The distribution network design is very important in optimising the supply chain performance and cost. There are different distribution policies that a company may have to select from, and consequently, the company should plan its resources and should select a planning horizon based on its choice.
The main objective is to design the distribution network of a fastmoving consumer goods company in order to optimise the transportation and inventory costs by determining the quantities to be shipped and the resources needed. This is analysed throughout different planning horizons and distribution policies.
A mixed integer quadratic problem model is developed to optimise transportation and inventory costs by determining the quantities to be shipped, the quantities to be stored and the types of trucks to be used. The model is applied to four different distribution policies and the performance of each is tested across different time horizons.
An analysis is carried out to optimise the distribution plan for each policy. The effect of the length of the planning horizon on the different plans is also shown.
The results show how each policy performs against the tradeoff between the ease of using the policy and its cost of operation. Also, the length of the planning horizon is shown to drastically reduce the total cost and affect the operating conditions when the Vendor Managed Inventory (VMI) policy is considered.
Distribution of fastmoving consumer goods (FMCG) is one of the fastest growing industries in Egypt. Most Egyptian FMCG manufacturers distribute their products all over the country. Today, the challenge faced by an FMCG supply chain is to establish efficient and successful patterns of distribution to the supply chain members. Because of the rapid increase in FMCG demand, companies are motivated to reconsider the design of their distribution networks. One main result from the increase in demand is the expansion of mass merchandisers which are considered as key customers to FMCG companies. This mandates that the distribution network design should be revised to ensure that the needs and wants of key customers are met through effective and efficient distribution networks. The distribution network design problem involves facility location, warehousing, transportation and inventory decisions. The lot size also affects the problem. This problem is called the integrated lot sizing and distribution problem.
In integrated lot sizing and distribution problems, the companies are concerned with minimising the total cost incurred in distributing the products by determining, for each period in the planning horizon, the quantity produced at each entity, the quantity shipped from each entity and to which customer, the quantity stored at each entity and which types of vehicles are to be used in each link for each period.
The aim of this article is to optimise the integrated lot sizing and vehicle routing problem in the distribution network of one of the leading FMCG companies in Egypt. The company wants to know whether their current practice is efficient or not. The company wants to determine the best distribution plan to adopt to fit its current distribution policy and the distribution plans that fit another three possible alternative distribution policies. Moreover, we want to investigate the effect of the length of the planning horizon and the effect of the collaboration between members on the performance of the distribution plan for the different distribution policies. More specifically, the company wants to find, for each period for a given planning horizon, the production quantity of each member, the stored quantity, the incoming quantity and from which member using which vehicle and the outgoing quantities to which member using which vehicle, with the aim of satisfying the demand at the lowest possible cost.
The rest of the article is structured as follows. In the ‘Literature review’ section, literature of the relevant research is discussed. In the section ‘Problem description and formulation’, the problem is described, and a formulation of the problem is introduced. In the section ‘Case study’, the case study is introduced. In the ‘Numerical results’ section, the numerical analysis is discussed. Finally, the discussion and recommendation are covered in the ‘Conclusion’ section.
Researchers have long considered the vehicle distribution problem and the lot sizing problem (LSP) as two different wellknown classical problems in supply chain management (Adulyasak, Cordeau & Jans
The distribution problem tries to deliver the ordered quantity to the customers with the aim of improving the companies’ strategic objectives, which could be reducing price, improving responsiveness or similar objectives. Companies nowadays rely on multichannel distribution networks to achieve different objectives, as surveyed by SimchiLevi, Kaminsky and SimchiLevi (2004), Kembro, Norrman and Eriksson (
