)

Demand (TEU)

20’ (Cont.)

40’ (Cont.)

20’ (Tons)

40’ (Tons)

940 878 766 840 790 710 643 649 702 663

320 68 737 68 340 35 138 43 41 9

58 21 197 20 86 13 51 16 13 1

140 27 285 28 136 14 46 17 16 4

233 61 612 61 304 31 102 38 37 8

53 20 181 15 76 15 50 11 14 3

127 24 263 23 117 11 42 16 15 4

20 18 19 21 22 21 20 19 19 23

24 23 22 25 22 25 22 25 19 26

Table 1: Estimated demand and containers available for each season (one container ship). Moreover, prices and weights are also given. and 40-foot containers were faster to load and unload, consequently 40-foot containers were preferable to 20-foot containers. However, heavier goods often had to be put in 20-foot containers to meet weight limits. In the past, APM had insisted that the ratio of 40-foot containers to 20-foot containers (40’/20’) should be between 1.2 and 2.0. Developing a variable pricing strategy APM’s traditional pricing system was coordinated by the marketing department at the Taiwan head office, which set all container rates. The pricing formula was based on the market shipping rate, the importance of the customers, the weight of cargo and the volume of the port. The prices charged for shipping from each Asian port to Dubai are shown in Table 1. These market-based prices, however did not take into account the “loadability” of the container. For example, a vessel that was loaded to near its weight limit but still had TEU capacity could ship low-weight 40-foot containers much more profitability than higher weight 20-foot containers. The marketing department had not yet found a good solution for adjusting prices to maximize revenue. Young was aware that he needed to investigate the possibility of improving revenues since costs were essentially sunk. As a regional manager, Young felt pressure from Jun Kim, APM’s CEO, to optimize revenue and profit. The company had two options: the first was to relate container shipping rates more closely to “loadability” and profitability; the second was to introduce techniques from revenue management, including variable pricing and possibly dynamic pricing. Young had substantial experience in international shipping and he recognized that, although freight was largely commoditized on many popular routes, APM faced limited competition on the Korea/China to Dubai routes and had earned a strong reputation with shippers on these routes. This led Young to believe that APM had some control of price. He estimated that during the high season, a price reduction of 3 per cent would result in a 5 per cent increase in the volume of containers, and during the low season, a price reduction of 5 per cent would increase container traffic by 10 per cent. Young realized these estimates were highly speculative but thought they might serve as a starting point to investigate APM’s pricing strategy. Young’s final concern was customer service. It was imperative that any changes in pricing or operations did not have a negative impact on APM’s customer base.

BUSINESS AND SOCIAL SCIENCES DEPARTMENT OF ECONOMICS AND BUSINESS ECONOMICS

Ata Jalili Marand [email protected]

APM Container - Logistics & Optimization

Spring 2020

Questions Thomas Young first makes an analysis given the current situation. 1. Assume that prices are fixed according to Table 1 and formulate a LP-model that finds the loading plan which maximize revenue. Consider the high and low season separately. Hint: define decision variables xij = number of containers loaded in harbor i of type j (i = 1, . . . , 10, j = 20, 40). and parameters pi = price ($/TEU) for containers loaded in harbor i, Di = demand (TEU) for containers in harbor i, Cij = containers avaliable of type j in harbor i, CTEU = capacity (TEU) per ship, Cton = capacity (ton) per ships δ = max loading factor, wij = weight of container loaded in harbor i of type j. 2. What is the optimal solution for each season? Is all demand satisfied? What is the ratio? What is shipped most and why? Which constraints are binding (what does this mean)? What about the service level? Thomas Young next considers a variable pricing strategy. Incorporating revenue management tools would require some effort: what revenue gains could APM expect? Could current levels of customer service be maintained? If APM’s marketing department was to be persuaded to apply these concepts to the Asia-Dubai routes, Young would need to show that significant revenues could be gained while maintaining a high level of customer service. 3. Assume that prices affect the demand (in TEU) as stated by Young. For instance at the harbour in Japan, we may write the demand D in the high season as a function of the price p:   0.05 · 320 0.05 · 320 p + 320 − · 940 . D(p) = −0.03 · 940 −0.03 · 940 Formulate a model that finds the loading plan which maximize revenue. Hint: prices now also are a decision variable. Is the model linear (comment)? 4. How should APM set its prices in the high season? What revenue gains could APM expect? Could the current level of customer service be maintained?

Answer to APM container shipping 1. Formulate a LP-model that finds the loading plan which maximize revenue First note that that Table 1 provide data for one ship, i.e. in our analysis we will assume that all 5 ships are identical and consider each ship separately. Given a fixed season, define decision variable xij = # of containers loaded in harbor i of type j (i = 1, . . . 10, j = 20, 40),

BUSINESS AND SOCIAL SCIENCES DEPARTMENT OF ECONOMICS AND BUSINESS ECONOMICS

Ata Jalili Marand [email protected]

APM Container - Logistics & Optimization

Spring 2020

and parameters pi = price ($/TEU) for containers loaded in harbor i, Di = demand (TEU) for containers in harbor i, Cij = containers avaliable of type j in harbor i, CTEU = capacity (TEU) per ship, Cton = capacity (ton) per ships δ = max loading factor, wij = weight of container loaded in harbor i of type j. We then can formulate the following IP-model which maximize the total revenue for each ship: max

10 X

pi (xi,20 + 2xi,40 )

i=1

s.t.

xi,20 + 2xi,40 xi,j

≤ Di ≤ Ci,j

10 X

≤ δCTEU,

(3)

≤ δCton,

(4)

(xi,20 + 2xi,40 )

∀i = 1, . . . , 10 ∀i = 1, . . . , 10, j = 20, 40

(1) (2)

i=1 10

X X

wi,j xi,j

i=1 j=20,40 10 X

xi,40 − 1.2

i=1 10 X

2

i=1

xi,20 −

10 X

i=1 10 X

xi,20 ≥ 0,

(5)

≥ 0,

(6)

xi,40

i=1

xij

≥ 0,

∀i = 1, . . . , 10, j = 20, 40

xij

integer,

∀i = 1, . . . , 10, j = 20, 40

where (1) are the demand constraint, (2) the capacity restriction on 20’ and 40’ containers, (3) is the capacity restriction on TEU, (4) the capacity restriction on weight and (5) and (6) the restrictions on that the ratio between 40’ and 20’ containers must be between 1.2 and 2. Note I add the constraint xij must be integer; however, if we have large values of xij , solving the model as an LP may be okay. 2. What is the optimal solution for each season? Is all demand satisfied? What is the ratio? What is shipped most and why? Which constraints are binding (what does this mean)? What about the service level? First we solve the problem for the high season. The optimal revenue and solution is shown in Figure 1 (per voyage - the model and formulas for the high season are given in Figure 2). For the high season, the solution can be obtained by satisfying demand for most ports. This is done using mostly 40-foot containers since the total weight constraint is binding. The total weight restriction drives the solution to ship 40-foot containers since these are lighter per TEU. However, we cannot ship more 40-foot containers because the ratio of 40-foot containers to 20-foot containers is at its highest. Not all demand can be satisfied (44 TEU), indeed, there is excess demand in India, Korea; Malaysia, Singapore and Thailand. This may not be seen as good customer service which is important for the company. For the low season, the maximum revenue is reduced (see Figure 1). All demand is satisfied and the vessel does not sail with full cargo (both weight and TEU constraint is non binding). The ratio of 40-foot containers to 20-foot containers is in the middle of the interval.

BUSINESS AND SOCIAL SCIENCES DEPARTMENT OF ECONOMICS AND BUSINESS ECONOMICS

Ata Jalili Marand [email protected]

APM Container - Logistics & Optimization

Spring 2020

Figure 1: Optimal solutions and solution value. 3. Assume that prices affect the demand (in TEU) as stated by Young. Formulate a model that finds the loading plan which maximize revenue. Is the model linear (comment)? We can write the demand Di in the high season as a function of the price pi : Di (pi ) = ai pi + bi , with slope and intercept 0.05 · demand , −0.03 · price bi = demand − ai · price,

ai =

where demand and price is taken from Table 1 in the case text. Since we now adjust price to satisfy a certain demand we have xi,20 + 2xi,40 = Di (pi ) the objective function then becomes max

10 X

pi (ai pi + bi ) =

i=1

10 X (ai pi2 + bi pi )

(7)

i=1

Note that (7) is not linear and can therefore not be solved using linear programming but quadratic programming (QP). However, in Excel the “GRG Nonlinear” solution method must be used. Note this solution method is not exact so a non-optimal solution may be found. The new model becomes max

10 X

pi (xi,20 + 2xi,40 )

i=1

BUSINESS AND SOCIAL SCIENCES DEPARTMENT OF ECONOMICS AND BUSINESS ECONOMICS

Ata Jalili Marand [email protected]

APM Container - Logistics & Optimization

Spring 2020

Figure 2: Model and formulas solution for the high season and solution value. s.t.

xi,20 + 2xi,40 − ai pi

= bi ,

∀i = 1, . . . , 10

xi,j

≤ Ci,j

∀i = 1, . . . , 10, j = 20, 40

10 X

(xi,20 + 2xi,40 )

i=1 10 X

X

wi,j xi,j

≤ δCTEU, ≤ δCton,

i=1 j=20,40

10 X

xi,40 − 1.2

10 X

i=1

xi,20 ≥ 0,

i=1

i=1

2

10 X

xi,20 −

10 X

xi,40

≥ 0,

i=1

BUSINESS AND SOCIAL SCIENCES DEPARTMENT OF ECONOMICS AND BUSINESS ECONOMICS

Ata Jalili Marand [email protected]

APM Container - Logistics & Optimization

Spring 2020

Figure 3: Optimal solutions and solution value variable prices. pi ≥ 0, xij ≥ 0 and integer, ∀i = 1, . . . , 10, j = 20, 40

4. How should APM set its prices in the high season? What revenue gains could APM expect? Could the current level of customer service be maintained? The solution of solving the model is show in Figure 3. As expected, the revenue maximization suggests that prices are too low (since all the available demand could not be satisfied). In most ports prices are now raised until demand is cut back to the point at which all containers can be loaded. The revenue after price optimization is increased by approximately 1%, i.e. not much. Note however, that the total TEU and containers loaded has decreased. This may reduce loading and unloading costs. The solution also increases the service level to 100 per cent since all containers are now shipped. Again, weight is the limiting factor, not TEU. In summary, this example illustrates that price optimization can increase revenues at virtually no additional operating cost, and has the additional benefit of increasing the service level (although it does this by raising prices and cutting back demand to match capacity). However, some costs will be imposed on marketing/sales and on the company in general since variable pricing will require some management effort.

BUSINESS AND SOCIAL SCIENCES DEPARTMENT OF ECONOMICS AND BUSINESS ECONOMICS

Ata Jalili Marand [email protected]...