On the other side, LSP focuses on determining the quantities and timing of production with the objective of production and inventory cost minimisation (ElBeheiry & Abdallah
It should be noted that the distribution problem and the LSP are both
One of the most important drivers in the performance of the integrated lot size and distribution problem is information sharing. When there is no information shared, the supply chain members are considered in a Stackelberg game situation as in Yan et al. (
This study presents a mixedinteger quadratic problem (MIQP) for the integrated lot sizing and distribution problem for an Egyptian FMCG company. The company has a heterogeneous fleet used in distribution. The company has its own distribution policy and wants to improve it, so another three distribution policies are proposed. There is a possibility for good information sharing between the members. The company selects the length of the planning horizon. For each period in that planning horizon, the company wants to find the quantity to be produced at different production sites, the quantity to be stored at different storing members, the quantity received at each location, the quantity shipped from each location and the type of vehicle used in each incoming or outgoing trip. This is performed with the objective of satisfying the demand at the lowest possible cost.
The novelty of this work is that: (1) it shows the effect of selecting planning horizon on the distribution–production decisions (distribution policies) and how these are sensitive to the selected planning horizon, (2) it gives insights to the decision takers on the performance characteristics of the discussed distribution policies and (3) it evaluates the reallife applicability of choosing a simple distribution policy that is easy to understand and apply by all members versus a more complex distribution policy.
Consider the supply chain of a company that consists of producers, warehouses and retailers. The company produces the products and transports them to the warehouses and retailers. The company has a fleet of different sizes to deliver the products. When a vehicle is utilised, fixed and variable costs are incurred. Also, when there are products stored at a location, a holding cost is incurred. Whilst planning the delivery of products, the company takes into its consideration a long planning horizon (e.g. a planning horizon of an entire year). This time horizon is divided into smaller operational periods (e.g. a monthly delivery period that can be utilised). When a product is delivered in an earlier period than its consumption period, the holding cost would increase.
Whilst planning for the distribution, the company wants to determine how many products to produce at production facilities in each period, how many to ship using which type of vehicles, the route and schedule of each vehicle at different times (i.e. source, destination and load from a location in the supply chain to another at different times within the time horizon) and the product quantity stored at each location across the planning horizon. Whilst taking these decisions, the company tries to satisfy all the demand and wants to minimise the cost. Also, the company wants to study the effect of the length of the planning horizon on the optimal decisions. Moreover, the company wants to know how different distribution policies would affect its decisions (e.g. having the policy of using only large vehicles to deliver to distribution centres and only small vehicles to deliver to the retailers).
The research is based on modelling a real case of an FMCG company to determine the optimal distribution policy and study the effect of the planning horizon on the optimal decisions. The model parameters are deduced from the actual cost values and the trucks’ capacities to help the company evaluating the distribution policies. This research is an experimental research as the effect of the planning horizon on the optimal solution is tested.
Consider a supply chain consisting of
General structure of a fastmoving consumer goods supply chain with three echelons.
The model minimises the total cost incurred in the supply chain, which is divided into transportation and holding costs. This is achieved by determining for every period
There are some assumptions in the considered models; without the loss of generality, the product size, variable cost and holding costs are normalised amongst all the products (i.e. all the products have the same size and variable cost). There is no backlog allowed at any entity, and shortage cost is not considered in the model, as in the FMCG’s industry the normal operation is to have the highest possible product availability. The truck type used for shipping from entity
The model uses the following nomenclature:
Parameters:
number of entities  
number of echelons  
types of trucks  
number of trucks available  
capacity of trucks of type 

length of the planning horizon, divided into 

number of delivery periods  
entities in the supply chain  
Product type  
incurred fixed cost when a truck of type 

incurred variable cost when a truck of type 

demand of each entity of the last echelon of the supply chain for delivery period 

capacity of entity 

production capacity of each entity 

holding cost when a product is kept at entity 

initial inventory at each entity 
Decision variables:
production quantity for each product 

quantity shipped from source entity 

binary value representing whether a truck of type 
The associated objective function (1) is divided into two parts: transportation cost and holding (inventory) cost. The transportation cost consists of a fixed cost and a variable cost based on the shipped quantity, the vehicle type and the route. A quantity can only be assigned to a truck if that truck is assigned to travel this link in this delivery period (e.g. for a truck of type 1 to be assigned to visit entity 7 from entity 4 in delivery period 3, the binary decision variable
Formulation of the model.
subject to:
The second term is the holding cost, which can be computed as the holding cost per unit at an entity multiplied by the inventory level. The inventory level for a certain entity at a specific delivery period is computed as the incoming products less the outgoing products. The incoming products include the initial inventory at the beginning, the production quantity for each product at this entity (if it is an entity at echelon 1) and all the incoming products for each delivery period from the first delivery period up through the current period, whilst the outgoing products include all shipped products and all customers’ orders from the current entity from the first delivery period up through the current period.
Constraints (2) indicate that the current inventory level at an entity at a specific delivery period is nonnegative and cannot exceed this entity’s capacity. The only exception is for the final delivery period of the planning horizon, where the remaining inventory level should be zero as shown in constraints 3. Constraints (4) ensure that the sum of all sorts of outgoing quantities is less than what is available at any entity for any single product at any given delivery period, except for the last delivery period where the quantity should all be used as in constraints (5). Constraints (6) limit the produced quantity at any production site for a certain product to its production capacity. Constraints (7) ensure that the sum of all shipped quantity of all products from one entity to another in a given delivery period using a truck of a certain type does not exceed its capacity. Constraints (8) ensure that no more than the available trucks of a certain type can be used in a delivery period. Constraints (9, 10, 11) ensure the nonnegativity of the decision variables.
The case study concerns a multinational FMCG company that distributes its goods throughout 120 distribution centres to its customers, covering all the Egyptian governorates, and these distribution centres are being supplied from the company’s eight factories. Two of the factories produce unique products (not produced at any other factories), whilst the other six factories may produce the same products. One of its DCs, located in the Ain Shams suburb of eastern Cairo, will be referred to as Ain Shams Distribution Center (ASDC), which is being supplied by four factories – out of the eight factories owned by the company – located in Alexandria (Alex), Cairo (CAI), 6th of October (OCT) and Qalyoub (Qly). Each factory supplies ASDC with a range of products that is not supplied by any of the other three factories; the quantities supplied will be expressed in number of pallets as each pallet must include the same product. There are two types of truck: trail trucks with a capacity of 30 pallets and common trucks with a capacity of 8 pallets. The company currently uses trailer trucks of capacity 30 pallets to deliver from each factory to ASDC.
ASDC supplies demand points within known territories. This study is concerned with one major territory called ElOubour city. ElOubour city has four key customers (KC):
Current distribution network design for ElObour city.
Product mix demand of the key customers.
Factory  Alex  CAI  OCT  Qly 

10  50  5  35 
Alex, Alexandria; CAI, Cairo; OCT, 6th of October; Qly, Qalyoub.
Transportation cost matrix for trailer trucks.
ToFrom  Alex  OCT  CAI  Qly  DC  KC1  KC2 

Alex  950  1100  1060  1060  1300  1300  
OCT  950  650  780  670  700  700  
CAI  1100  650  720  650  470  470  
Qly  1060  780  720  720  680  680  
DC  1060  670  650  720  710  710  
KC1  1300  700  470  680  710  50  
KC2  1300  700  470  680  710  50 
Alex, Alexandria; CAI, Cairo; OCT, 6th of October; Qly, Qalyoub; DC, distribution centres; KC1, key customer 1; KC2, key customer 2.
Transportation cost matrix for common trucks.
To From  Alex  OCT  CAI  Qly  DC  KC1  KC2 

Alex  450  500  480  480  550  550  
OCT  450  350  400  370  360  360  
CAI  500  350  370  350  340  340  
Qly  480  400  370  370  350  350  
DC  480  370  350  370  360  360  
KC1  550  360  340  350  360  5  
KC2  550  360  340  350  360  5 
Alex, Alexandria; CAI, Cairo; OCT, 6th of October; Qly, Qalyoub; DC, distribution centres; KC1, key customer 1; KC2, key customer 2.
The company wants to have a fixed distribution policy known for all the stakeholders so that they can better optimise their operations. Therefore, the company wants to investigate four different distribution policies, where each one represents a different distribution policy with different levels of coordination with the KCs. In each distribution policy, the quantities to be produced, shipped and stored must be optimised in addition to the type of trucks utilised. For each distribution policy, the company wants to investigate the effect of the planning horizon on the decisions taken and the total cost. Thus, for each distribution policy, the planning horizon will be changed starting from one period to six planning periods.
The current practice of the distribution network is to ship trailer trucks to the ASDC, which works as a cross dock, and then ship aggregated orders to the KCs, as given in
The four distribution policies of the considered distribution network designs.
In this case, shown in
In this case, all trucks are allowed to travel from any location to any other location, incurring the associated costs. The shipping may be done directly from the factories to KCs or through ASDC, as shown in
The company manages the inventory of the KCs, and they share information with the factories. This distribution policy is similar to the third one, yet the company may choose to pay some of the holding costs at the KCs, and in return, it may not need to ship every other day to them, as shown in
The developed model is tested on the FMCG company under study. The model is an MIQP that can be solved to optimality for up to intermediate planning horizons.
The quadratic model developed was solved using Lingo. The results are shown in
The total cost resulted from the mixed integer quadratic problem for different planning periods.
Planning period  Distribution policy 1  Distribution policy 2  Distribution policy 3  Distribution policy 4 

1  1885  1605  1500  1500 
2  3770  3210  3000  1517.8 
3  5655  4815  4500  2148.4 
4  7540  6420  6000  2186.8 
5  9425  8025  7500  2303 
6  11 310  9630  9000  2666.62 
The total cost per period resulted from the mixedinteger quadratic problem for different planning periods.
Planning period  Distribution policy 1  Distribution policy 2  Distribution policy 3  Distribution policy 4 

1  1885  1605  1500  1500 
2  1885  1605  1500  758.9 
3  1885  1605  1500  716.1333 
4  1885  1605  1500  546.7 
5  1885  1605  1500  460.6 
6  1885  1605  1500  444.4367 
For distribution policies 1, 2 and 3, some arcs are not allowed for certain types of trucks (e.g. common trucks between factories and DC in distribution policy 1 and arcs reaching the DC in distribution policy 2). The fixed transportation cost is set to an arbitrary large number, prohibiting the model from selecting these arcs. Whenever the inventory is prohibited at any entity, the holding cost is also set to a high value likewise.
It is observed that with distribution policies 1, 2 and 3, the cost per delivery period is the same across all the different planning periods, as shown in
Total cost versus planning period.
Cost per delivery period versus planning period.
It could be concluded from
From the above analysis, the results suggest that there is a tradeoff between the ease of the distribution policy and the cost of execution of the distribution plan. The cost of executing a simple distribution policy could be improved a bit by adequate planning. On the other hand, a complex distribution plan could improve the cost significantly, but will face challenges by being complex. Moreover, it is found that the planning horizon affects the cost of the execution of the operation policy. Choosing a small planning horizon could lead to missing the opportunity of aggregating several demands in one shipment. But using a large planning horizon diminishes the savings and may prove to be more expensive.
In this article, a mixedinteger quadratic model is introduced to solve the integrated lotsizing and vehicle routing problem applied to an international wellknown FMCG company in Egypt. The company faces a tradeoff between choosing a simple fixed policy that is easy to implement and easy to understand by all stakeholders or a sophisticated plan that involves more complicated planning from involved planners from all stakeholders. In addition to the simple distribution policy adopted by the company, two more simple distribution policies and another complex distribution policy are proposed.
This study finds that if the company chooses a simple fixed distribution policy, then distribution policy 3 with the flexibility of using any type of trucks available and shipping the exact demand for one planning period would be the cheapest choice. However, distribution policy 2 is not significantly more expensive and eliminates the DC along with its handling cost and the managerial effort in managing it.
If the company wants to further reduce its cost significantly, then the option of adopting VMI in distribution policy whilst paying some of the KCs’ holding costs would be a better choice. However, the company has to evaluate the tradeoff between reducing the costs and increasing the effort required to manage all the activities associated with the distribution. This is especially valid as there are three patterns of cost reductions that appear in the case study. It is clear from the numerical results that better utilisation of a small vehicle or higher utilisation of a bigger vehicle is better than just switching from a highly utilised small truck to a bigger underutilised vehicle.
The results prove that an important factor to consider in the problem is the number of planning periods considered in the planning horizon. Changing the number of planning periods affects the optimal decisions, as in the fourth distribution policy, and helps reduce the total costs. In the beginning of increasing the planning horizon, small vehicles start to be loaded by more products, increasing the utilisation and reducing the cost per period. In a moderate planning horizon, the vehicle becomes moderately utilised and the improvement by the increased utilisation is decreased by the holding cost. When the planning horizon is further increased, larger vehicles are needed, leading to improvement in the utilisation and hence improving the cost per delivery period. However, when the planning horizon becomes large, the holding cost reduces the gains.
This combinatorial problem is
The authors have declared that no competing interest exists.
Both authors contributed equally to the writing this article.
This article followed all ethical standards for a research without direct contact with human or animal subjects.
This research received no specific grant from any funding agency in the public, commercial or notforprofit sectors.
Data are available upon reasonable request to the corresponding author.
The views and opinions expressed in this article are those of the authors and do not necessarily reflect the official policy or position of any affiliated agency of the authors.